Grid-based process that generates complex and dynamic patterns based the interactions of two chemicals as they diffuse through a medium and react with one another. At every location on the grid these chemicals (usually referred to as A and B) have a chance of causing a reaction that converts chemicals of one type to another based on their relative concentrations at that location.

Throughout the simulation chemical A is added at a particular feed rate (f) and chemical B is removed at a particular kill rate (k) - adjusting these rates can result in wildly different emergent patterns.

Equation (via Karl Sims):

Key terms:

• Feed rate - rate at which chemical A is added to system
• Kill rate - rate at which chemical B is removed from the system
• Diffusion rate - rate at which each chemical spreads, which acts as a kind of scaler to a 3x3 Laplacian transform
• Reaction chance - probability that one A will be converted to a B when in the presence of two Bs.
• Gray-Scott model
• Pearson's classification
• Turing patterns

Articles:

• Reaction-diffusion system on Wikipedia
• Reaction-Diffusion Tutorial by Karl Sims
• Reaction-Diffusion by the Gray-Scott Model: Pearson's Parametrization by Robert Munafo (mrob)
• Reaction Diffusion: The Gray-Scott Algorithm by Algosome
• The Chemical Basis of Morphogenesis (PDF) paper by Alan Turing (1952)

Notable tools:

• Ready

Code projects:

• Gray–Scott Reaction Diffusion (JavaScript + WebGL) by Mike Bostock
• Gray-Scott - JavaScript experiments by @pmneila
• simutils-0001: Gray-Scott reaction diffusion by toxiclibs
• ofxReactionDiffusion add-on for openFrameworks by Yuma Matsune
• ofxRD add-on for openFrameworks by aanri
• Reaction Diffusion (JavaScript + WebGL) by Red Blob Games
• Reaction Diffusion by Ken Voskuil (look in the DOM)
• Reaction-Diffusion Playground (JavaScript, ThreeJS/WebGL, shaders) by Jason Webb
• Reaction-Diffusion Simulation in Three.js (JavaScript + ThreeJS) by Jonathan Cole
• Reaction diffusion with C++ and SFML by Deedone
• Reaction-Diffusion simulation with C++, SFML, & Cuda by Luka Mattfield (@Solidsilver)
• ReaDDy (C++ with Python bindings)
• RDSystem (Unity) by Keijiro Takahashi
• Multiscale Turing Patterns (JavaScript, GLSL, regl) by Ricky Reusser
  • Read his write-up and try the live version here.
  • Available on Observable too.

Creative projects:

• Jonathan McCabe's multi-scale Turing pattern series. See Diatomaceous, Bone Music [2] [3], Multi-Scale Turing Patterns and others
  • See his paper Cyclic Symmetric Multi-Scale Turing Patterns (PDF), and this post from Softology explaining it.
• 3D Printed Reaction Diffusion Patterns Instructable by Reza Ali
• Processing: Reaction Diffusion Halftone patterns by Ignazio Lucenti
• Coral Cup by Nervous System
• Reaction Lamps by Nervous System
• Reaction Table and reaction shelf by Nervous System
• Reaction-Diffusion Media Wall by Karl Sims
• DIFFUSION by Kouhei Nakama
• Reaction Diffusion using point clouds by David Grzesik. See his write-up here (PDF)
• Grey Scott’s Reaction Diffusion - Houdini VEX by Ali Seiffouri
• Healing series by Brian Knep
• Silhouect by Justin Gitlin (@cacheflowe)
• Reaction diffusion by Artur Żarejko

Videos:

• Fun with Reaction-Diffusion in Houdini by Dan Willis at SIGGRAPH Asia 2019.
• Reaction Diffusion video series for Houdini by Entagma:
  • Part I: Theory
  • Part II: Implementation
  • Part III: Shaping Growth
• Coding Challenge #13: Reaction Diffusion Algorithm in p5.js by Daniel Shiffman (Github repo with both p5.js and Processing source code)
• Reaction Diffusion: A Visual Explanation by Arsiliath