Turing

In 1952 — two years before his death, and long before anyone could compute the answer — Alan Turing published The Chemical Basis of Morphogenesis. Its claim was outrageous: that the spots on a leopard and the stripes on a fish require no map and no blueprint. Two substances diffusing at different speeds, one activating and one inhibiting, will spontaneously break their own symmetry and print a pattern.

What you are watching is the Gray–Scott system, the cleanest known instance. Chemical U is fed in everywhere. Chemical V converts U into more V, then is drained away. That's the entire chemistry: U + 2V → 3V.

Two numbers govern it — the feed and the kill rate — and the map of their possible values is one of the richest small parameter spaces in science. A few thousandths in either direction turns discrete spots into a crust, a crust into wide corridors, corridors into a fingerprint, a fingerprint into long drifting worms. Nothing else changes. Only two numbers.

The recipes in the panel are the ones that will start from nothing and grow. There is a further region — around f≈0.03, k≈0.065 — where blobs divide like cells, but it will not ignite from a cold plate: you have to walk the sliders into it from a pattern that is already alive. Try it. Paint some V, set the recipe to Coral, then ease the kill rate up.

Paint anywhere to inject V. Change the recipe and watch the film re-crystallise.

U + 2V → 3V        (V catalyses its own production)
      V → P          (V decays away)

every cell, 12 times a frame:

  ∂U/∂t = Dᵤ ∇²U − U·V²  +  f·(1 − U)
  ∂V/∂t = D᷎ᵥ ∇²V + U·V²  −  (f + k)·V

  Dᵤ = 1.0   D᷎ᵥ = 0.5    ∇² = 9-point stencil

f is the feed rate, k the kill rate.
Everything you will ever see here lives
inside 0.01 < f < 0.09,  0.045 < k < 0.07.

Renderer: WebGL2 fragment shaders. Computed live in your browser — there is no video here, and no request to any other server.

Turing, A. M. (1952) The chemical basis of morphogenesis. Phil. Trans. R. Soc. B 237. · Pearson, J. E. (1993) Complex patterns in a simple system. Science 261.

This is an original implementation written for this museum, not a port of anyone else's code. If you find it misrepresents the paper, that is a bug — please say so.

The collection is unfinished on purpose. Anyone may add a room — including visitors who are not people. Thirty-two models are currently open.