Draw Me a Leopard's Spots — Claude × Glyph showcase

Three stages of a pattern

The Gray-Scott PDE has no idea what a leopard is. But starting from a single seed in a uniform field, with these specific (F, k) parameters, it produces this specific outcome — every time.

STAGE 1

Steps 0 – 80

Uniform pelt + a seed

The pelt starts uniform (chemical U everywhere, V at zero except a small Gaussian bump in the center). Diffusion smooths the seed slightly outward; nothing dramatic yet.

STAGE 2

Steps 80 – 240

Instability wavefront

The seed becomes a wavefront. At F = k = 0.062, this regime is unstable to spot-formation: as V spreads, it splits — mitosis-like — into separated nuclei. The first ring of spots appears around the seed.

STAGE 3

Steps 240 – 400

Hexagonal lock

The spots reach a stable hexagonal spacing. New ones nucleate at the edges; old ones stay put. The pattern locks into a self-organized grid — the same way real leopards, jaguars, and giraffes get their coats during embryogenesis.

How Glyph drew it

Claude writes the JSON; Glyph integrates the PDE with explicit Euler on a 32×32 grid. Same spec → byte-identical SVG, every platform, every run.

The Glyph spec JSON

// leopard-spots.json — Gray-Scott RD at F = k = 0.062
{
  "version": "glyph/0.1",
  "title": "Leopard spots",
  "data": {
    "pde_solve": {
      "shape": "pde-solve",
      "kind": "reaction-diffusion",
      "domain": { "x": [-1,1],
                  "y": [-1,1] },
      "grid": { "rows": 32, "cols": 32 },
      "initial_U": "1",
      "initial_V": "exp(-25*(x*x + y*y))*0.4",
      "params": { "Du": 1.0, "Dv": 0.5,
                  "F": 0.062, "k": 0.062 },
      "boundary": "periodic",
      "steps": 400,
      "dt": 0.0008
    }
  },
  "layers": [{
    "mark": "heatmap",
    "encoding": {
      "x": { "field": "x" },
      "y": { "field": "y" },
      "color": { "field": "u" }
    }
  }]
}

CFL stability is verified at schema time: max(Du, Dv)·dt/dx² = 1·0.0008/(2/32)² = 0.20 ≤ 0.25 ✓. Drop dt and the schema refuses the spec before the renderer ever runs. View on GitHub.

Glyph compiler output SVG

Glyph-rendered Gray-Scott leopard-spot pattern, byte-locked across CI

Byte-stable across Ubuntu / macOS / Windows × Node 20 / 22. 1024 cells, each a deterministic function of the seed and the (F, k) parameters. Change F by 0.001 and you get a different pattern — but always reproducibly the same different pattern.

Your turn — prompts to try

The (F, k) parameter space holds dozens of recognizable patterns. Name the animal coat or skin pattern you want — Claude knows the parameters.

▸ Zebra

"Show me how a zebra gets its stripes. Gray-Scott reaction-diffusion at F = 0.029, k = 0.057 — the stripes regime. Same 32×32 grid; let me see the pattern lock in after 600 steps."

▸ Coral

"Show me coral-worm patterns: Gray-Scott at F = 0.055, k = 0.062, periodic boundary, 800 steps on a 48×48 grid. The pattern should look like a brain or a fingerprint."

▸ Phase boundary

"Make me a 4-up grid showing how the Gray-Scott pattern changes as k goes from 0.057 → 0.060 → 0.062 → 0.065. Same F = 0.055 in all four. Show the stripes-to-spots transition."

▸ History

"Make a visualization for Turing's 1952 paper. Show three pattern types (spots, stripes, labyrinth) side by side; label each with the Gray-Scott (F, k) values and a real-world animal that has that coat."

Draw me how the leopard
got his spots