I read Jonathan McCabe’s paper in the Bridges conference: Cyclic Symmetric Multi-Scale Turing Patterns and was inspired to play with reaction-diffusion systems.He’s made some amazing artwork by running multiple reaction-diffusion systems at different scales and applying symmetry and difference functions to them. Jason Rampe goes into more details about how Jonathan’s images are produced, and he has his own experiments. Ricky Reusser has an amazing web version.
For a background on reaction-diffusion systems, see Karl Sims’s fantastic explanation and then play with Pablo Márquez-Neila’s WebGL implementation. And definitely check out this parameter map of behaviors which includes math, descriptions, and videos! Ken Voskuil also has an explanation of the algorithm. In 2022 I discovered Phillip Compeau’s great online course that teaches reaction-diffusion; it helped me understand this model much better, and I revisited this topic and wrote some study notes.
This is an implementation of the formulas on Karl Sims’s page:
The behavior is rather sensitive to the parameters. I’ve seen it change drastically between kill=0.062 and kill=0.063. You can paint with the mouse or finger. This demo won’t work on some devices, because it uses some WebGL extensions (
Code is in reaction-diffusion.js
Note: this page seems to use a lot more RAM in Chrome than in Firefox. I haven’t tracked down why.