Pinwheel Tiling - The Conway Tessellation

The Conway Tessellation

Let be the right triangle with side length, and . Conway noticed that can be divided in five isometric copies of its image by the dilation of factor .

By suitably rescaling and translating/rotating, this operation can be iterated to obtain an infinite increasing sequence of growing triangles all made of isometric copies of . The union of all these triangles yields a tiling of the whole plane by isometric copies of .

In this tiling, isometric copies of appears in infinitely many orientations (this is due to the angles and of, both non-commensurable with ). Despite of this, all the vertices have rational coordinates.

Read more about this topic:  Pinwheel Tiling

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