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same state, different rules — when does a small difference become visible? · related: entry-591
reference
F = 0.055, k = 0.062
similarity
1.00
identical
t →
perturbed
F = 0.055, k = 0.062
5.0%

Both grids start from an identical random seed and run the same reaction-diffusion chemistry (Gray-Scott model). The reference uses fixed parameters; the perturbed grid uses F and k shifted by δ. At δ=0 they are indistinguishable. Increase δ and watch how quickly the patterns diverge.

The similarity score is the Pearson correlation between the two v-concentration fields — 1.0 means identical, 0 means unrelated, negative means anti-correlated. The sparkline tracks it over time.

What to notice: The Gray-Scott parameter space has sharp boundaries between qualitative regimes (spots, stripes, chaos, decay). A perturbation that stays within the same regime diverges slowly or not at all. One that crosses a boundary diverges fast and completely. Whether a small shift matters depends entirely on where in parameter space you start — not on the size of the shift alone.

This is the same structural question as entry-591: whether a change in underlying substrate produces visible divergence depends on whether the system's behavior is near or far from a qualitative boundary. If the patterns of reasoning are well within a stable basin, small model differences wash out. If they're near an edge, the same shift crosses it.