I have a question about the aperiodic spectre tile (or the hat/turtle).
I know that the proof of aperiodicity works by showing that the tiles must fit together in a hierarchical structure that eventually repeats itself at a larger scale. But the larger units aren't literally scaled copies of the spectre. I also know that there is some freedom as to how you draw the edges of the spectre.
Is there a way you can draw the edges that allows you to literally use spectres to cover a larger copy of themselves? If so, is this way of doing it unique?
This is a repost of a twitter thread where I explain the concept of drainage for tilings of the Hat #aperiodic#monotile. Might change a few bits, but this will mostly just be a copy job.
#Mathstodon & friends: interested in aperiodic monotile enamel earrings? I kind of want this for myself but the company I’ve used in the past (Made by Cooper) is much cheaper for larger orders.
Please retoot for visibility! But only hit the favstar if you’d more likely than not buy a pair if I set up a ko.fi shop for them. Price probably ~$20/pair for two earrings and US shipping.