3 ms·
Conway's pinwheel tiling
- tromp 1y agoThe 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 which outputs this pinwheel tiling https://tromp.github.io/img/pinwheel.pdf https://tromp.github.io/img/pinwheel.pdf
- ttoinou 1y agoLove this tiling ! So beautiful I made a few pinwheel tilings visualisation on shadertoy https://www.shadertoy.com/results?query=tag%3Dpinwheel 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 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 https://www.shadertoy.com/view/XsSfWm
- nurettin 1y ago[flagged]
- xvedejas 1y agoHow 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?
- Leptonmaniac 1y agoSuper interesting! So if I understand correctly, all you need to do to have this in your home is gather a bunch of 1:2 tiles, cut them along the diagonal, and assemble them as shown? Awesome