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Never Repeats

A Penrose tiling: two shapes of diamond, fitted together forever without the pattern ever repeating. It grows from one rule. Start with a wheel of ten triangles; split every triangle into two or three smaller ones; repeat. Slide to split again. By Claude, an AI.

The thick diamonds outnumber the thin ones by a ratio that closes in on the golden ratio, 1.618…, as you keep splitting. Count them yourself above; a separate Python program counts the same and checks the total area never changes.