WindingNumber.py

from manimlib.imports import *

import warnings
warnings.warn("""
    Warning: This file makes use of
    ContinualAnimation, which has since
    been deprecated
""")

import time

import mpmath
mpmath.mp.dps = 7


# Warning, this file uses ContinualChangingDecimal,
# which has since been been deprecated.  Use a mobject
# updater instead


# Useful constants to play around with
UL = UP + LEFT
UR = UP + RIGHT
DL = DOWN + LEFT
DR = DOWN + RIGHT
standard_rect = np.array([UL, UR, DR, DL])

# Used in EquationSolver2d, and a few other places
border_stroke_width = 10

# Used for clockwise circling in some scenes
cw_circle = Circle(color = WHITE).stretch(-1, 0)

# Used when walker animations are on black backgrounds, in EquationSolver2d and PiWalker
WALKER_LIGHT_COLOR = DARK_GREY

ODOMETER_RADIUS = 1.5
ODOMETER_STROKE_WIDTH = 20

# TODO/WARNING: There's a lot of refactoring and cleanup to be done in this code,
# (and it will be done, but first I'll figure out what I'm doing with all this...)
# -SR

# This turns counterclockwise revs into their color. Beware, we use CCW angles 
# in all display code, but generally think in this video's script in terms of 
# CW angles
def rev_to_rgba(alpha):
    alpha = (0.5 - alpha) % 1 # For convenience, to go CW from red on left instead of CCW from right
    # 0 is red, 1/6 is yellow, 1/3 is green, 2/3 is blue
    hue_list = [0, 0.5/6.0, 1/6.0, 1.1/6.0, 2/6.0, 3/6.0, 4/6.0, 5/6.0]
    num_hues = len(hue_list)
    start_index = int(np.floor(num_hues * alpha)) % num_hues
    end_index = (start_index + 1) % num_hues
    beta = (alpha % (1.0/num_hues)) * num_hues

    start_hue = hue_list[start_index]
    end_hue = hue_list[end_index]
    if end_hue < start_hue:
        end_hue = end_hue + 1
    hue = interpolate(start_hue, end_hue, beta)

    return color_to_rgba(Color(hue = hue, saturation = 1, luminance = 0.5))

    # alpha = alpha % 1
    # colors = colorslist
    # num_colors = len(colors)
    # beta = (alpha % (1.0/num_colors)) * num_colors
    # start_index = int(np.floor(num_colors * alpha)) % num_colors
    # end_index = (start_index + 1) % num_colors

    # return interpolate(colors[start_index], colors[end_index], beta)

def rev_to_color(alpha):
    return rgba_to_color(rev_to_rgba(alpha))

def point_to_rev(xxx_todo_changeme6, allow_origin = False):
    # Warning: np.arctan2 would happily discontinuously returns the value 0 for (0, 0), due to 
    # design choices in the underlying atan2 library call, but for our purposes, this is 
    # illegitimate, and all winding number calculations must be set up to avoid this
    (x, y) = xxx_todo_changeme6
    if not(allow_origin) and (x, y) == (0, 0):
        print("Error! Angle of (0, 0) computed!")
        return
    return fdiv(np.arctan2(y, x), TAU)

def point_to_size(xxx_todo_changeme7):
    (x, y) = xxx_todo_changeme7
    return np.sqrt(x**2 + y**2)

# rescaled_size goes from 0 to 1 as size goes from 0 to infinity
# The exact method is arbitrarily chosen to make pleasing color map
# brightness levels
def point_to_rescaled_size(p):
    base_size = point_to_size(p)

    return np.sqrt(fdiv(base_size, base_size + 1))

def point_to_rgba(point):
    rev = point_to_rev(point, allow_origin = True)
    rgba = rev_to_rgba(rev)
    rescaled_size = point_to_rescaled_size(point)
    return rgba * [rescaled_size, rescaled_size, rescaled_size, 1] # Preserve alpha

positive_color = rev_to_color(0)
negative_color = rev_to_color(0.5)
neutral_color = rev_to_color(0.25)
        
class EquationSolver1d(GraphScene, ZoomedScene):
    CONFIG = {
    "camera_config" : 
        {
            "use_z_coordinate_for_display_order": True,
        },
    "func" : lambda x : x,
    "targetX" : 0,
    "targetY" : 0,
    "initial_lower_x" : 0,
    "initial_upper_x" : 10,
    "num_iterations" : 10,
    "iteration_at_which_to_start_zoom" : None,
    "graph_label" : None,
    "show_target_line" : True,
    "base_line_y" : 0, # The y coordinate at which to draw our x guesses
    "show_y_as_deviation" : False, # Displays y-values as deviations from target,
    }

    def drawGraph(self):
        self.setup_axes()
        self.graph = self.get_graph(self.func)
        self.add(self.graph)

        if self.graph_label != None:
            curve_label = self.get_graph_label(self.graph, self.graph_label, 
                x_val = 4, direction = LEFT)
            curve_label.shift(LEFT)
            self.add(curve_label)
        
        if self.show_target_line:
            target_line_object = DashedLine(
                self.coords_to_point(self.x_min, self.targetY), 
                self.coords_to_point(self.x_max, self.targetY),
                dash_length = 0.1)
            self.add(target_line_object)

            target_label_num = 0 if self.show_y_as_deviation else self.targetY
            target_line_label = TexMobject("y = " + str(target_label_num))
            target_line_label.next_to(target_line_object.get_left(), UP + RIGHT)
            self.add(target_line_label)

        self.wait() # Give us time to appreciate the graph

        if self.show_target_line:
            self.play(FadeOut(target_line_label)) # Reduce clutter

        print("For reference, graphOrigin: ", self.coords_to_point(0, 0))
        print("targetYPoint: ", self.coords_to_point(0, self.targetY))

    # This is a mess right now (first major animation coded), 
    # but it works; can be refactored later or never
    def solveEquation(self):
        # Under special conditions, used in GuaranteedZeroScene, we let the 
        # "lower" guesses actually be too high, or vice versa, and color 
        # everything accordingly

        def color_by_comparison(val, ref):
            if val > ref:
                return positive_color
            elif val < ref:
                return negative_color
            else:
                return neutral_color

        lower_color = color_by_comparison(self.func(self.initial_lower_x), self.targetY)
        upper_color = color_by_comparison(self.func(self.initial_upper_x), self.targetY)

        if self.show_y_as_deviation:
            y_bias = -self.targetY
        else:
            y_bias = 0

        startBrace = TexMobject("|", stroke_width = 10) #TexMobject("[") # Not using [ and ] because they end up crossing over 
        startBrace.set_color(lower_color)
        endBrace = startBrace.copy().stretch(-1, 0)
        endBrace.set_color(upper_color)
        genericBraces = Group(startBrace, endBrace)
        #genericBraces.scale(1.5)

        leftBrace = startBrace.copy()
        rightBrace = endBrace.copy()
        xBraces = Group(leftBrace, rightBrace)

        downBrace = startBrace.copy()
        upBrace = endBrace.copy()
        yBraces = Group(downBrace, upBrace)
        yBraces.rotate(TAU/4)

        lowerX = self.initial_lower_x
        lowerY = self.func(lowerX)
        upperX = self.initial_upper_x
        upperY = self.func(upperX)

        leftBrace.move_to(self.coords_to_point(lowerX, self.base_line_y)) #, aligned_edge = RIGHT)
        leftBraceLabel = DecimalNumber(lowerX)
        leftBraceLabel.next_to(leftBrace, DOWN + LEFT, buff = SMALL_BUFF)
        leftBraceLabelAnimation = ContinualChangingDecimal(leftBraceLabel, 
            lambda alpha : self.point_to_coords(leftBrace.get_center())[0],
            tracked_mobject = leftBrace)
        
        rightBrace.move_to(self.coords_to_point(upperX, self.base_line_y)) #, aligned_edge = LEFT)
        rightBraceLabel = DecimalNumber(upperX)
        rightBraceLabel.next_to(rightBrace, DOWN + RIGHT, buff = SMALL_BUFF)
        rightBraceLabelAnimation = ContinualChangingDecimal(rightBraceLabel, 
            lambda alpha : self.point_to_coords(rightBrace.get_center())[0],
            tracked_mobject = rightBrace)

        downBrace.move_to(self.coords_to_point(0, lowerY)) #, aligned_edge = UP)
        downBraceLabel = DecimalNumber(lowerY)
        downBraceLabel.next_to(downBrace, LEFT + DOWN, buff = SMALL_BUFF)
        downBraceLabelAnimation = ContinualChangingDecimal(downBraceLabel, 
            lambda alpha : self.point_to_coords(downBrace.get_center())[1] + y_bias,
            tracked_mobject = downBrace)
        
        upBrace.move_to(self.coords_to_point(0, upperY)) #, aligned_edge = DOWN)
        upBraceLabel = DecimalNumber(upperY)
        upBraceLabel.next_to(upBrace, LEFT + UP, buff = SMALL_BUFF)
        upBraceLabelAnimation = ContinualChangingDecimal(upBraceLabel, 
            lambda alpha : self.point_to_coords(upBrace.get_center())[1] + y_bias,
            tracked_mobject = upBrace)

        lowerDotPoint = self.input_to_graph_point(lowerX, self.graph)
        lowerDotXPoint = self.coords_to_point(lowerX, self.base_line_y)
        lowerDotYPoint = self.coords_to_point(0, self.func(lowerX))
        lowerDot = Dot(lowerDotPoint + OUT, color = lower_color)
        upperDotPoint = self.input_to_graph_point(upperX, self.graph)
        upperDot = Dot(upperDotPoint + OUT, color = upper_color)
        upperDotXPoint = self.coords_to_point(upperX, self.base_line_y)
        upperDotYPoint = self.coords_to_point(0, self.func(upperX))

        lowerXLine = Line(lowerDotXPoint, lowerDotPoint, color = lower_color)
        upperXLine = Line(upperDotXPoint, upperDotPoint, color = upper_color)
        lowerYLine = Line(lowerDotPoint, lowerDotYPoint, color = lower_color)
        upperYLine = Line(upperDotPoint, upperDotYPoint, color = upper_color)

        x_guess_line = Line(lowerDotXPoint, upperDotXPoint, color = WHITE, stroke_width = 10)
        

        lowerGroup = Group(
            lowerDot, 
            leftBrace, downBrace,
            lowerXLine, lowerYLine,
            x_guess_line
        )
        
        upperGroup = Group(
            upperDot, 
            rightBrace, upBrace,
            upperXLine, upperYLine,
            x_guess_line
        )

        initialLowerXDot = Dot(lowerDotXPoint + OUT, color = lower_color)
        initialUpperXDot = Dot(upperDotXPoint + OUT, color = upper_color)
        initialLowerYDot = Dot(lowerDotYPoint + OUT, color = lower_color)
        initialUpperYDot = Dot(upperDotYPoint + OUT, color = upper_color)

        # All the initial adds and ShowCreations are here now:
        self.play(FadeIn(initialLowerXDot), FadeIn(leftBrace), FadeIn(leftBraceLabel))
        self.add_foreground_mobjects(initialLowerXDot, leftBrace)
        self.add(leftBraceLabelAnimation)
        self.play(ShowCreation(lowerXLine))
        self.add_foreground_mobject(lowerDot)
        self.play(ShowCreation(lowerYLine))
        self.play(FadeIn(initialLowerYDot), FadeIn(downBrace), FadeIn(downBraceLabel))
        self.add_foreground_mobjects(initialLowerYDot, downBrace)
        self.add(downBraceLabelAnimation)

        self.wait()

        self.play(FadeIn(initialUpperXDot), FadeIn(rightBrace), FadeIn(rightBraceLabel))
        self.add_foreground_mobjects(initialUpperXDot, rightBrace)
        self.add(rightBraceLabelAnimation)
        self.play(ShowCreation(upperXLine))
        self.add_foreground_mobject(upperDot)
        self.play(ShowCreation(upperYLine))
        self.play(FadeIn(initialUpperYDot), FadeIn(upBrace), FadeIn(upBraceLabel))
        self.add_foreground_mobjects(initialUpperYDot, upBrace)
        self.add(upBraceLabelAnimation)

        self.wait()

        self.play(FadeIn(x_guess_line))

        self.wait()

        for i in range(self.num_iterations):
            if i == self.iteration_at_which_to_start_zoom:
                self.activate_zooming()
                self.little_rectangle.move_to(
                    self.coords_to_point(self.targetX, self.targetY))
                inverseZoomFactor = 1/float(self.zoom_factor)
                self.play(
                    lowerDot.scale_in_place, inverseZoomFactor,
                    upperDot.scale_in_place, inverseZoomFactor)


            def makeUpdater(xAtStart, fixed_guess_x):
                def updater(group, alpha):
                    dot, xBrace, yBrace, xLine, yLine, guess_line = group
                    newX = interpolate(xAtStart, midX, alpha)
                    newY = self.func(newX)
                    graphPoint = self.input_to_graph_point(newX, 
                            self.graph)
                    dot.move_to(graphPoint)
                    xAxisPoint = self.coords_to_point(newX, self.base_line_y)
                    xBrace.move_to(xAxisPoint)
                    yAxisPoint = self.coords_to_point(0, newY)
                    yBrace.move_to(yAxisPoint)
                    xLine.put_start_and_end_on(xAxisPoint, graphPoint)
                    yLine.put_start_and_end_on(yAxisPoint, graphPoint)
                    fixed_guess_point = self.coords_to_point(fixed_guess_x, self.base_line_y)
                    guess_line.put_start_and_end_on(xAxisPoint, fixed_guess_point)
                    return group
                return updater

            midX = (lowerX + upperX)/float(2)
            midY = self.func(midX)

