This is just the beginning I hope. Next is 3D. Or shapes that are dynamic in time like lava lamps and the digits of pi.
Has anyone here read Neal Steve's Anathem?
It's a utopian book that I think a lot of idealists can relate to. Math being a sacred institution, a kind of royal society. It's a great explanation of these kinds of patterns but in the most hardcore way.
A note on these shapes for people who want to draw them from scratch...
I found it quite difficult to draw a nice looking tiling using the basic monotile. It's quite hard to draw it entirely from the angles directly on the paper - not for a single tile, but extending any patch to a much larger one.
Tracing and transferring the tile, on the other hand is easier to keep track of, but slight inaccuracies quickly propagate across the diagram. Since there is (by definition!) no larger-scale structure, there can be no guidelines to help correct this - unlike for repeated patterns.
The way I found was best was just to print out a patch of tiles, and then trace that. I suppose that using a metatile approach might also work, although doing that by hand is a little daunting.
(the second program has a bunch of variant versions)
this cheats a little: it turns out you always want to draw the H8 metatile (which will overlap) instead of keeping track of the zoo of metatiles. And the flipped hat is never drawn; it appears as a hole in the plot. Similar things happen with the spectre.
This was all done so I could make a program small enough to fit in a toot to generate patches using the bbc microbot:
Has anyone here read Neal Steve's Anathem?
It's a utopian book that I think a lot of idealists can relate to. Math being a sacred institution, a kind of royal society. It's a great explanation of these kinds of patterns but in the most hardcore way.