Aperiodic Tiling



In the 70’s very similar Penrose tiles to girih were identified in different alternating shapes, the rhombus making up P3 patterns. Each pattern features pairs of tiles that entirely fill a plane whist never repeating. As the surface increased, the mean of the numbers from each tile type nears the 1.618 or the golden ratio phi. A tessellation of P3 is below, using fish as cute fat and skinny rhombi.


You can use this Penrose Tiling Generator to make pattern in most any arrangement or color.



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References:
a href="https://plus.maths.org/content/roger-penrose-knight-tiles" target="blank"> Penrose
Penrose Tiling
Puzzles