At https://demonstrations.wolfram.com/SubstitutionTilings/ I was able to convert several Rauzy fractals into simple single polygon substitution tilings that had never been seen before. I'm convinced there is a nice 3D substitution tiling based on a single polyhedron that is currently unknown. --Ed Pegg Jr On Saturday, March 14, 2020, 06:01:38 PM CDT, Tom Karzes <karzes@sonic.net> wrote: Right, I use the magenta color to indicate overlap. When the components fit perfectly to form solid tiles, this only occurs at their perimeters, but for the intermediate stages there is lots of overlap. Tom Fred Lunnon writes:
Ah, I see --- magenta indicates overlapping!
https://en.wikipedia.org/wiki/Rauzy_fractal
On 3/14/20, Fred Lunnon <fred.lunnon@gmail.com> wrote:
Looks nice and runs fine for me on Firefox.
But the Rauzy stages have only 3 tile colours; what purpose is served by the magenta regions?
WFL
On 3/14/20, Tom Karzes <karzes@sonic.net> wrote:
Here's a GIF animation that shows the Rauzy fractal converging from an IFS by varying the angles in unison:
https://www.karzes.com/anim_rauzy.gif
Note that it converges at two distinct points in the sequence, in two different ways, so don't close it prematurely. At one point it almost looks like it's going to converge to a Heighway dragon, but of course it doesn't.
Tom
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun