Generating the P3 Tiling
21 days ago
- Penrose tilings are aperiodic tilings of the plane discovered by Roger Penrose in the 1970s, using only two prototiles.
- The article focuses on the P3 variant, which uses two types of Robinson triangles (acute and obtuse) and a set of four subdivision rules.
- The subdivision rules can be expressed as term rewriting rules, leveraging the golden ratio to compute new vertices.
- A recursive JavaScript function is provided to generate the tiling by repeatedly subdividing triangles.
- Coordinates in the tiling can be represented as integer linear combinations of four basis vectors, using cyclotomic polynomial identities to handle multiplication exactly.