Mini WorldLaplace Plate 16 — Patterns

Plate 16 · Life

Where Spots and Stripes Come From

Nobody paints the spots on a leopard or draws the stripes on a fish. In 1952 the mathematician Alan Turing realized that if two substances react with each other while spreading at different speeds, a pattern can grow all by itself.

Try it
Chapters · 6
  1. 01A Copier and Its Fuel
  2. 02Keeping Their Distance
  3. 03Change the Recipe
  4. 04Bigger Body, More Spots
  5. 05Real Animals
  6. 06Your Turn

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01

A Copier and Its Fuel

Imagine two substances in the skin. One can make copies of itself, but it uses up the other to do it. The other is like fuel, constantly topped up from all around.

The trick is speed: the fuel spreads twice as fast as the copier. Wherever copiers start to gather, they eat up the fuel nearby, and no new copiers can get going around them.

Red: the copier · blue: the fuel

02

Keeping Their Distance

So new copiers can only take hold far enough from an existing spot, where the fuel is still plentiful. The spots end up spaced about the same distance apart.

No blueprint is needed. Each point pays attention only to its neighbors, yet an orderly pattern appears across the whole skin.

03

Change the Recipe

Change, just a little, how fast the fuel is topped up and how fast the copier fades away, and the same rule grows completely different patterns: spots, winding stripes, or a mesh full of holes.

In nature, the different coats of leopards, giraffes, zebras and many fish may come from different recipes.

04

Bigger Body, More Spots

The recipe sets the distance between spots, not how many there are. Put the same recipe on a skin twice as wide and you get about four times as many spots, each the same size.

In animals whose patterns keep forming as they grow, like the angelfish below, a bigger body gains new stripes rather than wider ones. A leopard’s or giraffe’s spots, though, are laid down before birth and simply grow along with the animal.

One recipe · two body sizes

05

Real Animals

In 1995 the Japanese biologists Shigeru Kondo and Rihito Asai found that as a marine angelfish called the semicircle angelfish grows, new stripes appear in the gaps between the old ones, keeping the spacing about the same — just as Turing’s model predicts.

Later work showed that in zebrafish, different pigment cells play the part of the two “substances”: up close they push each other out, but from farther away one helps the other survive. Turing’s idea has also been used to explain how fingers and toes are spaced and the ridges on the roof of the mouth. But not every pattern forms this way, and scientists are still finding out which do.

06

Your Turn

Pick a recipe and watch the pattern grow. Tap the fish to drop in a little copier, and watch it spread, split and settle into the pattern.

Try thisPick “Spots” and press “Start again” twice: what changes, and what stays the same?

What the model leaves out

This is the Gray–Scott model, one of the simplest versions of Turing’s idea: one substance copies itself and uses up another. In real skin the players are usually cells and signaling molecules — many more than two — and the skin keeps growing. The fish is schematic; the pattern is computed on a square of “skin” and then wrapped around it.

A common misreading

Patterns are not painted on spot by spot by genes; no gene holds the position of each spot. Genes set how the substances react and how fast they spread. Where each spot ends up is settled as the animal develops, which is why no two leopards have the same spots.

Sources

  1. Turing (1952): The chemical basis of morphogenesis
  2. Pearson (1993): Complex patterns in a simple system
  3. Kondo & Asai (1995): A reaction–diffusion wave on the skin of the marine angelfish Pomacanthus
  4. Nakamasu et al. (2009): Interactions between zebrafish pigment cells responsible for the generation of Turing patterns
  5. Kondo & Miura (2010): Reaction–diffusion model as a framework for understanding biological pattern formation
  6. Sheth et al. (2012): Hox genes regulate digit patterning by controlling the wavelength of a Turing-type mechanism
  7. Economou et al. (2012): Periodic stripe formation by a Turing mechanism operating at growth zones in the mammalian palate

Follow the question

Plate 06The Arithmetic of a SunflowerCount the spirals its seeds make, and you will arrive at a famous sequence of numbers. Plate 08Why Snowflakes Have Six PointsEvery snowflake grows from one tiny six-sided crystal of ice.

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