Spectre Aperiodic Monotile

thingiverse

Over the years many sets of shapes have been found that will tile a surface only in an aperiodic manner. The most well known set of shapes to do this are "Penrose Tiles". However they all required multiple shapes to perform the tiling. This "einstein" tile (play on the German words "ein" "stein" or "one stone") was something of a holy grail. Earlier this year (2023) several researchers discovered one of these, an individual shape that could tile a surface in an aperiodic manner and over several months discovered many of them and satisfied various annoyances until they refined the shape to this one dubbed a "spectre" for its shape. https://arxiv.org/abs/2305.17743 While I found several sources where people had traced shapes from various articles and research papers, I couldn't find a source for a computationally created vector file (ideally tiled) so that I could laser cut a bunch of them so that I could play with them. So I wrote a python script to write an SVG file for me. The included SVG file is of 32 spectre tiles at 10mm per edge of the shape that will fit in a 200mm x 200mm (8" x 8") square. The python script to generate this SVG is available at https://github.com/Xuth/spectre/ . It's kinda ugly but it's works. Also the pattern generated isn't one that you can continue to tile with perpetually. But it does give something that allows you to quickly cut some shapes out to play with.