Spectre Monotile Jigsaw

2023-08-25 17:34:58

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Summary

The Chiral Spectre Aperiodic Monotile is an amazing shape discovered and analyzed in early 2023 by David Smith, Joseph Samuel Myers, Craig S. Kaplan and Chaim Goodman-Strauss. It's possible to tile an infinite plane with an infinite number of the same tile, but only aperiodicly; i.e., tiles cannot be arranged in any pattern that repeats forever.

The salient feature of this new tile is that all 14 edges are equal length (counting the one double-length side as two edges). Thus, one can curve successive edges alternately, in one style and its converse, to make it "chiral"; i.e., if a file is flipped upside-down, it will not mate to a tile that is right-side-up.

I designed this tile's edges in the shape of conventional jigsaw tabs and pockets so that tiles interlock. It's much more satisfying than trying to lay non-interlocking tiles side by side. Placing the tiles makes for a challenging puzzle. It's non-trivial to keep growing a round-ish mat of tiles by adding more around the edges without introducing holes.

Any printer bed should fit about 10 tiles at a time when duplicated in the slicer. By default, tiles are 4 mm thick with 15 mm edge length and 0.2 mm of kerf clearance for 3D printing. These parameters can be tuned in the OpenSCAD design or Thingiverse Customizer.

How I Designed This

The shape of the curved jigsaw tab is defined by a Bézier curve. If one is adventurous, they could add or modify control points to create other curves.