ResearchOriginal Research
Spots, Stripes and the Two Chemicals That Might Explain Both
In 1952 Alan Turing proposed that two substances reacting and diffusing at different rates could turn a uniform sheet into a patterned one with no template anywhere. We tested the mechanism by integrating the Gray-Scott system on a periodic 256 × 256 grid, and nothing here was observed in an organism or a beaker, because the club has no laboratory and the computation is the experiment. We derived the Turing conditions in closed form and evaluated them at , , , where the uniform state is stable without diffusion (, ) and unstable with it (). Growth rates measured mode by mode matched the analysis to a worst relative error of 1.08 × 10−5 over twelve modes, and during growth the pattern's wavelength came out at 13.6371 ± 0.1372 cells against a predicted 13.5612, a gap of +0.56% and z = +0.55 over 24 replicates. After the pattern stopped moving it had drifted to 13.8870 ± 0.0877 cells against the fastest-mode prediction of 12.7207, +9.17% and z = +13.30; a 512 × 512 control put the same number at 13.8186 ± 0.1150, ruling out the grid. Setting annihilated the pattern exactly as the theory requires: the surviving amplitude after 3000 steps was 6.47 × 10−14 against 0.1553 for the unequal case, and the measured decay rates sat within 2.78% of the analytic ones. A 169-point sweep of produced 123 uniform, 14 spots, 18 maze, 14 chaotic and zero aligned-stripe outcomes; stripes are stable when seeded but are never chosen out of isotropic noise. Wavelength fell with diffusion ratio as against a predicted , a gap of 0.26 standard errors, and at the low end of that sweep the pattern grew exactly on schedule and then collapsed to nothing at all. Seed 20250621.
Summer 2025Read 35 minSections 13
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