We made a new puzzle based on the Spectre tile, the aperiodic monotile discovered earlier this year by @Chaimgoodmanstrauss, @csk, and others. It is a set of 111 tiles with a truchet-style pattern printed on them
Though each piece is identical they create a pattern which never repeats. It's actually quite a bit more "puzzle-y" than you might expect from a tiling puzzle. That's because, even though it varies infinitely, there is really only one rule which allows you to keep tiling without hitting a dead end. You can assemble the pieces however you like, but figuring out the pattern that allows you to continue forever with no gaps is actually quite tricky
The discovery of an aperiodic monotile was greeted with much fanfare. It was not the Spectre tile, but the "hat" shown on the left. Of course we were also excited and almost immediately received requests to make some. However, some mathematicians were slightly dissatisfied, because the tiling actually required reflections or flipping over tiles. Therefore in some ways it was actually two shapes not one. This is not simply mathematical frippery, it is actually key to fabricating a puzzle. Because if you print a pattern on one side of the puzzle, it won’t work. The tiles must be flipped when assembling, so sometimes you would end up with the image side down. So we were delighted when the same team announced the Spectre on May 28, an aperiodic monotile that does not require reflections.
@aqo for hat tiles? Not totally unreasonable but at that point it’s probably just as easy to print both sides. I also prefer not to make things out of plastic when possible
The Spectre tile is not just one shape but, like any tiling, an infinite family of shapes that connect in a certain way. We prototyped a bunch of different tiles for our puzzle from simple curves to really funky edges. We wanted to balance a natural looking shape with pieces that would interlock well. The more complex the edge, the larger the pieces need to be and the harder it is to paint a continuous pattern across the tiles.
@fractalkitty@nervous_jesse this is amazing! will it work with overlapping hexaspectres in this level? looks like the orientation is wrong one level down but might be right here
@nervous_jesse@Chaimgoodmanstrauss@csk I love these tiles! I’m in the UK so I’ve had to make my own, but I still haven’t figured out the rule for placing a tile without preventing future tiling. Any tips or descriptions? I’m ready for the answer now 😅
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