            # If we run with an interval whose endpoints start off with same sign,
            # then nothing after this branching can be trusted to do anything reasonable
            # in terms of picking branches or assigning colors
            in_negative_branch = midY < self.targetY
            sign_color = negative_color if in_negative_branch else positive_color

            midCoords = self.coords_to_point(midX, midY)
            midColor = neutral_color
            # Hm... even the z buffer isn't helping keep this above x_guess_line

            midXBrace = startBrace.copy() # Had start and endBrace been asymmetric, we'd do something different here
            midXBrace.set_color(midColor)
            midXBrace.move_to(self.coords_to_point(midX, self.base_line_y) + OUT)

            # We only actually add this much later
            midXPoint = Dot(self.coords_to_point(midX, self.base_line_y) + OUT, color = sign_color)

            x_guess_label_caption = TextMobject("New guess: x = ", fill_color = midColor)
            x_guess_label_num = DecimalNumber(midX, fill_color = midColor)
            x_guess_label_num.move_to(0.9 * FRAME_Y_RADIUS * DOWN)
            x_guess_label_caption.next_to(x_guess_label_num, LEFT)
            x_guess_label = Group(x_guess_label_caption, x_guess_label_num)
            y_guess_label_caption = TextMobject(", y = ", fill_color = midColor)
            y_guess_label_num = DecimalNumber(midY, fill_color = sign_color)
            y_guess_label_caption.next_to(x_guess_label_num, RIGHT)
            y_guess_label_num.next_to(y_guess_label_caption, RIGHT)
            y_guess_label = Group(y_guess_label_caption, y_guess_label_num)
            guess_labels = Group(x_guess_label, y_guess_label)

            self.play(
                ReplacementTransform(leftBrace.copy(), midXBrace),
                ReplacementTransform(rightBrace.copy(), midXBrace),
                FadeIn(x_guess_label))

            self.add_foreground_mobject(midXBrace)

            midXLine = DashedLine(
                self.coords_to_point(midX, self.base_line_y), 
                midCoords, 
                color = midColor
            )
            self.play(ShowCreation(midXLine))
            midDot = Dot(midCoords, color = sign_color)
            if(self.iteration_at_which_to_start_zoom != None and 
                i >= self.iteration_at_which_to_start_zoom):
                midDot.scale_in_place(inverseZoomFactor)
            self.add(midDot)
            midYLine = DashedLine(midCoords, self.coords_to_point(0, midY), color = sign_color)
            self.play(
                ShowCreation(midYLine), 
                FadeIn(y_guess_label),
                ApplyMethod(midXBrace.set_color, sign_color),
                ApplyMethod(midXLine.set_color, sign_color),
                run_time = 0.25
            )
            midYPoint = Dot(self.coords_to_point(0, midY), color = sign_color)
            self.add(midXPoint, midYPoint)

            if in_negative_branch:
                self.play(
                    UpdateFromAlphaFunc(lowerGroup, 
                        makeUpdater(lowerX, 
                            fixed_guess_x = upperX
                        )
                    ),
                    FadeOut(guess_labels),
                )
                lowerX = midX
                lowerY = midY

            else:
                self.play(
                    UpdateFromAlphaFunc(upperGroup, 
                        makeUpdater(upperX, 
                            fixed_guess_x = lowerX
                        )
                    ),
                    FadeOut(guess_labels),
                )
                upperX = midX
                upperY = midY
            #mid_group = Group(midXLine, midDot, midYLine) Removing groups doesn't flatten as expected?
            self.remove(midXLine, midDot, midYLine, midXBrace)

        self.wait()

    def construct(self):
        self.drawGraph()
        self.solveEquation()

# Returns the value with the same fractional component as x, closest to m
def resit_near(x, m):
    frac_diff = (x - m) % 1
    if frac_diff > 0.5:
        frac_diff -= 1
    return m + frac_diff

# TODO?: Perhaps use modulus of (uniform) continuity instead of num_checkpoints, calculating 
# latter as needed from former?
#
# "cheap" argument only used for diagnostic testing right now
def make_alpha_winder(func, start, end, num_checkpoints, cheap = False):
    check_points = [None for i in range(num_checkpoints)]
    check_points[0] = func(start)
    step_size = fdiv(end - start, num_checkpoints)
    for i in range(num_checkpoints - 1):
        check_points[i + 1] = \
        resit_near(
            func(start + (i + 1) * step_size),
            check_points[i])
    def return_func(alpha):
        if cheap:
            return alpha # A test to see if this func is responsible for slowdown

        index = np.clip(0, num_checkpoints - 1, int(alpha * num_checkpoints))
        x = interpolate(start, end, alpha)
        if cheap:
            return check_points[index] # A more principled test that at least returns a reasonable answer
        else:
            return resit_near(func(x), check_points[index])
    return return_func

# The various inconsistent choices of what datatype to use where are a bit of a mess,
# but I'm more keen to rush this video out now than to sort this out.

def complex_to_pair(c):
    return np.array((c.real, c.imag))

def plane_func_from_complex_func(f):
    return lambda x_y4 : complex_to_pair(f(complex(x_y4[0],x_y4[1])))

def point3d_func_from_plane_func(f):
    def g(xxx_todo_changeme):
        (x, y, z) = xxx_todo_changeme
        f_val = f((x, y))
        return np.array((f_val[0], f_val[1], 0))
    return g

def point3d_func_from_complex_func(f):
    return point3d_func_from_plane_func(plane_func_from_complex_func(f))

def plane_zeta(xxx_todo_changeme8):
    (x, y) = xxx_todo_changeme8
    CLAMP_SIZE = 1000
    z = complex(x, y)
    try:
        answer = mpmath.zeta(z)
    except ValueError:
        return (CLAMP_SIZE, 0)
    if abs(answer) > CLAMP_SIZE:
        answer = answer/abs(answer) * CLAMP_SIZE
    return (float(answer.real), float(answer.imag))

def rescaled_plane_zeta(xxx_todo_changeme9):
    (x, y) = xxx_todo_changeme9
    return plane_zeta((x/FRAME_X_RADIUS, 8*y))

# Returns a function from 2-ples to 2-ples
# This function is specified by a list of (x, y, z) tuples, 
# and has winding number z (or total of all specified z) around each (x, y)
#
# Can also pass in (x, y) tuples, interpreted as (x, y, 1)
def plane_func_by_wind_spec(*specs):
    def embiggen(p):
        if len(p) == 3:
            return p
        elif len(p) == 2:
            return (p[0], p[1], 1)
        else:
            print("Error in plane_func_by_wind_spec embiggen!")
    specs = list(map(embiggen, specs))

    pos_specs = [x_y_z for x_y_z in specs if x_y_z[2] > 0]
    neg_specs = [x_y_z1 for x_y_z1 in specs if x_y_z1[2] < 0]

    neg_specs_made_pos = [(x_y_z2[0], x_y_z2[1], -x_y_z2[2]) for x_y_z2 in neg_specs]

    def poly(c, root_specs):
        return np.prod([(c - complex(x, y))**z for (x, y, z) in root_specs])

    def complex_func(c):
        return poly(c, pos_specs) * np.conjugate(poly(c, neg_specs_made_pos))
    
    return plane_func_from_complex_func(complex_func)

def scale_func(func, scale_factor):
    return lambda x : func(x) * scale_factor

# Used in Initial2dFunc scenes, VectorField scene, and ExamplePlaneFunc
example_plane_func_spec = [(-3, -1.3, 2), (0.1, 0.2, 1), (2.8, -2, -1)]
example_plane_func = plane_func_by_wind_spec(*example_plane_func_spec)

empty_animation = EmptyAnimation()

class WalkerAnimation(Animation):
    CONFIG = {
        "walk_func" : None, # Must be initialized to use
        "remover" : True,
        "rate_func" : None,
        "coords_to_point" : None
    }

    def __init__(self, walk_func, val_func, coords_to_point, 
        show_arrows = True, scale_arrows = False,
        **kwargs):
        self.walk_func = walk_func
        self.val_func = val_func
        self.coords_to_point = coords_to_point
        self.compound_walker = VGroup()
        self.show_arrows = show_arrows
        self.scale_arrows = scale_arrows

        if "walker_stroke_color" in kwargs:
            walker_stroke_color = kwargs["walker_stroke_color"]
        else:
            walker_stroke_color = BLACK

        base_walker = Dot().scale(5 * 0.35).set_stroke(walker_stroke_color, 2) # PiCreature().scale(0.8 * 0.35)
        self.compound_walker.walker = base_walker
        if show_arrows:
            self.compound_walker.arrow = Arrow(ORIGIN, 0.5 * RIGHT, buff = 0)
            self.compound_walker.arrow.match_style(self.compound_walker.walker)
        self.compound_walker.digest_mobject_attrs()
        Animation.__init__(self, self.compound_walker, **kwargs)

    # Perhaps abstract this out into an "Animation updating from original object" class
    def interpolate_submobject(self, submobject, starting_submobject, alpha):
        submobject.points = np.array(starting_submobject.points)

    def interpolate_mobject(self, alpha):
        Animation.interpolate_mobject(self, alpha)
        cur_x, cur_y = cur_coords = self.walk_func(alpha)
        cur_point = self.coords_to_point(cur_x, cur_y)
        self.mobject.shift(cur_point - self.mobject.walker.get_center())
        val = self.val_func(cur_coords)
        rev = point_to_rev(val)
        self.mobject.walker.set_fill(rev_to_color(rev))
        if self.show_arrows:
            self.mobject.arrow.set_fill(rev_to_color(rev))
            self.mobject.arrow.rotate(
                rev * TAU, 
                about_point = self.mobject.arrow.get_start()
            )

            if self.scale_arrows:
                size = point_to_rescaled_size(val)
                self.mobject.arrow.scale(
                    size * 0.3, # Hack constant; we barely use this feature right now
                    about_point = self.mobject.arrow.get_start()
                )

def walker_animation_with_display(
    walk_func, 
    val_func, 
    coords_to_point, 
    number_update_func = None,
    show_arrows = True,
    scale_arrows = False,
    num_decimal_places = 1,
    include_background_rectangle = True,
    **kwargs
    ):
    
    walker_anim = WalkerAnimation(
        walk_func = walk_func, 
        val_func = val_func, 
        coords_to_point = coords_to_point,
        show_arrows = show_arrows,
        scale_arrows = scale_arrows,
        **kwargs)
    walker = walker_anim.compound_walker.walker

    if number_update_func != None:
        display = DecimalNumber(0, 
            num_decimal_places = num_decimal_places, 
            fill_color = WHITE if include_background_rectangle else BLACK,
            include_background_rectangle = include_background_rectangle)
        if include_background_rectangle:
            display.background_rectangle.fill_opacity = 0.5
            display.background_rectangle.fill_color = GREY
            display.background_rectangle.scale(1.2)
        displaycement = 0.5 * DOWN # How about that pun, eh?
        # display.move_to(walker.get_center() + displaycement)
        display.next_to(walker, DOWN+RIGHT, SMALL_BUFF)
        display_anim = ChangingDecimal(display, 
            number_update_func, 
            tracked_mobject = walker_anim.compound_walker.walker,
            **kwargs)
        anim_group = AnimationGroup(walker_anim, display_anim, rate_func=linear)
        return anim_group
    else:
        return walker_anim

def LinearWalker(
    start_coords, 
    end_coords, 
    coords_to_point, 
    val_func, 
    number_update_func = None, 
    show_arrows = True,
    scale_arrows = False,
    include_background_rectangle = True,
    **kwargs
    ):
    walk_func = lambda alpha : interpolate(start_coords, end_coords, alpha)
    return walker_animation_with_display(
        walk_func = walk_func, 
        coords_to_point = coords_to_point, 
        val_func = val_func,
        number_update_func = number_update_func,
        show_arrows = show_arrows,
        scale_arrows = scale_arrows,
        include_background_rectangle = include_background_rectangle,
        **kwargs)

class ColorMappedByFuncScene(Scene):
    CONFIG = {
        "func" : lambda p : p,
        "num_plane" : NumberPlane(),
        "show_num_plane" : True,

