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Home/Biophysics, Fluids & Geoscience/Reaction-Diffusion Turing Patterns

Reaction-Diffusion Turing Patterns

Activator-inhibitor reaction-diffusion toy with spots, stripes, worms presets, diffusion ratio, and schematic dispersion relation.

Pattern presets

Activator-inhibitor parameters

0.16
0.08
0.055
0.062
8

Measured values

Diffusion ratio2.00
Feed f0.055
Kill k0.062
Iterations0

This Gray-Scott-style toy is a qualitative activator-inhibitor demo. The dispersion curve is schematic; the field itself evolves by an explicit finite-difference update with periodic boundaries.

Live graphs

About this model

Activator-inhibitor reaction-diffusion systems can amplify a finite band of spatial wavelengths, producing Turing-like spots and stripes. This page uses a Gray-Scott-style toy update with periodic boundaries, presets for different textures, and a schematic dispersion curve indicating wavelength selection.

Who it's for: Mathematical biology, pattern formation, nonlinear dynamics, and numerical PDE courses.

Key terms

  • Turing pattern
  • Reaction-diffusion
  • Activator-inhibitor
  • Diffusion ratio
  • Dispersion relation
  • Gray-Scott model

How it works

Activator-inhibitor reaction-diffusion toy showing Turing-like spots, stripes, and wavelength selection.

Key equations

u_t = D_u∇²u − uv² + f(1−u), v_t = D_v∇²v + uv² − (f+k)v
Turing patterns appear when reaction growth and diffusion select a positive finite-k band

Frequently asked questions

Are these exact biological patterns?
No. The model is a qualitative toy that captures how local reactions plus diffusion can organize spatial structure.
Why does diffusion create patterns instead of smoothing everything?
With the right reaction feedback, diffusion destabilizes a uniform state for some wavelengths while damping others.