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  "body": "\n## Summary\n\nA reaction–diffusion system is a system of [[parabolic|1CCTH8X2FT]] equations $\\partial_t u = D \\Delta u + R(u)$ for several quantities.\nEach quantity diffuses in space and reacts with the others at each point.\nIt models chemical reactions, population dynamics, the spread of epidemics and the formation of patterns in biology.\nDepending on the reaction term, solutions can show travelling fronts, spatial patterns or oscillations.\nTuring showed that diffusion can make a stable uniform state unstable and so create patterns.\n\n## Explanations\n\n### L1 human\n\nPicture several chemicals in a dish: each one spreads out by diffusion, and at each point they react and turn into each other.\nThe equation for each concentration has two parts, a diffusion part that evens it out and a reaction part that depends on the local amounts.\nWith one quantity and the reaction $u(1 - u)$, it describes a population that grows to a limit and spreads, leading to a wave that invades empty space.\nWith two quantities that diffuse at different speeds, it can produce spots and stripes like those on animal coats.\n",
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