Tag: geometry
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Turtle tiles part 2: Properties of coloured Kagome lattices
This is a direct sequel to the last post on the Turtle Tile. Please read that first to make sense of this post. In accounts of the discovery of the Hat aperiodic monotile such as [1], one of the first clues to the structure of its tilings was the fact that reflected Hat tiles seemed…
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Turtle tiles part 1: Forcing non-periodicity
This is a rework of a previous post proving that the Turtle tile is non-periodic, to be used as a starting point for further explorations. A edit has been made to change the defined term ‘irrational’ to ‘arational’ in the post. A follow-up post has also been posted. In March 2023, an aperiodic monotile was…
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Spar Lines, Hexagons, and Tiling a Finite Boundary
This post is follow-up to my proof that the Turtle prototile is not periodic. It is strongly recommended that you read that post first. This post will freely use terms from that post. When the Hat prototile was first unveiled, one of the first applications was jigsaw puzzles with only one shape of tile. One…
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The Turtle prototile is not periodic, a simple proof.
(This is a repost as the original is unavailable due to technical issues. An archive of the original post can be found here. Also, a re-worked version of this post to be built upon can be found here.) When a group of mathematicians and tiling hobbyists announced the discovery of the Hat aperiodic monotile I,…
The mathBlock shed 