Ammann A1 tilings
non-periodic tiling of the plane
In geometry, an Ammann A1 tiling is a tiling from the 6-piece prototile set shown on the right. They were found in 1977 by Robert Ammann. Ammann was inspired by the Robinson tilings, which were found by Robinson in 1971. The A1 tiles are one of five sets of tiles discovered by Ammann and described in Tilings and patterns.
The A1 tile set is aperiodic, i.e. they tile the whole Euclidean plane, but only without ever creating a periodic tiling.
Generation through matching
The prototiles are squares with indentations and protrusions on the sides and corners that force the tiling to form a pattern of a perfect binary tree that is continued indefinitely. The markings on the tiles in the pictures emphasize this hierarchical structure, however, they have only illustrative character and do not represent additional matching rules as this is already taken care of by the indentations and protrusions.
However, the tiling produced in this way is not unique, not even up to isometries of the Euclidean group, e.g. translations and rotations.
“Ammann A1 tilings” enters the record as non-periodic tiling of the plane. Crown Archives preserves that source wording while asking what Ammann, tilings and non-periodic can confirm, complicate or overturn.
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