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@LichenDaemon technically the definition of "repeating" is that the tiling does not have translational symmetry with itself. so, if you had two copies & you slid one around on top, there's only one place they'd line up. but rotational symmetry is allowed.
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@LichenDaemon the pattern is self-similar - each area of tiles is one of several types, which fit together in particular ways to form larger areas, which fit together in particular--- etc. which is part of the proof for how it is aperiodic. but the *whole thing* doesn't repeat exactly.