# Geometric Art ProjectsJune 7, 2021 3:04 PM   Subscribe

Penrose tiling quilt and Art by Josh Millard [via mefi projects].
posted by aniola (5 comments total) 22 users marked this as a favorite

... and I haven't read this, but see also Shape: The Hidden Geometry of Information, Biology, Strategy, Democracy, and Everything Else also via mefi projects.
posted by aniola at 3:07 PM on June 7, 2021 [1 favorite]

So those were all on the front page of projects. This one was posted to mefi projects 10 years ago: Dan's blog of math/art projects based on geometric curiosities
posted by aniola at 3:09 PM on June 7, 2021

This is lovely, as are the other examples he gives on the project page. In all of them though, my eye still tries to see a repeat, which makes for a slightly unsettling effect. I did think of doing a Penrose quilt a while ago, but foundered on the point where my ability to sew ran into my complete lack of mathematical ability, especially to work out how many colours to use. I would have expected to use English paper piecing (EPP), assuming I could have made accurate templates for the two Penrose shapes. I've never heard of the paper foundation technique used here,, but since I am already supposed to be making four EPP quilts already, and am ankle-deep in little paper hexagons I must resist the lure of a new method.
posted by Fuchsoid at 8:36 PM on June 7, 2021

Ooh, I am delighted to share a post with ubermuffin's quilting hijinks. His Penrose quilt came out so dang good and feels like yet another nudge from the universe for me to give quilting a go at some point.

I really like Penrose stuff but haven't really played with it myself yet; it's just a slightly different sort of geometry than I usually get up to. One of the slightly counter-intuitive things about the idea of Penrose configurations as aperiodic tilings is how the test of periodic tiling of the plane is tied to symmetry through, specifically, translation. If you can grab an infinite tiling of the plane, and just budge it up and to the right a certain distance and have the exact same layout you had before, it's a periodic tiling; if you can't, it isn't.

So a Penrose tiling shares that translational asymmetry with other kinds of aperiodic tiling—there's no budge you can execute that will leave it as it was before—but it's not actually an asymmetrical tiling in the more general sense: it has (or can have, at least, I don't know the territory enough to know if this is true for every Penrose tiling) five-fold rotational symmetry. So you can spin it 72 degrees and end up with what you started with. A notion of periodic tiling that included rotation as sufficient would see these as periodic rather than aperiodic, I figure!
posted by cortex at 8:56 PM on June 7, 2021 [1 favorite]

And speaking of quilting and math art and nudges from the universe: I was just collaborating recently with rad math nerd and textile artist Elizabeth Wickes, who has also made a bunch of stuff that is near and dear to my geometric art (e.g. these Recamán and Cantor pieces, hell yeah); we collided on twitter a while back over some bit of math art stuff. And she was just recently messing with some kite-and-dart piecing too. Check her stuff out, it's great.
posted by cortex at 9:03 PM on June 7, 2021 [2 favorites]

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