## A single fractal pinwheel tile.(English)Zbl 1382.52018

Summary: The pinwheel triangle of Conway and Radin is a standard example for tilings with self-similarity and statistical circular symmetry. Many modifications were constructed, all based on partitions of triangles or rectangles. The fractal example of Frank and Whittaker requires 13 different types of tiles. We present an example of a single tile with fractal boundary and very simple geometric structure which has the same symmetry and spectral properties as the pinwheel triangle.

### MSC:

 52C20 Tilings in $$2$$ dimensions (aspects of discrete geometry) 28A80 Fractals

### Keywords:

fractal pinwheel tile; pinwheel triangle

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### References:

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