Pinwheel tiling

In geometry, pinwheel tilings are non-periodic tilings defined by Charles Radin and based on a construction due to John Conway. They are the first known non-periodic tilings to each have the property that their tiles appear in infinitely many orientations.

Let ${\displaystyle T}$ be the right triangle with side length ${\displaystyle 1}$, ${\displaystyle 2}$ and ${\displaystyle {\sqrt {5}}}$. Conway noticed that ${\displaystyle T}$ can be divided in five isometric copies of its image by the dilation of factor ${\displaystyle 1/{\sqrt {5}}}$.

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