Aperiodic Tililng Turtles

thingiverse

Inspired by this: https://statmodeling.stat.columbia.edu/2023/03/24/the-hat-a-single-shape-that-can-tile-the-plane-aperiodically-but-not-periodically/ And then this twitter post: <blockquote class="twitter-tweet"><p lang="en" dir="ltr">An aperiodic turtle tessellation based on new aperiodic monotile Tile (1, 1.1).<br>In the tiling, it is said that around 12.7% of tiles are reflected. The green one is an instance. One more reflected turtle is hidden in the tiling. Who is the reflected? <a href="https://t.co/GZJRP35RIC">pic.twitter.com/GZJRP35RIC</a></p>— Yoshiaki Araki 荒木義明 (@alytile) <a href="https://twitter.com/alytile/status/1638532337016385537?ref_src=twsrc%5Etfw">March 22, 2023</a></blockquote> <script async src="https://platform.twitter.com/widgets.js" charset="utf-8"></script> Which seems to be related to this: https://aperiodical.com/2023/03/an-aperiodic-monotile-exists/ I decided to laser cut it. Since my Escher-style tiling turtles seemed popular (https://www.thingiverse.com/thing:2649164), I decided to upload this one as well. <br/> <br/> There should be no overlapping lines. I recommend optimizing your cuts to go inside to out so that you don't drop an entire group before cutting it apart. <br/><br/> This set can be cut in a 6x6 square blank. These tiles are meant to be flipped over to. So after cutting the sheet, I cut the shell pattern on the back of each piece by taping a piece of paper to the bed, cutting the outline of turtles out of it, and then a few at a time putting the back side face up to engrave the shell pattern (see photos). They are not 50-50 in the tiling (see the Twitter post above), which is why I have more facing one way than the other in the paper. I've included a single turtle to assist with this part. <br/> <br/> Enjoy! <br/> <br/> Note to original designer: I hope you appreciate the derived work here. If you object, please let me know and I'll take this down. Or even better, I'll be happy to link over to your website/whatever.