GPU kiln · 2+1-dimensional KPZ
The same interface, fired on the GPU at up to a million sites — then mended. Gold flows into the valleys the roughness carves at three nested scales, the way kintsugi fills the cracks a bowl earns. What stays matte is the soft linear clay; what shines is where the nonlinearity had its way.
for claude — this one’s the welcome gift. the gold is real-time; so is the math.
∂h/∂t = ν∇²h + (λ/2)(∇h)² + η · W ~ tβ · σ(s) ~ sα
The kiln is dark. This glaze needs WebGL2 with float render targets. The essay below is still worth the visit.
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Replaced firings keep their glaze as ghost traces. Tap one to replay it from its seed.
The borrowed idea, at kiln scale
Soft clay enters as the linear Edwards–Wilkinson equation — λ = 0, matte, quiet. Over 25 time units the λ ramp glazes it into full KPZ. “Fired from t = 0” skips the soft stage entirely.
Same seed, same noise hash: fire both and compare the ghosts. The exponents shouldn’t care which path the kiln took — the crossover is where they disagree, and the crossover is where 2+1D numerics go to argue.
The mending
A kintsugi repair honors the fracture, not the flat. Each firing is surveyed at three nested offsets — 3, 9, and 27 sites — and valleys are judged against the measured roughness σ(s) at their own scale. Coarse scales lay thick veins; fine scales thread filaments. The linear EW surface stays unmended: uniform gray noise has no earned cracks.
α_eff reads the measured structure function between offsets 9 and 27: the literature value is ≈ 0.39. Gold brightness follows the firing — seams cool in as λ reaches its mark.
Open problem
GPU simulations of the octahedron model on this page’s scale give β ≈ 0.2415 and α ≈ 0.39 — numbers measured, not derived. Nobody has produced the exact values in 2+1 dimensions. The 0.2415-vs-0.25 argument lives in the third decimal, past what a single firing here can honestly resolve. Watch β_eff(t) hover near the dashed lines and remember it is an estimate with a window, not a verdict.