        "show_output" : False,

        "hide_background" : False #Background used for color mapped objects, not as background
    }

    def short_path_to_long_path(self, filename_with_ext):
        return self.get_image_file_path(filename_with_ext)

    def setup(self):
        # The composition of input_to_pos and pos_to_color 
        # is to be equal to func (which turns inputs into colors)
        # However, depending on whether we are showing input or output (via a MappingCamera),
        # we color the background using either func or the identity map
        if self.show_output:
            self.input_to_pos_func = self.func
            self.pos_to_color_func = lambda p : p
        else:
            self.input_to_pos_func = lambda p : p
            self.pos_to_color_func = self.func

        self.pixel_pos_to_color_func = lambda x_y3 : self.pos_to_color_func(
            self.num_plane.point_to_coords_cheap(np.array([x_y3[0], x_y3[1], 0]))
        )

        jitter_val = 0.1
        line_coords = np.linspace(-10, 10) + jitter_val
        func_hash_points = it.product(line_coords, line_coords)

        def mini_hasher(p):
            rgba = point_to_rgba(self.pixel_pos_to_color_func(p))
            if rgba[3] != 1.0:
                print("Warning! point_to_rgba assigns fractional alpha", rgba[3])
            return tuple(rgba)

        to_hash = tuple(mini_hasher(p) for p in func_hash_points)
        func_hash = hash(to_hash)
        # We hash just based on output image
        # Thus, multiple scenes with same output image can re-use it
        # without recomputation
        full_hash = hash((func_hash, self.camera.get_pixel_width()))
        self.background_image_file = self.short_path_to_long_path(
            "color_mapped_bg_hash_" + str(full_hash) + ".png"
        )
        self.in_background_pass = not os.path.exists(self.background_image_file)

        print("Background file: " + self.background_image_file)
        if self.in_background_pass:
            print("The background file does not exist yet; this will be a background creation + video pass")
        else:
            print("The background file already exists; this will only be a video pass")

    def construct(self):
        if self.in_background_pass:
            self.camera.set_background_from_func(
                lambda x_y: point_to_rgba(
                    self.pixel_pos_to_color_func(
                        (x_y[0], x_y[1])
                    )
                )
            )
            self.save_image(self.background_image_file, mode="RGBA")

        if self.hide_background:
            # Clearing background
            self.camera.background_image = None
        else:
            # Even if we just computed the background, we switch to the file now
            self.camera.background_image = self.background_image_file
        self.camera.init_background()

        if self.show_num_plane:
            self.num_plane.fade()
            self.add(self.num_plane)

class PureColorMap(ColorMappedByFuncScene):
    CONFIG = {
        "show_num_plane" : False
    }

    def construct(self):
        ColorMappedByFuncScene.construct(self)
        self.wait()

# This sets self.background_image_file, but does not display it as the background
class ColorMappedObjectsScene(ColorMappedByFuncScene):
    CONFIG = {
        "show_num_plane" : False,
        "hide_background" : True,
    }

class PiWalker(ColorMappedByFuncScene):
    CONFIG = {
        "walk_coords" : [],
        "step_run_time" : 1,
        "scale_arrows" : False,
        "display_wind" : True,
        "wind_reset_indices" : [],
        "display_size" : False,
        "display_odometer" : False,
        "color_foreground_not_background" : False,
        "show_num_plane" : False,
        "draw_lines" : True,
        "num_checkpoints" : 10,
        "num_decimal_places" : 1,
        "include_background_rectangle" : False,
    }

    def construct(self):
        ColorMappedByFuncScene.construct(self)

        if self.color_foreground_not_background or self.display_odometer:
            # Clear background
            self.camera.background_image = None
            self.camera.init_background()

        num_plane = self.num_plane

        walk_coords = self.walk_coords
        points = [num_plane.coords_to_point(x, y) for x, y in walk_coords]
        polygon = Polygon(*points, color = WHITE)
        if self.color_foreground_not_background:
            polygon.stroke_width = border_stroke_width
            polygon.color_using_background_image(self.background_image_file)
        total_run_time = len(points) * self.step_run_time
        polygon_anim = ShowCreation(polygon, run_time = total_run_time, rate_func=linear)
        walker_anim = empty_animation

        start_wind = 0
        for i in range(len(walk_coords)):
            start_coords = walk_coords[i]
            end_coords = walk_coords[(i + 1) % len(walk_coords)]
            
            # We need to do this roundabout default argument thing to get the closure we want,
            # so the next iteration changing start_coords, end_coords doesn't change this closure
            val_alpha_func = lambda a, start_coords = start_coords, end_coords = end_coords : self.func(interpolate(start_coords, end_coords, a))

            if self.display_wind:
                clockwise_val_func = lambda p : -point_to_rev(self.func(p))
                alpha_winder = make_alpha_winder(clockwise_val_func, start_coords, end_coords, self.num_checkpoints)
                number_update_func = lambda alpha, alpha_winder = alpha_winder, start_wind = start_wind: alpha_winder(alpha) - alpha_winder(0) + start_wind
                start_wind = 0 if i + 1 in self.wind_reset_indices else number_update_func(1)
            elif self.display_size:
                # We need to do this roundabout default argument thing to get the closure we want,
                # so the next iteration changing val_alpha_func doesn't change this closure
                number_update_func = lambda a, val_alpha_func = val_alpha_func : point_to_rescaled_size(val_alpha_func(a)) # We only use this for diagnostics
            else:
                number_update_func = None

            new_anim = LinearWalker(
                start_coords = start_coords, 
                end_coords = end_coords,
                coords_to_point = num_plane.coords_to_point,
                val_func = self.func,
                remover = (i < len(walk_coords) - 1),
                show_arrows = not self.show_output,
                scale_arrows = self.scale_arrows,
                number_update_func = number_update_func,
                run_time = self.step_run_time,
                walker_stroke_color = WALKER_LIGHT_COLOR if self.color_foreground_not_background else BLACK,
                num_decimal_places = self.num_decimal_places,
                include_background_rectangle = self.include_background_rectangle,
            )

            if self.display_odometer:
                # Discard above animation and show an odometer instead

                # We need to do this roundabout default argument thing to get the closure we want,
                # so the next iteration changing val_alpha_func doesn't change this closure
                rev_func = lambda a, val_alpha_func = val_alpha_func : point_to_rev(val_alpha_func(a))
                base_arrow = Arrow(ORIGIN, RIGHT, buff = 0)
                new_anim = FuncRotater(base_arrow, 
                    rev_func = rev_func,
                    run_time = self.step_run_time,
                    rate_func=linear,
                    remover = i < len(walk_coords) - 1,
                )

            walker_anim = Succession(walker_anim, new_anim)

        # TODO: Allow smooth paths instead of breaking them up into lines, and 
        # use point_from_proportion to get points along the way

        if self.display_odometer:
            color_wheel = Circle(radius = ODOMETER_RADIUS)
            color_wheel.stroke_width = ODOMETER_STROKE_WIDTH
            color_wheel.color_using_background_image(self.short_path_to_long_path("pure_color_map.png")) # Manually inserted here; this is unclean
            self.add(color_wheel)
            self.play(walker_anim)
        else:
            if self.draw_lines:
                self.play(polygon_anim, walker_anim)
            else:
                # (Note: Turns out, play is unhappy playing empty_animation, as had been
                # previous approach to this toggle; should fix that)
                self.play(walker_anim)

        self.wait()

class PiWalkerRect(PiWalker):
    CONFIG = {
        "start_x" : -1,
        "start_y" : 1,
        "walk_width" : 2,
        "walk_height" : 2,
        "func" : plane_func_from_complex_func(lambda c: c**2),
        "double_up" : False,

        # New default for the scenes using this:
        "display_wind" : True
    }

    def setup(self):
        TL = np.array((self.start_x, self.start_y))
        TR = TL + (self.walk_width, 0)
        BR = TR + (0, -self.walk_height)
        BL = BR + (-self.walk_width, 0)
        self.walk_coords = [TL, TR, BR, BL]
        if self.double_up:
            self.walk_coords = self.walk_coords + self.walk_coords
        PiWalker.setup(self)

class PiWalkerCircle(PiWalker):
    CONFIG = {
        "radius" : 1,
        "num_steps" : 100,
        "step_run_time" : 0.01
    }

    def setup(self):
        r = self.radius
        N = self.num_steps
        self.walk_coords = [r * np.array((np.cos(i * TAU/N), np.sin(i * TAU/N))) for i in range(N)]
        PiWalker.setup(self)

def split_interval(xxx_todo_changeme10):
    (a, b) = xxx_todo_changeme10
    mid = (a + b)/2.0
    return ((a, mid), (mid, b))

# I am surely reinventing some wheel here, but what's done is done...
class RectangleData():
    def __init__(self, x_interval, y_interval):
        self.rect = (x_interval, y_interval)

    def get_top_left(self):
        return np.array((self.rect[0][0], self.rect[1][1]))

    def get_top_right(self):
        return np.array((self.rect[0][1], self.rect[1][1]))

    def get_bottom_right(self):
        return np.array((self.rect[0][1], self.rect[1][0]))

    def get_bottom_left(self):
        return np.array((self.rect[0][0], self.rect[1][0]))

    def get_top(self):
        return (self.get_top_left(), self.get_top_right())

    def get_right(self):
        return (self.get_top_right(), self.get_bottom_right())

    def get_bottom(self):
        return (self.get_bottom_right(), self.get_bottom_left())

    def get_left(self):
        return (self.get_bottom_left(), self.get_top_left())

    def get_center(self):
        return interpolate(self.get_top_left(), self.get_bottom_right(), 0.5)

    def get_width(self):
        return self.rect[0][1] - self.rect[0][0]

    def get_height(self):
        return self.rect[1][1] - self.rect[1][0]

    def splits_on_dim(self, dim):
        x_interval = self.rect[0]
        y_interval = self.rect[1]

        # TODO: Can refactor the following; will do later
        if dim == 0:
            return_data = [RectangleData(new_interval, y_interval) for new_interval in split_interval(x_interval)]
        elif dim == 1:
            return_data = [RectangleData(x_interval, new_interval) for new_interval in split_interval(y_interval)[::-1]]        
        else: 
            print("RectangleData.splits_on_dim passed illegitimate dimension!")

        return tuple(return_data)

    def split_line_on_dim(self, dim):
        x_interval = self.rect[0]
        y_interval = self.rect[1]

        if dim == 0:
            sides = (self.get_top(), self.get_bottom())
        elif dim == 1:
            sides = (self.get_left(), self.get_right())
        else:
            print("RectangleData.split_line_on_dim passed illegitimate dimension!")

        return tuple([mid(x, y) for (x, y) in sides])


class EquationSolver2dNode(object):
    def __init__(self, first_anim, children = []):
        self.first_anim = first_anim
        self.children = children

    def depth(self):
        if len(self.children) == 0:
            return 0

        return 1 + max([n.depth() for n in self.children])

    def nodes_at_depth(self, n):
        if n == 0:
            return [self]

        # Not the efficient way to flatten lists, because Python + is linear in list size,
        # but we have at most two children, so no big deal here
        return sum([c.nodes_at_depth(n - 1) for c in self.children], [])

    # This is definitely NOT the efficient way to do BFS, but I'm just trying to write something
    # quick without thinking that gets the job done on small instances for now
    def hacky_bfs(self):
        depth = self.depth()

        # Not the efficient way to flatten lists, because Python + is linear in list size,
        # but this IS hacky_bfs...
        return sum([self.nodes_at_depth(i) for i in range(depth + 1)], [])

    def display_in_series(self):
        return Succession(self.first_anim, *[n.display_in_series() for n in self.children])

    def display_in_parallel(self):
        return Succession(self.first_anim, AnimationGroup(*[n.display_in_parallel() for n in self.children]))

    def display_in_bfs(self):
        bfs_nodes = self.hacky_bfs()
        return Succession(*[n.first_anim for n in bfs_nodes])

    def play_in_bfs(self, scene, border_anim):
        bfs_nodes = self.hacky_bfs()
        print("Number of nodes: ", len(bfs_nodes))

        if len(bfs_nodes) < 1:
            print("Less than 1 node! Aborting!")
            return

        scene.play(bfs_nodes[0].first_anim, border_anim)
        for node in bfs_nodes[1:]:
            scene.play(node.first_anim)

class EquationSolver2d(ColorMappedObjectsScene):
    CONFIG = {
        "camera_config" : {"use_z_coordinate_for_display_order": True},
        "initial_lower_x" : -5,
        "initial_upper_x" : 5,
        "initial_lower_y" : -3,
        "initial_upper_y" : 3,
        "num_iterations" : 0,
        "num_checkpoints" : 10,

