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trippy tilings
Meinrenken's Theorem come to life! ![]()
So I recently posted a paper where I take a look at a certain family of tilings of space coming from finite and affine groups generated by reflections. If you're interested in the math, feel free to checkout the paper. Even if you're not, plug some random numbers into this fun little web applet I made and press play. (Thanks @jackeown for help with the canvas coding!)
Replies (6)
What is Meinrenken's Theorem? I know it's in the paper, but not everybody will click that.
:-)
And thanks for sharing your research. Upvoted and resteemed.
You may also be interested in this
The theorem of Meinrenken that I am referring to is theorem 1.3 in this paper. (I know links are no fun to click on, but the paper has some good pictures.)
Informally the theorem says that one may deform the Coxeter complex up to a certain point where things collapse...
In my (default) simulation the collapse happens when t=1. Three of the triangles collapse to line segments, and one of them collapses to a point.
In general, you can pick your favorite 2x2 matrix, there will be some time, t, where such a collapse first happens.
My paper concentrates on the case when this matrix is the identity, and I show that there is (pardon the pun) "beauty in the break down".
The "Coxeter complex" in this picture is the six triangles giving a hexagon when t=0.
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STOPIt seems as though you didn't resteem this. No worries, just curious.
This post received a 3.8% upvote from @randowhale thanks to @mckeown12! For more information, click here!