Penrose Tiling Generator
Penrose tilings cover the infinite plane with just two rhombus shapes yet never repeat periodically — a discovery that reshaped crystallography when the same five-fold symmetry turned up in real quasicrystals. This generator builds the tiling by recursive subdivision of Robinson triangles: each step splits every triangle by the golden ratio, and a few steps in, the thin and thick rhombi lock into their famous star-and-sun patterns. Step the depth up and down to watch the aperiodic order unfold.
Runs 100% in your browser — simulations are computed locally on your device.
Read the full guide to this tool
Notes
- The two rhombi appear in golden-ratio proportion: thick to thin tends to φ ≈ 1.618.
- Matching rules force aperiodicity — no translation ever maps the tiling onto itself.
- Shechtman’s Nobel-winning quasicrystals show exactly this "forbidden" five-fold diffraction symmetry.
- Runs 100% in your browser — simulations are computed locally on your device.
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