        # Should really merge this into one enum-style variable
        "display_in_parallel" : False,
        "display_in_bfs" : False,

        "use_fancy_lines" : True,
        "line_color" : WHITE, # Only used for non-fancy lines
        

        # TODO: Consider adding a "find_all_roots" flag, which could be turned off 
        # to only explore one of the two candidate subrectangles when both are viable

        # Walker settings
        "show_arrows" : True,
        "scale_arrows" : False,

        # Special case settings
        # These are used to hack UhOhScene, where we display different colors than 
        # are actually, secretly, guiding the evolution of the EquationSolver2d
        #
        # replacement_background_image_file has to be manually configured
        "show_winding_numbers" : True,

        # Used for UhOhScene; 
        "manual_wind_override" : None,

        "show_cursor" : True,

        "linger_parameter" : 0.5,

        "use_separate_plays" : False,

        "use_cheap_winding_numbers" : False, # To use this, make num_checkpoints large
    }

    def construct(self):
        if self.num_iterations == 0:
            print("You forgot to set num_iterations (maybe you meant to subclass something other than EquationSolver2d directly?)")
            return

        ColorMappedObjectsScene.construct(self)
        num_plane = self.num_plane

        clockwise_val_func = lambda p : -point_to_rev(self.func(p))

        base_line = Line(UP, RIGHT, stroke_width = border_stroke_width, color = self.line_color)

        if self.use_fancy_lines:
            base_line.color_using_background_image(self.background_image_file)

        def match_style_with_bg(obj1, obj2):
            obj1.match_style(obj2)
            bg = obj2.get_background_image_file()
            if bg != None:
                obj1.color_using_background_image(bg)

        run_time_base = 1
        run_time_with_lingering = run_time_base + self.linger_parameter
        base_rate = lambda t : t
        linger_rate = squish_rate_func(lambda t : t, 0, 
                        fdiv(run_time_base, run_time_with_lingering))

        cursor_base = TextMobject("?")
        cursor_base.scale(2)

        # Helper functions for manual_wind_override
        def head(m):
            if m == None:
                return None
            return m[0]

        def child(m, i):
            if m == None or m == 0:
                return None
            return m[i + 1]

        def Animate2dSolver(cur_depth, rect, dim_to_split, 
            sides_to_draw = [0, 1, 2, 3], 
            manual_wind_override = None):
            print("Solver at depth: " + str(cur_depth))

            if cur_depth >= self.num_iterations:
                return EquationSolver2dNode(empty_animation)

            def draw_line_return_wind(start, end, start_wind, should_linger = False, draw_line = True):
                alpha_winder = make_alpha_winder(clockwise_val_func, start, end, self.num_checkpoints, cheap = self.use_cheap_winding_numbers)
                a0 = alpha_winder(0)
                rebased_winder = lambda alpha: alpha_winder(alpha) - a0 + start_wind
                colored_line = Line(num_plane.coords_to_point(*start) + IN, num_plane.coords_to_point(*end) + IN)
                match_style_with_bg(colored_line, base_line)

                walker_anim = LinearWalker(
                    start_coords = start, 
                    end_coords = end,
                    coords_to_point = num_plane.coords_to_point,
                    val_func = self.func, # Note: This is the image func, and not logic_func
                    number_update_func = rebased_winder if self.show_winding_numbers else None,
                    remover = True,
                    walker_stroke_color = WALKER_LIGHT_COLOR,

                    show_arrows = self.show_arrows,
                    scale_arrows = self.scale_arrows,
                )
                
                if should_linger: # Do we need an "and not self.display_in_parallel" here?
                    run_time = run_time_with_lingering
                    rate_func = linger_rate
                else:
                    run_time = run_time_base
                    rate_func = base_rate

                opt_line_anim = ShowCreation(colored_line) if draw_line else empty_animation

                line_draw_anim = AnimationGroup(
                    opt_line_anim, 
                    walker_anim,
                    run_time = run_time,
                    rate_func = rate_func)
                return (line_draw_anim, rebased_winder(1))

            wind_so_far = 0
            anim = empty_animation
            sides = [
                rect.get_top(), 
                rect.get_right(), 
                rect.get_bottom(), 
                rect.get_left()
            ]
            for (i, (start, end)) in enumerate(sides):
                (next_anim, wind_so_far) = draw_line_return_wind(start, end, wind_so_far, 
                    should_linger = i == len(sides) - 1,
                    draw_line = i in sides_to_draw)
                anim = Succession(anim, next_anim)

            if self.show_cursor:
                cursor = cursor_base.copy()
                center_x, center_y = rect.get_center()
                width = rect.get_width()
                height = rect.get_height()
                
                cursor.move_to(num_plane.coords_to_point(center_x, center_y) + 10 * IN)
                cursor.scale(min(width, height))

                # Do a quick FadeIn, wait, and quick FadeOut on the cursor, matching rectangle-drawing time
                cursor_anim = Succession(
                    FadeIn(cursor, run_time = 0.1),
                    Animation(cursor, run_time = 3.8), 
                    FadeOut(cursor, run_time = 0.1)
                )

                anim = AnimationGroup(anim, cursor_anim)

            override_wind = head(manual_wind_override)
            if override_wind != None:
                total_wind = override_wind
            else:
                total_wind = round(wind_so_far)

            if total_wind == 0:
                coords = [
                    rect.get_top_left(), 
                    rect.get_top_right(), 
                    rect.get_bottom_right(), 
                    rect.get_bottom_left()
                ]
                points = np.array([num_plane.coords_to_point(x, y) for (x, y) in coords]) + 3 * IN
                # TODO: Maybe use diagonal lines or something to fill in rectangles indicating
                # their "Nothing here" status?
                # Or draw a large X or something
                fill_rect = polygonObject = Polygon(*points, fill_opacity = 0.8, color = DARK_GREY)
                return EquationSolver2dNode(Succession(anim, FadeIn(fill_rect)))
            else:
                (sub_rect1, sub_rect2) = rect.splits_on_dim(dim_to_split)
                if dim_to_split == 0:
                    sub_rect_and_sides = [(sub_rect1, 1), (sub_rect2, 3)]
                else:
                    sub_rect_and_sides = [(sub_rect1, 2), (sub_rect2, 0)]
                children = [
                    Animate2dSolver(
                        cur_depth = cur_depth + 1,
                        rect = sub_rect,
                        dim_to_split = 1 - dim_to_split,
                        sides_to_draw = [side_to_draw],
                        manual_wind_override = child(manual_wind_override, index)
                    )
                    for (index, (sub_rect, side_to_draw)) in enumerate(sub_rect_and_sides)
                ]
                mid_line_coords = rect.split_line_on_dim(dim_to_split)
                mid_line_points = [num_plane.coords_to_point(x, y)  + 2 * IN for (x, y) in mid_line_coords]
                mid_line = DashedLine(*mid_line_points)

                return EquationSolver2dNode(Succession(anim, ShowCreation(mid_line)), children)

        lower_x = self.initial_lower_x
        upper_x = self.initial_upper_x
        lower_y = self.initial_lower_y
        upper_y = self.initial_upper_y

        x_interval = (lower_x, upper_x)
        y_interval = (lower_y, upper_y)

        rect = RectangleData(x_interval, y_interval)

        print("Starting to compute anim")

        node = Animate2dSolver(
            cur_depth = 0, 
            rect = rect,
            dim_to_split = 0,
            sides_to_draw = [],
            manual_wind_override = self.manual_wind_override
        )

        print("Done computing anim")

        if self.display_in_parallel:
            anim = node.display_in_parallel()
        elif self.display_in_bfs:
            anim = node.display_in_bfs()
        else:
            anim = node.display_in_series()

        # Keep timing details here in sync with details above
        rect_points = [
            rect.get_top_left(), 
            rect.get_top_right(), 
            rect.get_bottom_right(), 
            rect.get_bottom_left(),
        ]
        border = Polygon(*[num_plane.coords_to_point(*x) + IN for x in rect_points])
        match_style_with_bg(border, base_line)

        rect_time_without_linger = 4 * run_time_base
        rect_time_with_linger = 3 * run_time_base + run_time_with_lingering
        def rect_rate(alpha):
            time_in = alpha * rect_time_with_linger
            if time_in < 3 * run_time_base:
                return fdiv(time_in, 4 * run_time_base)
            else:
                time_in_last_leg = time_in - 3 * run_time_base
                alpha_in_last_leg = fdiv(time_in_last_leg, run_time_with_lingering)
                return interpolate(0.75, 1, linger_rate(alpha_in_last_leg))

        border_anim = ShowCreation(
            border, 
            run_time = rect_time_with_linger, 
            rate_func = rect_rate
        )

        print("About to do the big Play; for reference, the current time is ", time.strftime("%H:%M:%S"))

        if self.use_separate_plays:
            node.play_in_bfs(self, border_anim)
        else:
            self.play(anim, border_anim)

        print("All done; for reference, the current time is ", time.strftime("%H:%M:%S"))

        self.wait()

# TODO: Perhaps have option for bullets (pulses) to fade out and in at ends of line, instead of 
# jarringly popping out and in?
#
# TODO: Perhaps have bullets change color corresponding to a function of their coordinates?
# This could involve some merging of functoinality with PiWalker
class LinePulser(ContinualAnimation):
    def __init__(self, line, bullet_template, num_bullets, pulse_time, output_func = None, **kwargs):
        self.line = line
        self.num_bullets = num_bullets
        self.pulse_time = pulse_time
        self.bullets = [bullet_template.copy() for i in range(num_bullets)]
        self.output_func = output_func
        ContinualAnimation.__init__(self, VGroup(*self.bullets), **kwargs)

    def update_mobject(self, dt):
        alpha = self.external_time % self.pulse_time
        start = self.line.get_start()
        end = self.line.get_end()
        for i in range(self.num_bullets):
            position = interpolate(start, end, 
                fdiv((i + alpha),(self.num_bullets)))
            self.bullets[i].move_to(position)
            if self.output_func:
                position_2d = (position[0], position[1])
                rev = point_to_rev(self.output_func(position_2d))
                color = rev_to_color(rev)
                self.bullets[i].set_color(color)

class ArrowCircleTest(Scene):
    def construct(self):
        circle_radius = 3
        circle = Circle(radius = circle_radius, color = WHITE)
        self.add(circle)

        base_arrow = Arrow(circle_radius * 0.7 * RIGHT, circle_radius * 1.3 * RIGHT)

        def rev_rotate(x, revs):
            x.rotate(revs * TAU, about_point = ORIGIN)
            x.set_color(rev_to_color(revs))
            return x

        num_arrows = 8 * 3

        # 0.5 - fdiv below so as to get a clockwise rotation from left
        arrows = [rev_rotate(base_arrow.copy(), 0.5 - (fdiv(i, num_arrows))) for i in range(num_arrows)]
        arrows_vgroup = VGroup(*arrows)

        self.play(ShowCreation(arrows_vgroup), run_time = 2.5, rate_func=linear)

        self.wait()

class FuncRotater(Animation):
    CONFIG = {
        "rev_func" : lambda x : x, # Func from alpha to CCW revolutions,
    }

    # Perhaps abstract this out into an "Animation updating from original object" class
    def interpolate_submobject(self, submobject, starting_submobject, alpha):
        submobject.points = np.array(starting_submobject.points)

    def interpolate_mobject(self, alpha):
        Animation.interpolate_mobject(self, alpha)
        angle_revs = self.rev_func(alpha)
        self.mobject.rotate(
            angle_revs * TAU, 
            about_point = ORIGIN
        )
        self.mobject.set_color(rev_to_color(angle_revs))

class TestRotater(Scene):
    def construct(self):
        test_line = Line(ORIGIN, RIGHT)
        self.play(FuncRotater(
            test_line,
            rev_func = lambda x : x % 0.25,
            run_time = 10))

# TODO: Be careful about clockwise vs. counterclockwise convention throughout!
# Make sure this is correct everywhere in resulting video.
class OdometerScene(ColorMappedObjectsScene):
    CONFIG = {
        # "func" : lambda p : 100 * p # Full coloring, essentially
        "rotate_func" : lambda x : 2 * np.sin(2 * x * TAU), # This is given in terms of CW revs
        "run_time" : 40,
        "dashed_line_angle" : None,
        "biased_display_start" : None,
        "pure_odometer_background" : False
    }

    def construct(self):
        ColorMappedObjectsScene.construct(self)

        radius = ODOMETER_RADIUS
        circle = Circle(center = ORIGIN, radius = radius)
        circle.stroke_width = ODOMETER_STROKE_WIDTH
        circle.color_using_background_image(self.background_image_file)
        self.add(circle)

        if self.pure_odometer_background:
            # Just display this background circle, for compositing in Premiere with PiWalker odometers
            self.wait()
            return

        if self.dashed_line_angle:
            dashed_line = DashedLine(ORIGIN, radius * RIGHT)
            # Clockwise rotation
            dashed_line.rotate(-self.dashed_line_angle * TAU, about_point = ORIGIN)
            self.add(dashed_line)
        
        num_display = DecimalNumber(0, include_background_rectangle = False)
        num_display.move_to(2 * DOWN)

        caption = TextMobject("turns clockwise")
        caption.next_to(num_display, DOWN)
        self.add(caption)

        display_val_bias = 0
        if self.biased_display_start != None:
            display_val_bias = self.biased_display_start - self.rotate_func(0)
        display_func = lambda alpha : self.rotate_func(alpha) + display_val_bias

        base_arrow = Arrow(ORIGIN, RIGHT, buff = 0)

        self.play(
            FuncRotater(base_arrow, rev_func = lambda x : -self.rotate_func(x)),
            ChangingDecimal(num_display, display_func),
            run_time = self.run_time,
            rate_func=linear)

