Penrose tiling quilt
June 2, 2021 5:46 PM   Subscribe

Penrose tiling quilt
My 2021 pandemic project was learning to quilt, and I started out with a fussy geometrical monstrosity. Penrose tilings are aperiodic tilings (i.e. they can cover the plane infinitely without repeating) that exhibit fivefold symmetry (so no right angles anywhere). My brother nerd-sniped me by wondering what it would be like to quilt one, which launched me on a four-month long journey that I documented on twitter. Here's the first tweet in the series describing the project, and a thread comparing to previous Penrose quilts by other folks.
Role: programmer, designer, quilter
posted by ubermuffin (8 comments total) 9 users marked this as a favorite
This project was posted to MetaFilter by aniola on June 7, 2021: Geometric Art Projects

OH MY GOSH
posted by cortex at 5:47 PM on June 2 [2 favorites]


cortex: *squee!!*
posted by ubermuffin at 6:09 PM on June 2


Love it!
posted by ellieBOA at 1:45 AM on June 3


That's beautiful. Looks like it could have been created any time from the 1830s to the 2030s.
posted by bonobothegreat at 6:51 PM on June 3 [1 favorite]


This is amazing. I love the comparison thread with lots of other examples!
posted by jacquilynne at 7:33 AM on June 7


I don't understand penrose tiling. I read the intro on the Wikipedia page and I still don't get it. Can someone explain this in very simple terms? Also I like the rose coloring on the quilt.
posted by aniola at 8:14 AM on June 7


aniola: it's a challenge to explain very simply, but I'll take a stab at it...

What makes Penrose tiling aperiodic (as opposed to a checkerboard or a honeycomb) is that there is no fixed-sized grid you can draw on top of the tiling to find the "repeats". For example, here's a periodic hexagonal pattern:
##########################################
#\___/   \___/   \___/   \___/   \___/   #
#/   \___/   \___/   \___/   \___/   \___#
#\___/   \___/   \___/   \___/   \___/   #
#/   \___/   \___/   \___/   \___/   \___#
#\___/   \___/   \___/   \___/   \___/   #
#/   \___/   \___/   \___/   \___/   \___#
#\___/   \___/   \___/   \___/   \___/   #
#/   \___/   \___/   \___/   \___/   \___#
##########################################
But really you can think of the tiling above as a bunch of copies of this single repeating template:
##########
#\___/   #
#/   \___#
##########
(If you look closely you'll see that the big hexagonal tiling is 4 templates high and 5 templates wide.)

Even though the hexagon shapes themselves aren't rectangles, there is still some underlying rectangular element that you can cut and paste endlessly to obtain the overall tiling at any size you want.

Hence, you could use this template to make hexagon wallpaper.

The point of Penrose tilings (or other aperiodic tilings) is that it's impossible to make wallpaper out of it, because there's no regularly repeating collection of shapes.

Instead, if you consider any very small group of tiles (e.g. 1-3 tiles large) within a Penrose tiling, you can often find an identical group very close by (perhaps rotated or flipped), but as the group you're looking at gets bigger and bigger, you'd have to travel further and further away from where you started to find a duplicate.

When Penrose began studying these concepts in the 1970s, people were surprised to learn that there was such a thing as aperiodic tilings – patterns made of very simple shapes that appeared to fill space endlessly, but would be impossible to make wallpaper out of.
posted by ubermuffin at 1:32 PM on June 7 [7 favorites]


Thanks, ubermuffin! I think I'm following, now. I had to go look at your quilt again with that in mind :D
posted by aniola at 2:59 PM on June 7


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