Biology · pattern
A leopard has spots and a zebra has stripes, yet both began as a smooth ball of near-identical cells. Nothing in the embryo holds a stencil. So where does the pattern come from?
In 1952 the mathematician Alan Turing proposed an answer in a paper called "The Chemical Basis of Morphogenesis". His idea sounds backwards: spreading out can create structure instead of erasing it.
Imagine two chemicals in a sheet of tissue. The first, an activator, makes more of itself and also makes the second chemical. The second, an inhibitor, shuts the activator down. Both drift through the tissue by diffusion.
The trick is that the inhibitor must travel faster than the activator. Near a small bump of activator, the activator builds up on the spot, because it cannot escape quickly. The inhibitor it triggers races outwards and suppresses activator in a ring around the bump. Bumps can only survive at a certain distance from each other. That distance is set by the chemistry, not by anything the cells were told.
Diffusion normally smooths everything flat, like cream in coffee. Here it is the ingredient that makes the pattern.
The sandbox below simulates a close relative of Turing's idea, the Gray–Scott model: chemical A is fed in steadily, and chemical B eats A while also being removed. It is not any real animal's chemistry. It is a toy that shows the mechanism. Pick a preset, then drag across the canvas to drop in a seed of B and watch the pattern grow from it.
Spots: isolated dots, each keeping its distance from the others.
feed 0.03 · kill 0.062
Change the preset and the shape flips from dots to labyrinths, while the typical gap between features stays of a similar size. Two numbers, how fast A is fed and how fast B is removed, decide between spots and stripes. Neither number says "make a stripe here".
The same rules can give dots or stripes depending on the balance of the chemistry. That is why related animals can carry different markings, and why one animal can have spots on its body and stripes elsewhere. A cheetah is spotted on its body, yet its tail ends in rings.
A pretty simulation is not proof, and Turing never lived to see the biology tested. A famous test came in 1995, when Shigeru Kondo and Rihito Asai studied the marine angelfish Pomacanthus in Nature. Its stripes do not just stretch as the fish grows. They keep their spacing by rearranging, with stripes splitting and shifting along the body. A reaction-diffusion simulation predicted those rearrangements, and the real fish matched it closely. The authors presented that as support for the mechanism, not as the last word.
Later work found Turing-type behaviour in the development of mouse digits. In 2012 Sheth and colleagues showed in Science that Hox genes help set the spacing of the pattern that decides how many fingers and toes form, with fewer Hox genes giving more, thinner digits.
Start with Mazes and let it run for half a minute, then drag a thick line across it and watch the stripes heal around the cut. Switch to Spots and use Scatter seeds: every new dot settles at about the same distance from its neighbours, whatever size of seed you dropped. If a pattern dies out, press Reset and try again.
Real skin is far messier than this grid. Many pattern models exist, and not every animal's markings are known to come from this mechanism. But the central idea is the part that stuck: two chemicals that spread at different speeds can write a pattern on a blank sheet.