Indexing the archive…
Your Universe of Digital Possibilities
Two chemicals, one that breeds itself and one that holds it in check, left to diffuse and react. From a flat, featureless sheet they break — without a blueprint — into spots, stripes, mazes and dividing cells. Pick a species off the rail, push the feed and kill, and paint the surface to seed new growth. This is the maths Turing gave biology in 1952.
Two morphogens, each diffusing and reacting. Turing’s shock: diffusion, usually a smoother, can destabilise a uniform state and manufacture pattern.
B autocatalyses through the AB² term — it eats A to make more of itself; feed F tops up A, kill k removes B.
Short-range activation, long-range inhibition: when the inhibitor diffuses faster (Dv ≫ Du), one wavelength λ* wins and tiles the plane.
Diffusion on the grid is a weighted blur of the eight neighbours minus the centre — the only spatial coupling in the whole system.
A leopard and a zebra run the same chemistry — they just sit at different points of the (F, k) plane, and that is the whole difference between a spot and a stripe. The same reaction–diffusion logic draws the whorls of a seashell, the ridges of a fingerprint, the ripples in wind-blown sand, the spacing of vegetation in a drying landscape, even the folds of the cortex. Form doesn’t need a designer — it falls out of the rules.