A visualization of the continuum of aperiodic monotiles containing the hat and turtle.
https://media.mathstodon.xyz/media_attachments/files/110/454/676/740/680/722/original/f9575677f1dde7b3.png
Recall that the hat and the turtle belong to a continuum of shapes denoted Tile(a,b) for edge lengths a and b. The hat is Tile(1,sqrt(3)), and the "turtle" is Tile(sqrt(3),1). All members of that continuum are aperiodic except for the equilateral polygon Tile(1,1). Dave became curious about Tile(1,1) after seeing Yoshi Araki playing around visually with its close relative Tile(1,1.01). (2/n)
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