How could one prove this is aperiodic? I'm guessing maybe you can prove that some or most of the triangles have globally unique rotations regardless of N?
tromp
The bottom of my home page has this as a PostScript signature:
%!PS % -John Tromp http://tromp.github.io/
/t{dup 1 sub gsave dup 0 gt{[.4 .2 -.2 .4 .4 .2]concat t currentgray
.8 mul .2 add setgray -1 1 scale t -1 2 translate t 1 -1 scale t[0 1
1 0 0 2]concat t pop}{0 moveto 1 0 lineto 0 2 lineto closepath clip
fill}ifelse grestore}def 10 10 translate 600 600 scale 5 t showpage
Love this tiling ! So beautiful
I made a few pinwheel tilings visualisation on shadertoy https://www.shadertoy.com/results?query=tag%3Dpinwheel including a few original use of pinwheel to simulate a "snake" walking inside the tiling https://www.shadertoy.com/view/4sSBRy . and this one gets really trippy if you wait a few minutes there are interferences patterns in the colors that become really crazy https://www.shadertoy.com/view/XsSfWm
How could one prove this is aperiodic? I'm guessing maybe you can prove that some or most of the triangles have globally unique rotations regardless of N?
The bottom of my home page has this as a PostScript signature:
which outputs this pinwheel tiling https://tromp.github.io/img/pinwheel.pdf