Turing patterns that grow into seamless repeats

The new Turing pattern maker runs a reaction-diffusion simulation and draws what grows: spots, mitosis, coral, labyrinths, stripes, worms, holes and bubbles. Set the grid, the number of steps and which way the chemicals spread, choose filled shapes, outlines or two bands, then download a seamless repeat or a printable PDF.

Samples to start from

• Generating…Coral, filledOpen with these settings
• Generating…A labyrinth in outlineOpen with these settings
• Generating…Mitosis on a finer gridOpen with these settings
• Generating…A labyrinth stretched across into stripesOpen with these settings
• Generating…Holes, in two bandsOpen with these settings
• Generating…Worms, still growing after 1,000 stepsOpen with these settings

Why there's no seam

Each cell trades chemicals only with its eight neighbors, and the grid's left edge counts as the right edge's neighbor, as the top does the bottom's, so the pattern grows on the surface of a doughnut. The edge of each shape is traced where the second chemical crosses the level you pick, then smoothed into curves whose bends carry over the join, so a shape cut by the edge of the repeat comes back in on the other side exactly where it left. The start is seeded and the arithmetic is fixed, so the same settings grow the same pattern every time.

Where the presets come from

In 1993 John Pearson ran this model, the Gray-Scott model, across a wide range of feed and kill rates and mapped what each region grows (Science 261). Each preset is a pair from one of those regions. The mitosis and coral pairs, and the simulation step itself, follow Karl Sims' tutorial. Both are credited on the acknowledgements page.