A penrose tiling is an example of an aperiodic tiling here a tiling is a covering of the plane by non overlapping polygons or other shapes and aperiodic means that shifting any tiling with these shapes by any finite distance without rotation cannot produce the same tiling.
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However despite their lack of translational symmetry penrose tilings may have both reflection symmetry and fivefold.
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Today the most famous are the penrose aperiodic tiles discovered in the early 1970s which can cover a plane using only two shapes.
The tiling can be recursively generated.
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A penrose tiling is a non periodic tiling generated by an aperiodic set of prototiles.
This means that the patches of webbing can be tiled as penrose tiles yet be subdivided such that the result is a valid penrose tiling with smaller tiles.
Penrose tilings are named after mathematician and physicist roger penrose who investigated these sets in the 1970s.
Called inflation and deflation that is starting from a penrose tiling another one with smaller tiles can be generated.
The aperiodicity of the penrose prototiles implies that a shifted copy of a penrose tiling will never match the original.
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