Implementation of Hamid Naderi Yeganeh's art in Rust.

cargo run
cargo run --bin sunflower_field

Implemented:

• Sunflower Field (Workings)

Ideas:

• Consider using rayon instead of std::thread
• Consider using winit UserEvent instead of std::mpsc::channel
• Consider porting to rust-gpu
• Position of cursor gives you a popup of the history of that value (i.e. all the computations that led to the colour of that pixel)
• Write a proc-macro to write more math-like expressions, which will auto-generate the functions (and the metadata needed for the history)
• sunflower_field optimisation: v is always a constant integer

Workings are PNG images with the Excalidraw scene embedded into them.

Decoding the math

v or the colour component

v appears to be used, in many of the formulas (starting with H(v, x, y)), as a way to select a value for a colour, and is 0 for red, 1 for green, and 2 for blue. So we need to find an equation such that f(0) = r, f(1) = g, f(2) = b. A parabola is one equation with this behaviour. We have the generalised formula for a parabola f(v) = mv^2 + nv + o.

We can solve for m, n and o:

f(0) = r
-> 0m + 0n + o = r
-> o = r

f(1) = g
-> 1m + 1n + r = g
-> m + n = -r + g

f(2) = b
-> 4m + 2n + r = b
-> 4m + 2n = -r + b

f(2) - 2f(1)
-> (4 - 2)m + (2 - 2)n = -r + b - 2(-r + g)
-> 2m + 0n = -r + b + 2r - 2g
-> 2m = (r - 2g + b)
-> m = (r - 2g + b) / 2

m + n = -r + g
-> n = -r + g - m
-> 2n = -2r + 2g - 2m
-> 2n = -2r + 2g -(r - 2g + b)
-> 2n = -2r + 2g - r + 2g - b
-> 2n = -3r + 4g - b
-> n = (-3r + 4g - b) / 2

Testing this equation:

r = 70% = 70/100
g = 70% = 70/100
b = 100% = 100/100

m = (r - 2g + b) / 2
-> m = (70 - 2*70 + 100) / 100 / 2
-> m = 30/200
-> m = 3/20

n = (-3r + 4g - b) / 2
-> n = (-3*70 + 4*70 - 100) / 100 / 2
-> n = -30/200
-> n = -3/20

o = r
-> o = 100/100
-> o = 20/20

f(v) = 3/20*v^2 - 3/20*v + 20/20
-> f(v) = (3*v^2 - 3*v + 20) / 20

This is the equation for the colour of the sky in sunflower_field H(v, x, y)