#############
# Above are mostly general tools; here, we list, in order, finished or near-finished scenes

class FirstSqrtScene(EquationSolver1d):
    CONFIG = {
        "x_min" : 0,
        "x_max" : 2.5,
        "y_min" : 0,
        "y_max" : 2.5**2,
        "graph_origin" : 2.5*DOWN + 5.5*LEFT,
        "x_axis_width" : 12,
        "zoom_factor" : 3,
        "zoomed_canvas_center" : 2.25 * UP + 1.75 * LEFT,
        "func" : lambda x : x**2,
        "targetX" : np.sqrt(2),
        "targetY" : 2,
        "initial_lower_x" : 1,
        "initial_upper_x" : 2,
        "num_iterations" : 5,
        "iteration_at_which_to_start_zoom" : 3,
        "graph_label" : "y = x^2",
        "show_target_line" : True,
        "x_tick_frequency" : 0.25
    }

class TestFirstSqrtScene(FirstSqrtScene):
    CONFIG = {
        "num_iterations" : 1,
    }

FirstSqrtSceneConfig = FirstSqrtScene.CONFIG
shiftVal = FirstSqrtSceneConfig["targetY"]

class SecondSqrtScene(FirstSqrtScene):
        CONFIG = {
            "graph_label" : FirstSqrtSceneConfig["graph_label"] + " - " + str(shiftVal),
            "show_y_as_deviation" : True,
        }

class TestSecondSqrtScene(SecondSqrtScene):
    CONFIG = {
        "num_iterations" : 1
    }

class GuaranteedZeroScene(SecondSqrtScene):
     CONFIG = {
        # Manual config values, not automatically synced to anything above
        "initial_lower_x" : 1.75,
        "initial_upper_x" : 2
     }

class TestGuaranteedZeroScene(GuaranteedZeroScene):
    CONFIG = {
        "num_iterations" : 1
    }

# TODO: Pi creatures intrigued

class RewriteEquation(Scene):
    def construct(self):
        # Can maybe use get_center() to perfectly center Groups before and after transform

        f_old = TexMobject("f(x)")
        f_new = f_old.copy()
        equals_old = TexMobject("=")
        equals_old_2 = equals_old.copy()
        equals_new = equals_old.copy()
        g_old = TexMobject("g(x)")
        g_new = g_old.copy()
        minus_new = TexMobject("-")
        zero_new = TexMobject("0")
        f_old.next_to(equals_old, LEFT)
        g_old.next_to(equals_old, RIGHT)
        minus_new.next_to(g_new, LEFT)
        f_new.next_to(minus_new, LEFT)
        equals_new.next_to(g_new, RIGHT)
        zero_new.next_to(equals_new, RIGHT)

        # where_old = TextMobject("Where does ")
        # where_old.next_to(f_old, LEFT)
        # where_new = where_old.copy()
        # where_new.next_to(f_new, LEFT)
        
        # qmark_old = TextMobject("?")
        # qmark_old.next_to(g_old, RIGHT)
        # qmark_new = qmark_old.copy()
        # qmark_new.next_to(zero_new, RIGHT)
        
        self.add(f_old, equals_old, equals_old_2, g_old) #, where_old, qmark_old)
        self.wait()
        self.play(
            ReplacementTransform(f_old, f_new),
            ReplacementTransform(equals_old, equals_new), 
            ReplacementTransform(g_old, g_new), 
            ReplacementTransform(equals_old_2, minus_new),
            ShowCreation(zero_new),
            # ReplacementTransform(where_old, where_new),
            # ReplacementTransform(qmark_old, qmark_new),
        )
        self.wait()

class SignsExplanation(Scene):
    def construct(self):
        num_line = NumberLine()
        largest_num = 10
        num_line.add_numbers(*list(range(-largest_num, largest_num + 1)))
        self.add(num_line)
        self.wait()

        pos_num = 3
        neg_num = -pos_num

        pos_arrow = Arrow(
                num_line.number_to_point(0), 
                num_line.number_to_point(pos_num),
                buff = 0,
                color = positive_color)
        neg_arrow = Arrow(
                num_line.number_to_point(0), 
                num_line.number_to_point(neg_num),
                buff = 0,
                color = negative_color)

        plus_sign = TexMobject("+", fill_color = positive_color)
        minus_sign = TexMobject("-", fill_color = negative_color)

        plus_sign.next_to(pos_arrow, UP)
        minus_sign.next_to(neg_arrow, UP)
        
        #num_line.add_numbers(pos_num)
        self.play(ShowCreation(pos_arrow), FadeIn(plus_sign))

        #num_line.add_numbers(neg_num)
        self.play(ShowCreation(neg_arrow), FadeIn(minus_sign))

class VectorField(Scene):
    CONFIG = {
        "func" : example_plane_func,
        "granularity" : 10,
        "arrow_scale_factor" : 0.1,
        "normalized_arrow_scale_factor" : 5
    }

    def construct(self):
        num_plane = NumberPlane()
        self.add(num_plane)

        x_min, y_min = num_plane.point_to_coords(FRAME_X_RADIUS * LEFT + FRAME_Y_RADIUS * UP)
        x_max, y_max = num_plane.point_to_coords(FRAME_X_RADIUS * RIGHT + FRAME_Y_RADIUS * DOWN)

        x_points = np.linspace(x_min, x_max, self.granularity)
        y_points = np.linspace(y_min, y_max, self.granularity)
        points = it.product(x_points, y_points)

        sized_arrows = Group()
        unsized_arrows = Group()
        for (x, y) in points:
            output = self.func((x, y))
            output_size = np.sqrt(sum(output**2))
            normalized_output = output * fdiv(self.normalized_arrow_scale_factor, output_size) # Assume output has nonzero size here
            arrow = Vector(output * self.arrow_scale_factor)
            normalized_arrow = Vector(normalized_output * self.arrow_scale_factor)
            arrow.move_to(num_plane.coords_to_point(x, y))
            normalized_arrow.move_to(arrow)
            sized_arrows.add(arrow)
            unsized_arrows.add(normalized_arrow)

        self.add(sized_arrows)
        self.wait()

        self.play(ReplacementTransform(sized_arrows, unsized_arrows))
        self.wait()

class HasItsLimitations(Scene):
    CONFIG = {
        "camera_config" : {"use_z_coordinate_for_display_order": True},
    }

    def construct(self):
        num_line = NumberLine()
        num_line.add_numbers()
        self.add(num_line)

        self.wait()

        # We arrange to go from 2 to 4, a la the squaring in FirstSqrtScene
        base_point = num_line.number_to_point(2) + OUT

        dot_color = ORANGE

        DOT_Z = OUT
        # Note: This z-buffer value is needed for our static scenes, but is
        # not sufficient for everything, in that we still need to use 
        # the foreground_mobjects trick during animations.
        # At some point, we should figure out how to have animations
        # play well with z coordinates.
        
        input_dot = Dot(base_point + DOT_Z, color = dot_color)
        input_label = TextMobject("Input", fill_color = dot_color)
        input_label.next_to(input_dot, UP + LEFT)
        input_label.add_background_rectangle()
        self.add_foreground_mobject(input_dot)
        self.add(input_label)

        curved_arrow = Arc(0, color = MAROON_E)
        curved_arrow.set_bound_angles(np.pi, 0)
        curved_arrow.generate_points()
        curved_arrow.add_tip()
        curved_arrow.move_arc_center_to(base_point + RIGHT)
        # Could do something smoother, with arrowhead moving along partial arc?
        self.play(ShowCreation(curved_arrow))

        output_dot = Dot(base_point + 2 * RIGHT + DOT_Z, color = dot_color)
        output_label = TextMobject("Output", fill_color = dot_color)
        output_label.next_to(output_dot, UP + RIGHT)
        output_label.add_background_rectangle()

        self.add_foreground_mobject(output_dot)
        self.add(output_label)
        self.wait()

        num_plane = NumberPlane()
        num_plane.add_coordinates()

        new_base_point = base_point + 2 * UP
        new_input_dot = input_dot.copy().move_to(new_base_point)
        new_input_label = input_label.copy().next_to(new_input_dot, UP + LEFT)
        
        new_curved_arrow = Arc(0).match_style(curved_arrow)
        new_curved_arrow.set_bound_angles(np.pi * 3/4, 0)
        new_curved_arrow.generate_points()
        new_curved_arrow.add_tip()

        input_diff = input_dot.get_center() - curved_arrow.points[0]
        output_diff = output_dot.get_center() - curved_arrow.points[-1]

        new_curved_arrow.shift((new_input_dot.get_center() - new_curved_arrow.points[0]) - input_diff)

        new_output_dot = output_dot.copy().move_to(new_curved_arrow.points[-1] + output_diff)
        new_output_label = output_label.copy().next_to(new_output_dot, UP + RIGHT)

        dot_objects = Group(input_dot, input_label, output_dot, output_label, curved_arrow)
        new_dot_objects = Group(new_input_dot, new_input_label, new_output_dot, new_output_label, new_curved_arrow)

        self.play(
            FadeOut(num_line), FadeIn(num_plane), 
            ReplacementTransform(dot_objects, new_dot_objects),
        )

        self.wait()

        self.add_foreground_mobject(new_dot_objects)

        complex_plane = ComplexPlane()
        complex_plane.add_coordinates()
        
        # This looks a little wonky and we may wish to do a crossfade in Premiere instead
        self.play(FadeOut(num_plane), FadeIn(complex_plane))

        self.wait()
        

class ComplexPlaneIs2d(Scene):
    def construct(self):
        com_plane = ComplexPlane()
        self.add(com_plane)
        # TODO: Add labels to axes, specific complex points
        self.wait()

class NumberLineScene(Scene):
    def construct(self):
        num_line = NumberLine()
        self.add(num_line)
        # TODO: Add labels, arrows, specific points
        self.wait()

        border_color = PURPLE_E
        inner_color = RED
        stroke_width = 10

        left_point = num_line.number_to_point(-1)
        right_point = num_line.number_to_point(1)
        # TODO: Make this line a thin rectangle
        interval_1d = Line(left_point, right_point, 
            stroke_color = inner_color, stroke_width = stroke_width)
        rect_1d = Rectangle(stroke_width = 0, fill_opacity = 1, fill_color = inner_color)
        rect_1d.replace(interval_1d)
        rect_1d.stretch_to_fit_height(SMALL_BUFF)
        left_dot = Dot(left_point, stroke_width = stroke_width, color = border_color)
        right_dot = Dot(right_point, stroke_width = stroke_width, color = border_color)
        endpoints_1d = VGroup(left_dot, right_dot)
        full_1d = VGroup(rect_1d, endpoints_1d)
        self.play(ShowCreation(full_1d))
        self.wait()

        # TODO: Can polish the morphing above; have dots become left and right sides, and 
        # only then fill in the top and bottom

        num_plane = NumberPlane()

        random_points = [UP + LEFT, UP + RIGHT, DOWN + RIGHT, DOWN + LEFT]

        border_2d = Polygon(
            *random_points,
            stroke_color = border_color,
            stroke_width = stroke_width)

        filling_2d = Polygon(
            *random_points,
            fill_color = inner_color,
            fill_opacity = 0.8,
            stroke_width = stroke_width)
        full_2d = VGroup(filling_2d, border_2d)

        self.play(
            FadeOut(num_line), 
            FadeIn(num_plane),
            ReplacementTransform(full_1d, full_2d))

        self.wait()

class Initial2dFuncSceneBase(Scene):
    CONFIG = {
        "func" : point3d_func_from_complex_func(lambda c : c**2 - c**3/5 + 1)
        # We don't use example_plane_func because, unfortunately, the sort of examples
        # which are good for demonstrating our color mapping haven't turned out to be
        # good for visualizing in this manner; the gridlines run over themselves multiple 
        # times in too confusing a fashion
    }

    def show_planes(self):
        print("Error! Unimplemented (pure virtual) show_planes")

    def shared_construct(self):
        points = [LEFT + DOWN, RIGHT + DOWN, LEFT + UP, RIGHT + UP]
        for i in range(len(points) - 1):
            line = Line(points[i], points[i + 1], color = RED)
            self.obj_draw(line)

        def wiggle_around(point):
             radius = 0.2
             small_circle = cw_circle.copy()
             small_circle.scale(radius)
             small_circle.move_to(point + radius * RIGHT)
             small_circle.set_color(RED)
             self.obj_draw(small_circle)

        wiggle_around(points[-1])

    def obj_draw(self, input_object):
        self.play(ShowCreation(input_object))

    def construct(self):
        self.show_planes()
        self.shared_construct()

