Gray-Scott
Two reacting, diffusing chemicals paint spots, mazes, and stripes that look almost biological.
Introduction
Two virtual chemicals, U and V, spread across the grid and react: V consumes U to make more of itself, U is fed in, and V is removed. From this tug of war emerge self-replicating spots, branching mazes, and fingerprint stripes. Tiny shifts in the feed and kill rates jump between completely different patterns.
Background
The reaction scheme comes from Gray and Scott's study of chemical reactors in the early 1980s. John Pearson mapped its full pattern-forming behaviour in 1993, charting which feed and kill rates give spots, stripes, or chaos, and connecting it to Alan Turing's 1952 theory of morphogenesis.
Pearson, J. E. (1993). Complex patterns in a simple system. Science, 261(5118), 189-192.
How it works
- Each patch reads its own U and V concentrations.
- Apply the reaction: V uses up U at a rate proportional to U times V squared, turning it into more V.
- Feed fresh U in proportional to how depleted it is, and remove V at the kill rate.
- Diffuse U and V outward to neighbours, with U spreading faster than V.
Parameters
feed- Rate at which U is replenished. Together with kill it selects the entire pattern regime.
kill- Rate at which V is removed. Shifts of 0.001 in feed or kill can flip spots to mazes to stripes.
Du / Dv- How fast each chemical diffuses. U must spread faster than V for patterns to form at all.
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