The Tickle Trunk
Turing's Reaction-Diffusion Model of Morphogenesis
This is a small companion piece to my page on L-systems. As mentioned there, in 1952 Alan Turing wrote a paper  proposing a reaction-diffusion model as the basis of the development of patterns such as the spots and stripes seen in animal skin. Inspired by the methods described in , I wrote the small applet that appears on this page. By entering different constants for the equations, it is possible to produce a variety of natural-looking textures. Since the state of the system is initially random noise, repeating the computation with the same constants will produce a different image with a similar pattern. The algorithm behaves as if the "cells" were arranged on the surface of a torus, which results in textures that can be tiled seamlessly.
Many animals develop their coat patterns in stages. Typically, a secondary pattern will emerge as the animal transitions to adulthood. The following examples all use multiple stages:
To create a multi-stage texture, uncheck the Randomize Cells at the Start of Each Run box and drop the number of iterations to a low value (between 100–400) to give you better control over the results.
The applet requires that your browser support at least the Java 6 runtime. If the applet doesn't work properly, this is almost certainly the problem. Click this button to install the latest version of Java:
Some combinations of constant values will not reach a stable state. Typically, trying to solve such a system will eventually underflow the floating point arithmetic used by the applet, producing a blank image. Just pick a different set of values and try again.
 Rafael Collantes. Algorithm Alley. Dr. Dobb's Journal, December 1996.
 Alan M. Turing. The chemical basis of morphogenesis. Philosophical Transactions of the Royal Society of London. B 327, 37–72 (1952)
April 14, 2002 — Updated January 01, 2011