# Alternative to the below, using MappingCameras, but no morphing animation
class Initial2dFuncSceneWithoutMorphing(Initial2dFuncSceneBase):

    def setup(self):
        left_camera = Camera(**self.camera_config)
        right_camera = MappingCamera(
            mapping_func = self.func,
            **self.camera_config)
        split_screen_camera = SplitScreenCamera(left_camera, right_camera, **self.camera_config)
        self.camera = split_screen_camera

    def show_planes(self):
        self.num_plane = NumberPlane()
        self.num_plane.prepare_for_nonlinear_transform()
        #num_plane.fade()
        self.add(self.num_plane)

# Alternative to the above, manually implementing split screen with a morphing animation
class Initial2dFuncSceneMorphing(Initial2dFuncSceneBase):
    CONFIG = {
        "num_needed_anchor_curves" : 10,
    }

    def setup(self):
        split_line = DashedLine(FRAME_Y_RADIUS * UP, FRAME_Y_RADIUS * DOWN)
        self.num_plane = NumberPlane(x_radius = FRAME_X_RADIUS/2)
        self.num_plane.to_edge(LEFT, buff = 0)
        self.num_plane.prepare_for_nonlinear_transform()
        self.add(self.num_plane, split_line)

    def squash_onto_left(self, object):
        object.shift(FRAME_X_RADIUS/2 * LEFT)

    def squash_onto_right(self, object):
        object.shift(FRAME_X_RADIUS/2 * RIGHT)

    def obj_draw(self, input_object):
        output_object = input_object.copy()
        if input_object.get_num_curves() < self.num_needed_anchor_curves:
            input_object.insert_n_curves(self.num_needed_anchor_curves)
        output_object.apply_function(self.func)
        self.squash_onto_left(input_object)
        self.squash_onto_right(output_object)
        self.play(
            ShowCreation(input_object), 
            ShowCreation(output_object)
            )

    def show_planes(self):
        right_plane = self.num_plane.copy()
        right_plane.center()
        right_plane.prepare_for_nonlinear_transform()
        right_plane.apply_function(self.func)
        right_plane.shift(FRAME_X_RADIUS/2 * RIGHT)
        self.right_plane = right_plane
        crappy_cropper = FullScreenFadeRectangle(fill_opacity = 1)
        crappy_cropper.stretch_to_fit_width(FRAME_X_RADIUS)
        crappy_cropper.to_edge(LEFT, buff = 0)
        self.play(
            ReplacementTransform(self.num_plane.copy(), right_plane),
            FadeIn(crappy_cropper), 
            Animation(self.num_plane),
            run_time = 3
        )

class DemonstrateColorMapping(ColorMappedObjectsScene):
    CONFIG = {
        "show_num_plane" : False,
        "show_full_color_map" : True
    }

    def construct(self):
        ColorMappedObjectsScene.construct(self)

        # Doing this in Premiere now instead
        # output_plane_label = TextMobject("Output Plane", color = WHITE)
        # output_plane_label.move_to(3 * UP)
        # self.add_foreground_mobject(output_plane_label)

        if self.show_full_color_map:
            bright_background = Rectangle(width = 2 * FRAME_X_RADIUS + 1, height = 2 * FRAME_Y_RADIUS + 1, fill_opacity = 1)
            bright_background.color_using_background_image(self.background_image_file)
            dim_background = bright_background.copy()
            dim_background.fill_opacity = 0.3
            
            background = bright_background.copy()
            self.add(background)
            self.wait()
            self.play(ReplacementTransform(background, dim_background))

        self.wait()

        ray = Line(ORIGIN, 10 * LEFT)


        circle = cw_circle.copy()
        circle.color_using_background_image(self.background_image_file)

        self.play(ShowCreation(circle))

        self.wait()

        scale_up_factor = 5
        scale_down_factor = 20
        self.play(ApplyMethod(circle.scale, fdiv(1, scale_down_factor)))

        self.play(ApplyMethod(circle.scale, scale_up_factor * scale_down_factor))

        self.play(ApplyMethod(circle.scale, fdiv(1, scale_up_factor)))

        self.wait()
        self.remove(circle)

        ray = Line(ORIGIN, 10 * LEFT)
        ray.color_using_background_image(self.background_image_file)

        self.play(ShowCreation(ray))

        self.wait()

        self.play(Rotating(ray, about_point = ORIGIN, radians = -TAU/2))

        self.wait()

        self.play(Rotating(ray, about_point = ORIGIN, radians = -TAU/2))

        self.wait()

        if self.show_full_color_map:
            self.play(ReplacementTransform(background, bright_background))
            self.wait()

# Everything in this is manually kept in sync with WindingNumber_G/TransitionFromPathsToBoundaries
class LoopSplitScene(ColorMappedObjectsScene):
    CONFIG = {
        "func" : plane_func_by_wind_spec(
            (-2, 0, 2), (2, 0, 1)
        ),
        "use_fancy_lines" : True,
    }

    def PulsedLine(self, 
        start, end, 
        bullet_template, 
        num_bullets = 4, 
        pulse_time = 1, 
        **kwargs):
        line = Line(start, end, color = WHITE, stroke_width = 4, **kwargs)
        if self.use_fancy_lines:
            line.color_using_background_image(self.background_image_file)
        anim = LinePulser(
            line = line, 
            bullet_template = bullet_template, 
            num_bullets = num_bullets, 
            pulse_time = pulse_time, 
            output_func = self.func,
            **kwargs)
        return (line, VMobject(*anim.bullets), anim)

    def construct(self):
        ColorMappedObjectsScene.construct(self)

        scale_factor = 2
        shift_term = 0

        # TODO: Change all this to use a wider than tall loop, made of two squares

        # Original loop
        tl = (UP + 2 * LEFT) * scale_factor
        tm = UP * scale_factor
        tr = (UP + 2 * RIGHT) * scale_factor
        bl = (DOWN + 2 * LEFT) * scale_factor
        bm = DOWN * scale_factor
        br = (DOWN + 2 * RIGHT) * scale_factor

        top_line = Line(tl, tr) # Invisible; only used for surrounding circle
        bottom_line = Line(br, bl) # Invisible; only used for surrounding circle

        stroke_width = top_line.stroke_width

        default_bullet = PiCreature()
        default_bullet.scale(0.15)

        def pl(a, b):
            return self.PulsedLine(a, b, default_bullet)

        def indicate_circle(x, double_horizontal_stretch = False):
            circle = Circle(color = WHITE, radius = 2 * np.sqrt(2))
            circle.move_to(x.get_center())

            if x.get_slope() == 0:
                circle.stretch(0.2, 1)
                if double_horizontal_stretch:
                    circle.stretch(2, 0)
            else:
                circle.stretch(0.2, 0)
            return circle

        tl_line_trip = pl(tl, tm)
        midline_left_trip = pl(tm, bm)
        bl_line_trip = pl(bm, bl)
        left_line_trip = pl(bl, tl)

        left_square_trips = [tl_line_trip, midline_left_trip, bl_line_trip, left_line_trip]
        left_square_lines = [x[0] for x in left_square_trips]
        left_square_lines_vmobject = VMobject(*left_square_lines)
        left_square_bullets = [x[1] for x in left_square_trips]
        left_square_anims = [x[2] for x in left_square_trips]

        tr_line_trip = pl(tm, tr)
        right_line_trip = pl(tr, br)
        br_line_trip = pl(br, bm)
        midline_right_trip = pl(bm, tm)

        right_square_trips = [tr_line_trip, right_line_trip, br_line_trip, midline_right_trip]
        right_square_lines = [x[0] for x in right_square_trips]
        right_square_lines_vmobject = VMobject(*right_square_lines)
        right_square_bullets = [x[1] for x in right_square_trips]
        right_square_anims = [x[2] for x in right_square_trips]

        midline_trips = [midline_left_trip, midline_right_trip]
        midline_lines = [x[0] for x in midline_trips]
        midline_lines_vmobject = VMobject(*midline_lines)
        midline_bullets = [x[1] for x in midline_trips]
        midline_anims = [x[1] for x in midline_trips]

        left_line = left_line_trip[0]
        right_line = right_line_trip[0]

        for b in left_square_bullets + right_square_bullets:
            b.set_fill(opacity = 0)

        faded = 0.3

        # Workaround for FadeOut/FadeIn not playing well with ContinualAnimations due to 
        # Transforms making copies no longer identified with the ContinualAnimation's tracked mobject
        def bullet_fade(start, end, mob):
            return UpdateFromAlphaFunc(mob, lambda m, a : m.set_fill(opacity = interpolate(start, end, a)))

        def bullet_list_fade(start, end, bullet_list):
            return [bullet_fade(start, end, b) for b in bullet_list]

        def line_fade(start, end, mob):
            return UpdateFromAlphaFunc(mob, lambda m, a : m.set_stroke(width = interpolate(start, end, a) * stroke_width))

        def play_combined_fade(start, end, lines_vmobject, bullets):
            self.play(
                line_fade(start, end, lines_vmobject), 
                *bullet_list_fade(start, end, bullets)
            )

        def play_fade_left(start, end):
            play_combined_fade(start, end, left_square_lines_vmobject, left_square_bullets)

        def play_fade_right(start, end):
            play_combined_fade(start, end, right_square_lines_vmobject, right_square_bullets)

        def play_fade_mid(start, end):
            play_combined_fade(start, end, midline_lines_vmobject, midline_bullets)

        def flash_circles(circles):
            self.play(LaggedStartMap(FadeIn, VGroup(circles)))
            self.wait()
            self.play(FadeOut(VGroup(circles)))
            self.wait()

        self.add(left_square_lines_vmobject, right_square_lines_vmobject)
        self.remove(*midline_lines)
        self.wait()
        self.play(ShowCreation(midline_lines[0]))
        self.add(midline_lines_vmobject)
        self.wait()

        self.add(*left_square_anims)
        self.play(line_fade(1, faded, right_square_lines_vmobject), *bullet_list_fade(0, 1, left_square_bullets))
        self.wait()
        flash_circles([indicate_circle(l) for l in left_square_lines])
        self.play(line_fade(faded, 1, right_square_lines_vmobject), *bullet_list_fade(1, 0, left_square_bullets))
        self.wait()

        self.add(*right_square_anims)
        self.play(line_fade(1, faded, left_square_lines_vmobject), *bullet_list_fade(0, 1, right_square_bullets))
        self.wait()
        flash_circles([indicate_circle(l) for l in right_square_lines])
        self.play(line_fade(faded, 1, left_square_lines_vmobject), *bullet_list_fade(1, 0, right_square_bullets))
        self.wait()
        
        self.play(*bullet_list_fade(0, 1, left_square_bullets + right_square_bullets))
        self.wait()

        outside_circlers = [
            indicate_circle(left_line), 
            indicate_circle(right_line), 
            indicate_circle(top_line, double_horizontal_stretch = True), 
            indicate_circle(bottom_line, double_horizontal_stretch = True)
        ]
        flash_circles(outside_circlers)

        inner_circle = indicate_circle(midline_lines[0])
        self.play(FadeIn(inner_circle))
        self.wait()
        self.play(FadeOut(inner_circle), line_fade(1, 0, midline_lines_vmobject), *bullet_list_fade(1, 0, midline_bullets))
        self.wait()
        
        # Repeat for effect, goes well with narration
        self.play(FadeIn(inner_circle), line_fade(0, 1, midline_lines_vmobject), *bullet_list_fade(0, 1, midline_bullets))
        self.wait()
        self.play(FadeOut(inner_circle), line_fade(1, 0, midline_lines_vmobject), *bullet_list_fade(1, 0, midline_bullets))
        self.wait()

