Reaction–diffusion system

A mathematical model in which interacting substances change through local reactions and spatial diffusion. Differences in diffusion rates can destabilize uniform states and generate patterns.

Reaction–diffusion equation: A partial differential equation describing how concentrations change through reactions and spatial diffusion. It expresses the system’s central interaction between local chemistry and spatial spreading.
Animal coat pattern: A spatial arrangement of pigmentation or markings on an animal’s body. Reaction–diffusion models can generate stripes and spots resembling coat markings.
Partial differential equation: An equation relating a function to its derivatives with respect to multiple independent variables. Reaction–diffusion dynamics are commonly expressed as coupled equations in space and time.
Activator–inhibitor system: A reaction–diffusion model in which one substance promotes production while another suppresses it. This common architecture gives a concrete route to diffusion-driven patterns.
Diffusion: The net movement of particles from regions of higher concentration toward regions of lower concentration. Diffusion transports each substance through space at its own rate.
Morphogenesis: The biological process by which an organism develops its shape and spatial organization. Diffusing signals can help organize cell behavior into tissue-scale form.
Fick's laws of diffusion: Equations relating diffusive flux to concentration gradients and their resulting time evolution. They provide the standard mathematical description of molecular spreading.
Cellular automaton: A discrete model whose cells update state according to local rules. It can generate spatial patterns without continuous diffusion equations.
Chemical reaction network: A representation of chemical species and the reactions that transform them. Its reaction rules determine which local concentration changes diffusion can amplify.
Liesegang ring: A periodic banding pattern formed by precipitation in a chemical medium. Chemical transport and reaction can produce repeated bands in space.

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