Conway's pinwheel tiling

5 comments

• ttoinou 2 days ago ago

  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

• tromp 6 days ago ago

  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
  

  which outputs this pinwheel tiling https://tromp.github.io/img/pinwheel.pdf
• Leptonmaniac 2 days ago ago

  Super 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

• xvedejas 2 days ago ago

  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?

• nurettin 2 days ago ago

  [flagged]