# TODO: Perhaps do extra illustration of zooming out and winding around a large circle, 
# to illustrate relation between degree and large-scale winding number
class FundThmAlg(EquationSolver2d):
    CONFIG = {
        "func" : plane_func_by_wind_spec((1, 2), (-1, 1.5), (-1, 1.5)),
        "num_iterations" : 2,
    }

class SolveX5MinusXMinus1(EquationSolver2d):
    CONFIG = {
        "func" : plane_func_from_complex_func(lambda c : c**5 - c - 1),
        "num_iterations" : 10,
        "show_cursor" : True,
        "display_in_bfs" : True,
    }

class PureColorMapOfX5Thing(PureColorMap):
    CONFIG = {
        "func" : plane_func_from_complex_func(lambda c : c**5 - c - 1),
    }

class X5ThingWithRightHalfGreyed(SolveX5MinusXMinus1):
    CONFIG = {
        "num_iterations" : 3,
        "manual_wind_override" : (1, None, (1, (0, None, None), (0, None, None)))
    }

class SolveX5MinusXMinus1_5Iterations(EquationSolver2d):
    CONFIG = {
        "func" : plane_func_from_complex_func(lambda c : c**5 - c - 1),
        "num_iterations" : 5,
        "show_cursor" : True,
        "display_in_bfs" : True,
        "manual_wind_override" : (None, None, (None, (0, None, None), (0, None, None)))
    }

class X5_Monster_Red_Lines(SolveX5MinusXMinus1_5Iterations):
    CONFIG = {
        "use_separate_plays" : True,
        "use_fancy_lines" : False,
        "line_color" : RED,
    }

class X5_Monster_Green_Lines(X5_Monster_Red_Lines):
    CONFIG = {
        "line_color" : GREEN,
    }

class X5_Monster_Red_Lines_Long(X5_Monster_Red_Lines):
    CONFIG = {
        "num_iterations" : 6
    }

class X5_Monster_Green_Lines_Long(X5_Monster_Green_Lines):
    CONFIG = {
        "num_iterations" : 6
    }

class X5_Monster_Red_Lines_Little_More(X5_Monster_Red_Lines_Long):
    CONFIG = {
        "num_iterations" : 7
    }

class X5_Monster_Green_Lines_Little_More(X5_Monster_Green_Lines_Long):
    CONFIG = {
        "num_iterations" : 7
    }

class X5_Monster_Red_Lines_No_Numbers(X5_Monster_Red_Lines):
    CONFIG = {
        "num_iterations" : 3,
        "show_winding_numbers" : False,
    }

class X5_Monster_Green_Lines_No_Numbers(X5_Monster_Green_Lines):
    CONFIG = {
        "num_iterations" : 3,
        "show_winding_numbers" : False,
    }

class SolveX5MinusXMinus1_3Iterations(EquationSolver2d):
    CONFIG = {
        "func" : plane_func_from_complex_func(lambda c : c**5 - c - 1),
        "num_iterations" : 3,
        "show_cursor" : True,
        "display_in_bfs" : True,
    }

class Diagnostic(SolveX5MinusXMinus1_3Iterations):
    CONFIG = {
        # I think the combination of these two makes things slow
        "use_separate_plays" : not False, # This one isn't important to set any particular way, so let's leave it like this
        "use_fancy_lines" : True, 

        # This causes a small slowdown (before rendering, in particular), but not the big one, I think
        "show_winding_numbers" : True,

        # This doesn't significantly matter for rendering time, I think
        "camera_config" : {"use_z_coordinate_for_display_order" : True}
    }

# All above flags False (meaning not db = False): just under 30 it/s
# not db = True: 30
# use_fancy_lines = True: 30 at first (if scene.play(bfs_nodes[0].first_anim, border_anim is off), but then drops to 3 (or drops right away if that simultaneous play is on)
# use_z_coordinate = True: 30
# show_winding_numbers = True: 10
# winding AND use_fancy_lines: 10
# not db AND fancy_lines AND z_coords = true, winding = false: 3. Not 30, but 3. Slow.
# db AND use_fancy: 3. Slow.
# fancy AND z_coords: 30. Fast. [Hm, this may have been a mistake; fancy and z_coords is now slow?]
# fancy, winding, AND z_coords, but not (not db): 10
# not db, winding, AND z_coords, but not fancy: 10

# class DiagnosticB(Diagnostic):
#     CONFIG = {
#         "num_iterations" : 3,
#         #"num_checkpoints" : 100,
#         #"show_winding_numbers" : False,
#         #"use_cheap_winding_numbers" : True,
#     }

class SolveX5MinusXMinus1Parallel(SolveX5MinusXMinus1):
    CONFIG = {
        "display_in_parallel" : True
    }

class SolveX5MinusXMinus1BFS(SolveX5MinusXMinus1):
    CONFIG = {
        "display_in_bfs" : True
    }

class PreviewClip(EquationSolver2d):
    CONFIG = {
        "func" : example_plane_func,
        "num_iterations" : 5,
        "display_in_parallel" : True,
        "use_fancy_lines" : True,
    }

class ParallelClip(EquationSolver2d):
    CONFIG = {
        "func" : plane_func_by_wind_spec(
            (-3, -1.3, 2), (0.1, 0.2, 1), (2.8, -2, 1)
        ),
        "num_iterations" : 5,
        "display_in_parallel" : True,
    }

class EquationSolver2dMatchBreakdown(EquationSolver2d):
    CONFIG = {
        "func" : plane_func_by_wind_spec(
            (-2, 0.3, 2), (2, -0.2, 1) # Not an exact match, because our breakdown function has a zero along midlines...
        ),
        "num_iterations" : 5,
        "display_in_parallel" : True,
        "show_cursor" : True
    }

class EquationSolver2dMatchBreakdown_parallel(EquationSolver2dMatchBreakdown):
    CONFIG = {
        "display_in_parallel" : True,
        "display_in_bfs" : False,
    }

class EquationSolver2dMatchBreakdown_bfs(EquationSolver2dMatchBreakdown):
    CONFIG = {
        "display_in_parallel" : False,
        "display_in_bfs" : True,
    }

class QuickPreview(PreviewClip):
    CONFIG = {
        "num_iterations" : 3,
        "display_in_parallel" : False,
        "display_in_bfs" : True,
        "show_cursor" : True
    }

class LongEquationSolver(EquationSolver2d):
    CONFIG = {
        "func" : example_plane_func,
        "num_iterations" : 10,
        "display_in_bfs" : True,
        "linger_parameter" : 0.4,
        "show_cursor" : True,
    }

class QuickPreviewUnfancy(LongEquationSolver):
    CONFIG = {
        # "use_fancy_lines" : False,
    }

# TODO: Borsuk-Ulam visuals
# Note: May want to do an ordinary square scene, then MappingCamera it into a circle
# class BorsukUlamScene(PiWalker):

# 3-way scene of "Good enough"-illustrating odometers; to be composed in Premiere
left_func = lambda x : x**2 - x + 1
diff_func = lambda x : np.cos(1.4 * (x - 0.1) * (np.log(x + 0.1) - 0.3) * TAU)/2.1

class LeftOdometer(OdometerScene):
    CONFIG = {
        "rotate_func" : left_func,
        "biased_display_start" : 0
    }

class RightOdometer(OdometerScene):
    CONFIG = {
        "rotate_func" : lambda x : left_func(x) + diff_func(x),
        "biased_display_start" : 0
    }

class DiffOdometer(OdometerScene):
    CONFIG = {
        "rotate_func" : diff_func,
        "dashed_line_angle" : 0.5,
        "biased_display_start" : 0
    }

class CombineInterval(Scene):
    def construct(self):
        plus_sign = TexMobject("+", fill_color = positive_color)
        minus_sign = TexMobject("-", fill_color = negative_color)

        left_point = Dot(LEFT, color = positive_color)
        right_point = Dot(RIGHT, color = negative_color)
        line1 = Line(LEFT, RIGHT)
        interval1 = Group(line1, left_point, right_point)

        plus_sign.next_to(left_point, UP)
        minus_sign.next_to(right_point, UP)

        self.add(interval1, plus_sign, minus_sign)
        self.wait()
        self.play(
            CircleIndicate(plus_sign),
            CircleIndicate(minus_sign),
        )
        self.wait()

        mid_point = Dot(ORIGIN, color = GREY)

        question_mark = TexMobject("?", fill_color = GREY)
        plus_sign_copy = plus_sign.copy()
        minus_sign_copy = minus_sign.copy()
        new_signs = Group(question_mark, plus_sign_copy, minus_sign_copy)
        for sign in new_signs: sign.next_to(mid_point, UP)

        self.play(FadeIn(mid_point), FadeIn(question_mark))
        self.wait()

        self.play(
            ApplyMethod(mid_point.set_color, positive_color),
            ReplacementTransform(question_mark, plus_sign_copy),
        )
        self.play(
            CircleIndicate(plus_sign_copy),
            CircleIndicate(minus_sign),
        )

        self.wait()

        self.play(
            ApplyMethod(mid_point.set_color, negative_color),
            ReplacementTransform(plus_sign_copy, minus_sign_copy),
        )
        self.play(
            CircleIndicate(minus_sign_copy),
            CircleIndicate(plus_sign),
        )

        self.wait()

class CombineInterval2(Scene):
    def construct(self):
        plus_sign = TexMobject("+", fill_color = positive_color)

        def make_interval(a, b):
            line = Line(a, b)
            start_dot = Dot(a, color = positive_color)
            end_dot = Dot(b, color = positive_color)
            start_sign = plus_sign.copy().next_to(start_dot, UP)
            end_sign = plus_sign.copy().next_to(end_dot, UP)
            return Group(start_sign, end_sign, line, start_dot, end_dot)

        def pair_indicate(a, b):
            self.play(
                CircleIndicate(a),
                CircleIndicate(b)
            )

        left_interval = make_interval(2 * LEFT, LEFT)
        right_interval = make_interval(RIGHT, 2 * RIGHT)

        self.play(FadeIn(left_interval), FadeIn(right_interval))

        pair_indicate(left_interval[0], left_interval[1])

        pair_indicate(right_interval[0], right_interval[1])

        self.play(
            ApplyMethod(left_interval.shift, RIGHT),
            ApplyMethod(right_interval.shift, LEFT),
        )

        pair_indicate(left_interval[0], right_interval[1])

        self.wait()

tiny_loop_func = scale_func(plane_func_by_wind_spec((-1, -2), (1, 1), (1, 1)), 0.3)

class TinyLoopScene(ColorMappedByFuncScene):
    CONFIG = {
        "func" : tiny_loop_func,
        "show_num_plane" : False,
        "loop_point" : ORIGIN,
        "circle_scale" : 0.7
    }

    def construct(self):
        ColorMappedByFuncScene.construct(self)

        circle = cw_circle.copy()
        circle.scale(self.circle_scale)
        circle.move_to(self.loop_point)

        self.play(ShowCreation(circle))
        self.wait()

class TinyLoopInInputPlaneAroundNonZero(TinyLoopScene):
    CONFIG = {
        "loop_point" : 0.5 * RIGHT
    }

class TinyLoopInInputPlaneAroundZero(TinyLoopScene):
    CONFIG = {
        "loop_point" : UP + RIGHT
    }

class TinyLoopInOutputPlaneAroundNonZero(TinyLoopInInputPlaneAroundNonZero):
    CONFIG = {
        "camera_class" : MappingCamera,
        "camera_config" : {"mapping_func" : point3d_func_from_plane_func(tiny_loop_func)},
        "show_output" : True,
        "show_num_plane" : False,
    }

class TinyLoopInOutputPlaneAroundZero(TinyLoopInInputPlaneAroundZero):
    CONFIG = {
        "camera_class" : MappingCamera,
        "camera_config" : {"mapping_func" : point3d_func_from_plane_func(tiny_loop_func)},
        "show_output" : True,
        "show_num_plane" : False,
    }

class BorderOf2dRegionScene(Scene):
    def construct(self):
        num_plane = NumberPlane()
        self.add(num_plane)

        points = standard_rect + 1.5 * UP + 2 * RIGHT
        interior = Polygon(*points, fill_color = neutral_color, fill_opacity = 1, stroke_width = 0)
        self.play(FadeIn(interior))

        border = Polygon(*points, color = negative_color, stroke_width = border_stroke_width)
        self.play(ShowCreation(border))

big_loop_no_zeros_func = lambda x_y5 : complex_to_pair(np.exp(complex(10, x_y5[1] * np.pi)))

class BigLoopNoZeros(ColorMappedObjectsScene):
    CONFIG = {
        "func" : big_loop_no_zeros_func
    }

    def construct(self):
        ColorMappedObjectsScene.construct(self)
        points = 3 * np.array([UL, UR, DR, DL])
        polygon = Polygon(*points)
        polygon.color_using_background_image(self.background_image_file)
        self.play(ShowCreation(polygon))

        self.wait()

        polygon2 = polygon.copy()
        polygon2.fill_opacity = 1
        self.play(FadeIn(polygon2))

        self.wait()

class ExamplePlaneFunc(ColorMappedByFuncScene):
    CONFIG = {
        "show_num_plane" : False,
        "func" : example_plane_func
    }

    def construct(self):
        ColorMappedByFuncScene.construct(self)

        radius = 0.5

        def circle_point(point):
            circle = cw_circle.copy().scale(radius).move_to(point)
            self.play(ShowCreation(circle))
            return circle

        def circle_spec(spec):
            point = spec[0] * RIGHT + spec[1] * UP
            return circle_point(point)

        nonzero_point = ORIGIN # Manually chosen, not auto-synced with example_plane_func
        nonzero_point_circle = circle_point(nonzero_point)
        self.wait()
        self.play(FadeOut(nonzero_point_circle))
        self.wait()

        zero_circles = Group()

        for spec in example_plane_func_spec:
            zero_circles.add(circle_spec(spec))

        self.wait()

