Spectroids
Neat looking pictures related to aperiodic tiles
Inspired by the Spectre tile I’ve generated more ‘spectroids’ which have what I believe are the most notable features of the Spectre: Alternating hexagonal and square angles, and if you color the edges in two colors so that they change color whenever it takes a 90 degree angle and otherwise stays the same then taking just the edges of each color forms a closed loop.
Craig Kaplan has made this very nice applet for exploring these and larger ones and Dave Smith has made this fun post about the Golem, a shape he pulled out of a more expanded list.
Disappointingly none of these other than the Spectre tile only aperiodically but maybe they have other interesting properties.
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I found a few of those on my own. Fascinating to see so many more. 100 seems arbitrary. Is there more? How does the proof work, that none other than the spectre are purely aperiodic?