02 may 2016
And I mistook the title for something else already, hahaha.
What better way to start off, though, than a harmless mistake?
I guess I should talk about something, though. Maybe randomness, which is a theme that my page has picked up.
The mazes use the Aldous-Broder algorithm, a random walk which is supposed to be slow, but not actually slow enough to matter. I think it ends up being O(N^2 log N), where N is the number of cells, but more importantly, even on tilde.town's shared server, runs immediately at the sizes on the site, and is incredibly easy to implement. The two actually use a slightly different variation on the random walk: the cube "breaks" the walls while the orb "makes" them, because I realized the latter would also work and not require me to keep track of the topology.
The cubes is based on reading a math blog post about "plane partitions" and their relation to tilings of a hexagon by rhombi. It made me think about doing something based on that and continuously adding cubes; initially I thought about tiling a torus (i.e. a tiling background) that way but then realized that starting with an empty cube and then repeatedly adding until I reach a full cube gives an interesting combinatorial property of starting out with just a few options, continuing to a combinatorial explosion, and then near the end returning to a regular option. I made it 7x7x7 and have it add a cube every 4 minutes so that the cycle ends up close to but not quite equal to a day; I'm a bit embarrassed that this keeps my page near the top of recent changes all the time, but I like the page nonetheless.
The binary bumblebee (currently inactive) doesn't have any randomness, but I was planning on adding another set of 16, a scramble puzzle where one configuration creates the actual image, and then having the moves swap on both the two triangle-based parts of the puzzle and the scramble puzzle, so that unscrambling would create a random pattern on the "bumblebee". Maybe I'll get back to that sometime.
There's something interesting to me about randomness; even though I don't believe, say, Tarot cards, I have a strange attraction to the idea of getting deep truths about the universe from shuffling cards and pulling them out. And then there's tabletop RPGs, where the direction of a story is based, at least in part, on the roll of the dice. Maybe running one on tilde.town would be worth doing, someday...?