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Programming and Math
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<h1 class="record-title">Programming and Math</h1>
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<h2 id="minkovski-plane-cellular-automata-simulator"><a href="minkovski-ca/">Minkovski plane cellular automata simulator</a></h2>
<p><img alt="Minkovski plane cellular automata" src="images/minkovski-ca.png"/></p>
<p>Simulator of <a href="https://en.wikipedia.org/wiki/Cellular_automaton">cellular automata</a>
that live on the <a href="https://en.wikipedia.org/wiki/Minkowski_plane">Minkovski plane</a> - a pseudo-metric space, where the distance between two points is given by Δx²−Δy². It has hyperbolas instead of circles, and every cell has infinite number of neighbors. It is inspired by the "<a href="https://www.gregegan.net/DICHRONAUTS/DICHRONAUTS.html">Dichronauts</a>" novel by Greg Egan.</p>
<h2 id="hyperbolic-cellular-automata-simulator"><a href="hyperbolic-ca-simulator/index.html">Hyperbolic cellular automata simulator</a></h2>
<p><img alt="Random cells on a {7;3} tiling" src="images/hyperbolic-cells.png"/></p>
<p>Simulator of <a href="https://en.wikipedia.org/wiki/Cellular_automaton">cellular automata</a>, acting on an <a href="https://en.wikipedia.org/wiki/Uniform_tilings_in_hyperbolic_plane">regular tiling</a>of the <a href="https://en.wikipedia.org/wiki/Hyperbolic_geometry">hyperbolic plane</a>.</p>
<p>It supports arbitrary large configurations of cells, limited only by available memory.</p>
<h2 id="reversible-cellular-automata-simulator"><a href="js-revca/index.html">Reversible Cellular Automata Simulator</a></h2>
<p><a href="images/simulator-interface.png"><img alt="Interface" src="images/s640-simulator-interface.png"/></a>
Online (no installation needed) simulator of reversible cellular automata with Margolus neighborhood.
Blog posts:</p>
<ul>
<li><a href="http://dmishin.blogspot.com/2013/10/reversible-cellular-automata.html">Introduction to reversible cellular automata and simulator</a>.</li>
<li><a href="http://dmishin.blogspot.com/2013/11/the-single-rotation-rule-remarkably.html">Single Rotation rule</a>: remarkably simple and rich rule.</li>
<li><a href="http://dmishin.blogspot.com/2014/06/alternating-rules-and-knightships.html">Alternating rules and knightships</a></li>
</ul>
<h2 id="spaceships-of-the-single-rotation-rule"><a href="singlerot-spaceships/singlerot-spaceships.html">Spaceships of the Single Rotation rule</a></h2>
<p>Single Rotation is a simple reversible cellular automaton, that operates on a field with Margolus neighborhood. Random initial conditions in this rule produce lots of different spaceships, some of them are in this catalog.
See <a href="#">blog post</a> for details.</p>
<h2 id="single-rotation-cellular-automaton-with-smooth-interpolation"><a href="singlerot-smooth/singlerot-smooth.html">Single Rotation cellular automaton with smooth interpolation</a></h2>
<p><a href="singlerot-smooth/singlerot-smooth.html"><img alt="" src="singlerot-smooth/images/singlerot-smooth.png"/></a></p>
<p>A simulator of the <a href="http://dmishin.blogspot.com/2013/11/the-single-rotation-rule-remarkably.html">Single Rotation</a> cellular automaton, that tracks positions of the cells and uses Lancsoz interpolation to add an intermediate frames. Its primary purpose is a nice visual effect, for experimenting with reversible cellular automata see <a href="http://dmishin.github.io/js-revca/index.html?rule=0,2,8,3,1,5,6,7,4,9,10,11,12,13,14,15&step=8&frame_delay=100&size=64x64&cell_size=6,1&phase=0">online simulator</a>.</p>
<h2 id="reversible-ca-collider"><a href="reversible-ca-collider.html">Reversible CA Collider</a></h2>
<p>A tool to automatically catalogize collisions of simple patterns in reversible cellular automata.</p>
<h2 id="3d-version-of-the-single-rotation-simulator-with-smoothing"><a href="singlerot-smooth/3d/singlerot-3d.html">3D version of the Single Rotation simulator with smoothing</a></h2>
<p><a href="singlerot-smooth/3d/singlerot-3d.html"><img alt="3D version of the Single Rotation simulator" src="singlerot-smooth/images/singlerot-3d.png"/></a></p>
<p>3-dimensonal version of the above application, using Web GL for visualization. It displays world lines of the moving cells, as a 3-dimensional curves.</p>
<ul>
<li>Sources: <a href="https://github.com/dmishin/singlerot-smooth">github.com/dmishin/singlerot-smooth</a>, in the "3d" folder.</li>
<li><a href="http://dmishin.blogspot.com/2015/01/3d-single-rotation.html">Blog post</a></li>
<li><a href="http://youtu.be/XX4igr8ufeA">Demonstration video</a></li>
</ul>
<h2 id="reversible-cellular-automata-applied-to-image"><a href="image-revca/index.html">Reversible Cellular Automata applied to image</a></h2>
<p>What if block reversible cellular automaton rule is applied to a raster image? The effect might be curious.
This simulator lets you to watch the evolution of the image under reversible rule. The rule is:</p>
<ul>
<li>If a 2x2 block of pixeld contains 1 pixel of highly different color, then this block is rotated CV.</li>
</ul>
<h2 id="simulator-of-cellular-automata-with-2-dimensions-of-time"><a href="t2dca/2dca.html">Simulator of cellular automata with 2 dimensions of time</a></h2>
<p><a href="t2dca/2dca.html"><img alt="" src="t2dca/images/screenshot-150-60.png"/></a></p>
<p>Simulate elementary cellular automata with 1 spatial and 2 temporal dimensions.
Simulation result is displayed as static 3d object, visualized with Tree.js.
See also <a href="http://dmishin.blogspot.com/2014/06/cellular-automata-with-2-temporal.html">blog post</a> about it.</p>
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