Pattern

In 1952 Alan Turing published The chemical basis of morphogenesis, one of the few papers in which a mathematician explains how a leopard comes by its spots. His claim: you need no blueprint. Two substances that react with one another and travel through tissue at different speeds will produce a pattern by themselves — provided the inhibitor travels faster than the activator.

This is counter-intuitive. Diffusion is precisely the process that smooths differences away: a drop of ink in water disappears, it does not appear. Turing showed that diffusion, combined with the right reaction, does the opposite, and that a perfectly even liquid can therefore be unstable. Any minute irregularity grows into structure.

What runs above is the Gray-Scott variant, with two dials: how much A is added and how much B is removed. Two numbers, and with them the entire world is fixed. One small region of that plane gives spots, the region beside it gives stripes, and on the border between two regions you get patterns that never settle: worms that keep splitting and dissolving.

Turing wrote the paper two years before his death. He did not live to see biologists find his patterns in fish skin and animal coats.