        # TODO: Fix the code in Fade to automatically propagate correctly 
        # to subobjects, even with special vectorized object handler. 
        # Also, remove the special handling from FadeOut, have it implemented
        # solely through Fade.
        #
        # But for now, I'll just take care of this stuff myself here.
        # self.play(*[FadeOut(zero_circle) for zero_circle in zero_circles])
        self.play(FadeOut(zero_circles))
        self.wait()

        # We can reuse our nonzero point from before for "Output doesn't go through ever color"
        # Do re-use in Premiere

        # We can also re-use the first of our zero-circles for "Output does go through every color",
        # but just in case it would be useful, here's another one, all on its own

        specific_spec_index = 0
        temp_circle = circle_spec(example_plane_func_spec[specific_spec_index])
        self.play(FadeOut(temp_circle))

        self.wait()

class PiWalkerExamplePlaneFunc(PiWalkerRect):
    CONFIG = {
        "show_num_plane" : False,
        "func" : example_plane_func,
        # These are just manually entered, not 
        # automatically kept in sync with example_plane_func:
        "start_x" : -4,
        "start_y" : 3,
        "walk_width" : 8,
        "walk_height" : 6,
    }

class NoticeHowOnThisLoop(PiWalkerRect):
    CONFIG = {
        "show_num_plane" : False,
        "func" : example_plane_func,
        # These are just manually entered, not 
        # automatically kept in sync with example_plane_func:
        "start_x" : 0.5,
        "start_y" : -0.5,
        "walk_width" : -1, # We trace from bottom-right clockwise on this one, to start at a red point
        "walk_height" : -1,
    }

class ButOnThisLoopOverHere(NoticeHowOnThisLoop):
    CONFIG = {
        # These are just manually entered, not 
        # automatically kept in sync with example_plane_func:
        "start_x" : -1,
        "start_y" : 0,
        "walk_width" : 1,
        "walk_height" : 1,
    }

class PiWalkerExamplePlaneFuncWithScaling(PiWalkerExamplePlaneFunc):
    CONFIG = {
        "scale_arrows" : True,
        "display_size" : True,
    }

class TinyLoopOfBasicallySameColor(PureColorMap):
    def construct(self):
        PureColorMap.construct(self)
        radius = 0.5
        circle = cw_circle.copy().scale(radius).move_to(UP + RIGHT)
        self.play(ShowCreation(circle))
        self.wait()

def uhOhFunc(xxx_todo_changeme11):
    (x, y) = xxx_todo_changeme11
    x = -np.clip(x, -5, 5)/5
    y = -np.clip(y, -3, 3)/3

    alpha = 0.5 # Most things will return green

    # These next three things should really be abstracted into some "Interpolated triangle" function

    if x >= 0 and y >= x and y <= 1:
        alpha = interpolate(0.5, 1, y - x)

    if x < 0 and y >= -2 * x and y <= 1:
        alpha = interpolate(0.5, 1, y + 2 * x)

    if x >= -1 and y >= 2 * (x + 1) and y <= 1:
        alpha = interpolate(0.5, 0, y - 2 * (x + 1))

    return complex_to_pair(100 * np.exp(complex(0, TAU * (0.5 - alpha))))

class UhOhFuncTest(PureColorMap):
    CONFIG = {
        "func" : uhOhFunc
    }


class UhOhScene(EquationSolver2d):
    CONFIG = {
        "func" : uhOhFunc,
        "manual_wind_override" : (1, None, (1, None, (1, None, None))), # Tailored to UhOhFunc above
        "show_winding_numbers" : False,
        "num_iterations" : 5,
    }

class UhOhSceneWithWindingNumbers(UhOhScene):
    CONFIG = {
        "show_winding_numbers" : True,
    }

class UhOhSceneWithWindingNumbersNoOverride(UhOhSceneWithWindingNumbers):
    CONFIG = {
        "manual_wind_override" : None,
        "num_iterations" : 2
    }

class UhOhSalientStill(ColorMappedObjectsScene):
    CONFIG = {
        "func" : uhOhFunc
    }

    def construct(self):
        ColorMappedObjectsScene.construct(self)

        new_up = 3 * UP
        new_left = 5 * LEFT

        thin_line = Line(UP, RIGHT, color = WHITE)

        main_points = [new_left + new_up, new_up, ORIGIN, new_left]
        polygon = Polygon(*main_points, stroke_width = border_stroke_width)
        thin_polygon = polygon.copy().match_style(thin_line)
        polygon.color_using_background_image(self.background_image_file)

        midline = Line(new_up + 0.5 * new_left, 0.5 * new_left, stroke_width = border_stroke_width)
        thin_midline = midline.copy().match_style(thin_line)
        midline.color_using_background_image(self.background_image_file)

        self.add(polygon, midline)

        self.wait()

        everything_filler = FullScreenFadeRectangle(fill_opacity = 1)
        everything_filler.color_using_background_image(self.background_image_file)

        thin_white_copy = Group(thin_polygon, thin_midline)

        self.play(FadeIn(everything_filler), FadeIn(thin_white_copy))

        self.wait()


# TODO: Brouwer's fixed point theorem visuals
# class BFTScene(Scene):

# TODO: Pi creatures wide-eyed in amazement

#################

# TODOs, from easiest to hardest:

# Minor fiddling with little things in each animation; placements, colors, timing, text

# Initial odometer scene (simple once previous Pi walker scene is decided upon)

# Writing new Pi walker scenes by parametrizing general template

# (All the above are basically trivial tinkering at this point)

# ----

# Pi creature emotion stuff

# BFT visuals

# Borsuk-Ulam visuals

####################

# Random test scenes and test functions go here:

def rect_to_circle(xxx_todo_changeme12):
    (x, y, z) = xxx_todo_changeme12
    size = np.sqrt(x**2 + y**2)
    max_abs_size = max(abs(x), abs(y))
    return fdiv(np.array((x, y, z)) * max_abs_size, size)

class MapPiWalkerRect(PiWalkerRect):
    CONFIG = {
        "camera_class" : MappingCamera,
        "camera_config" : {"mapping_func" : rect_to_circle},
        "show_output" : True
    }

class ShowBack(PiWalkerRect):
    CONFIG = {
         "func" : plane_func_by_wind_spec((1, 2), (-1, 1.5), (-1, 1.5))
    }

class PiWalkerOdometerTest(PiWalkerExamplePlaneFunc):
    CONFIG = {
        "display_odometer" : True
    }

class PiWalkerFancyLineTest(PiWalkerExamplePlaneFunc):
    CONFIG = {
        "color_foreground_not_background" : True
    }

class NotFoundScene(Scene):
    def construct(self):
        self.add(TextMobject("SCENE NOT FOUND!"))
        self.wait()

criticalStripYScale = 100
criticalStrip = Axes(x_min = -0.5, x_max = 1.5, x_axis_config = {"unit_size" : FRAME_X_RADIUS, 
    "number_at_center" : 0.5}, 
    y_min = -criticalStripYScale, y_max = criticalStripYScale, 
    y_axis_config = {"unit_size" : fdiv(FRAME_Y_RADIUS, criticalStripYScale)})

class ZetaViz(PureColorMap):
    CONFIG = {
        "func" : plane_zeta,
        #"num_plane" : criticalStrip,
        "show_num_plane" : True
    }

class TopLabel(Scene):
    CONFIG = {
        "text" : "Text"
    }
    def construct(self):
        label = TextMobject(self.text)
        label.move_to(3 * UP)
        self.add(label)
        self.wait()

# This is a giant hack that doesn't handle rev wrap-around correctly; should use 
# make_alpha_winder instead
class SpecifiedWinder(PiWalker):
    CONFIG = {
        "start_x" : 0,
        "start_y" : 0,
        "x_wind" : 1, # Assumed positive
        "y_wind" : 1, # Assumed positive
        "step_size" : 0.1
    }

    def setup(self):
        rev_func = lambda p : point_to_rev(self.func(p))
        start_pos = np.array((self.start_x, self.start_y))
        cur_pos = start_pos.copy()
        start_rev = rev_func(start_pos)

        mid_rev = start_rev
        while (abs(mid_rev - start_rev) < self.x_wind):
            cur_pos += (self.step_size, 0)
            mid_rev = rev_func(cur_pos)

        print("Reached ", cur_pos, ", with rev ", mid_rev - start_rev)
        mid_pos = cur_pos.copy()

        end_rev = mid_rev
        while (abs(end_rev - mid_rev) < self.y_wind):
            cur_pos -= (0, self.step_size)
            end_rev = rev_func(cur_pos)

        end_pos = cur_pos.copy()

        print("Reached ", cur_pos, ", with rev ", end_rev - mid_rev)

        self.walk_coords = [start_pos, mid_pos, end_pos]
        print("Walk coords: ", self.walk_coords)
        PiWalker.setup(self)

class OneFifthTwoFifthWinder(SpecifiedWinder):
    CONFIG = {
        "func" : example_plane_func,
        "start_x" : -2.0,
        "start_y" : 1.0,
        "x_wind" : 0.2,
        "y_wind" : 0.2,
        "step_size" : 0.01,
        "show_num_plane" : False,
        "step_run_time" : 6,
        "num_decimal_places" : 2,
    }

class OneFifthOneFifthWinderWithReset(OneFifthTwoFifthWinder):
    CONFIG = {
        "wind_reset_indices" : [1]
    }

class OneFifthTwoFifthWinderOdometer(OneFifthTwoFifthWinder):
    CONFIG = {
        "display_odometer" : True,
    }

class ForwardBackWalker(PiWalker):
    CONFIG = {
        "func" : example_plane_func,
        "walk_coords" : [np.array((-2, 1)), np.array((1, 1))],
        "step_run_time" : 3,
    }

class ForwardBackWalkerOdometer(ForwardBackWalker):
    CONFIG = {
        "display_odometer" : True,
    }

class PureOdometerBackground(OdometerScene):
    CONFIG = {
        "pure_odometer_background" : True
    }

class CWColorWalk(PiWalkerRect):
    CONFIG = {
        "func" : example_plane_func,
        "start_x" : example_plane_func_spec[0][0] - 1,
        "start_y" : example_plane_func_spec[0][1] + 1,
        "walk_width" : 2,
        "walk_height" : 2,
        "draw_lines" : False,
        "display_wind" : False,
        "step_run_time" : 2
    }

class CWColorWalkOdometer(CWColorWalk):
    CONFIG = {
        "display_odometer" : True,
    }

class CCWColorWalk(CWColorWalk):
    CONFIG = {
        "start_x" : example_plane_func_spec[2][0] - 1,
        "start_y" : example_plane_func_spec[2][1] + 1,
    }

class CCWColorWalkOdometer(CCWColorWalk):
    CONFIG = {
        "display_odometer" : True,
    }

class ThreeTurnWalker(PiWalkerRect):
    CONFIG = {
        "func" : plane_func_from_complex_func(lambda c: c**3 * complex(1, 1)**3),
        "double_up" : True,
        "wind_reset_indices" : [4]
    }

class ThreeTurnWalkerOdometer(ThreeTurnWalker):
    CONFIG = {
        "display_odometer" : True,
    }

class FourTurnWalker(PiWalkerRect):
    CONFIG = {
        "func" : plane_func_by_wind_spec((0, 0, 4))
    }

class FourTurnWalkerOdometer(FourTurnWalker):
    CONFIG = {
        "display_odometer" : True,
    }

class OneTurnWalker(PiWalkerRect):
    CONFIG = {
        "func" : plane_func_from_complex_func(lambda c : np.exp(c) + c)
    }

class OneTurnWalkerOdometer(OneTurnWalker):
    CONFIG = {
        "display_odometer" : True,
    }

class ZeroTurnWalker(PiWalkerRect):
    CONFIG = {
        "func" : plane_func_by_wind_spec((2, 2, 1), (-1, 2, -1))
    }

class ZeroTurnWalkerOdometer(ZeroTurnWalker):
    CONFIG = {
        "display_odometer" : True,
    }

class NegOneTurnWalker(PiWalkerRect):
    CONFIG = {
        "step_run_time" : 2,
        "func" : plane_func_by_wind_spec((0, 0, -1))
    }

class NegOneTurnWalkerOdometer(NegOneTurnWalker):
    CONFIG = {
        "display_odometer" : True,
    }

# FIN