Aperiodic monotile

a:

b:

curve:

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This tool draws the aperiodic monotile discovered by Smith, Myers, Kaplan and Goodman-Strauss.

There's a family of related shapes, each made of 14 edges (though two of the edges are parallel and adjacent so look like a single long edge).

Each ledge is one of two lengths, 𝑎 or 𝑏. The angles in the shape don't change.

𝑎 = 1, 𝑏 = √3 is the "hat" tile. 𝑎 = √3, 𝑏=1 is the 'turtle' tile. 𝑎 = 𝑏 = 1 is the "spectre" chiral tile; it can be forced to tile aperiodically by increasing the "curve" parameter.

This tool made by clp.

Tiles in more formats.