Math That Goes On Forever but Never Repeats | Quanta Magazine

A retired print technician recently discovered the first “aperiodic monotile” — a single tile that fills up the plane in a non-repeating pattern.

When a tiling is equivalent to itself after a translation, it has “translational symmetry” This shows that the two tilings fo Two w the same pattern.

A-tiles: A, AA, AAA, AAAA, B, BB, BBB, BBBB, ABABA, AABABAABABABA.

The new rules allow us to generate tiling mosques unlike our first example, don’t repeat.

In the resulting pattern — BAB — will never appear again.

David Smith, a recreational mathematician, artist and tiling enthusiast, discovered the first known aperiodic monotile last November.

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