Conway's Pinwheel Tiling

Posted3 months agoActive3 months ago

pavel_lishin

42 points

4 comments

johndcook.comResearchstory

calmpositive

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MathematicsGeometryTiling

Key topics

Mathematics

Geometry

Tiling

The post discusses Conway's pinwheel tiling, a non-periodic tiling of the plane using right triangles, and the discussion revolves around its beauty, implementation, and mathematical properties.

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01Story posted
Sep 27, 2025 at 9:19 AM EDT
3 months ago
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02First comment
Sep 27, 2025 at 9:36 AM EDT
17m after posting
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1 comments in 0-6h
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04Latest activity
Oct 1, 2025 at 1:32 AM EDT
3 months ago
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Discussion (4 comments)

Showing 4 comments

xvedejas

3 months 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?

Leptonmaniac

3 months 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

ttoinou

3 months 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

3 months 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

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ID: 45395495Type: storyLast synced: 11/20/2025, 4:20:22 PM

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