Trilobite and crab, tiles and puzzle

This Thing constructs trilobite-and-crab tilings. They are described in The Trilobyte and Crab: A Full Explanation, by Chaim Goodman-Strauss. These tiles can be assembled into patterns that fill the entire plane, but no such pattern can have a translational symmetry. This Thing contains three versions:

• A pair of tiles that have markings on top. A proper tiling matches these markings, and the markings illuminate the non-periodic but systematic structure of a tiling.
• A 50-piece jigsaw puzzle that is a 3D map of the Earth's topography and bathymetry. There are only two piece shapes, apart from the edges, and these pieces interlock in such a way that they can only go together in a way that would match the markings above.
• A pair of pieces with both markings and interlocking for use as a doormat. (Work in progress.)
  The code in the Jupyter notebook is not very general but can be adapted to produce other variants, for example a jigsaw puzzle with more pieces (this one fits on a single mk3 bed).

Print instructions

Category: Math Print Settings

Printer Brand: Prusa

Printer: i3 MK3

Rafts: No

Supports: No

Resolution: 0.1 mm or 0.35 mm

Infill: default

Filament: any PLA blue, green, white
Notes:

Although these objects make much more sense in color, they are designed so that a single color change at each specified altitude produces the desired effect. For the marked tiles the altitudes should be obvious; for the jigsaw puzzle the altitudes corresponding to deep water, shallow water, sea level, and mountain are indicated in the Jupyter notebook and set in the 3mf file.

The files for download here do not include the bathymetry plus topography data set I used; the Jupyter notebook should indicate where to get it (it's in the public domain, from the US government, available as long as that organization is not shut down).