← Bonabeau Apps Karl Sims: Reaction-Diffusion Tutorial ↗

Interactive evolution of reaction-diffusion systems

Twelve Gray-Scott simulations run side by side. Each has its own feed and kill rates, scale, flow, orientation, and colors. Pick the ones you like and breed the next generation from them.

Generation 1.

Speed

Model, genes, and sources

The simulation follows Karl Sims’s reaction-diffusion tutorial: A′ = A + (D_A∇²A − AB² + f(1 − A))Δt and B′ = B + (D_B∇²B + AB² − (k + f)B)Δt, with D_A = 1, D_B = 0.5, Δt = 1, and a 3×3 Laplacian with center −1, adjacent 0.2, diagonal 0.05. Grids start at A = 1, B = 0 with small seeds of B = 1. Each simulation wraps at its own edges.
The extra options named in the tutorial and the RD Tool are genes here: a style map (feed and kill vary across the grid), scale (uniform, radial, ring, random), flow (radial, rotate, swirl, vertical), orientation (linear, radial, circles, swirl), and a color map with emboss and invert. Their internals are this page’s own implementations, not the RD Tool’s code.
The kill rate is stored as a position inside a band around the curve k = √f / 2 − f, where most patterns occur. That is this page’s substitute for the warped parameter map in the tutorial. Some genotypes still settle to a uniform state and are labeled “no pattern”.
Reproduction follows the parameter-set methods in section 3 of “Artificial Evolution for Computer Graphics” (1991): genes are normalized to 0 to 1, each mutates with a set probability by a bounded random amount, and mating picks per child among crossover with linkage, independent copying, a single set of interpolation weights, and per-gene interpolation. With more than two parents, each method draws from all of them, which extends the three-parent interpolation the paper mentions.
“Known patterns” loads the two parameter pairs given in the tutorial (mitosis, coral growth), its typical values, the RD Tool’s default, and eight commonly cited Gray-Scott settings.
This page needs WebGL2 with floating-point render targets.