🧵THREAD: When I was designing and sewing my Penrose tiling quilt, I didn't want to look closely at Penrose quilts by other people until after I finished mine, because spoilers.
So here's a deep dive into the other Penrose quilts I discovered. But first, a quick digression about tiling types and quilting techniques.
There are actually two different Penrose tilings you can quilt. They are the P2 tiling which uses kite and dart shapes, and the P3 tiling which uses rhombuses. Rhombi? (There's also a P1 but it would be a pain in the ass to quilt.)
Now let's talk technique – most Penrose quilts seem to use English Paper Piecing (EPP), in which you hand-sew fabric pieces that have been wrapped and glued ("basted") around paper cutouts of a precise shape and size. allpeoplequilt.com/how-to-quilt/p…
Quilters reach for EPP as when they have a pattern that involves sewing into inside corners or when there are regular tiles that don't meet at right angles, like between the hexagons in the website preview image above.
For my quilt, I used Foundation Paper Piecing (FPP), in which you machine-sew through a sandwich of fabric and paper templates. The machine needle perforates the paper for tearing off and removing later. gathered.how/sewing-and-qui…
Generally with FPP, as opposed to EPP, the paper-backed blocks or assemblies (like the squares in the preview image above) must meet up along straight seams – no inside corners except possibly within the block itself.
That's it for the background, lets go look at some Penrose quilts!
First up is this P2 tiling quilt by Lisbeth G. Clemens from 1993. It's described by R.A.G. Seely at math.mcgill.ca/rags/PenroseQu… and looks to be fabricated using EPP. It's one of a few where the quilter decided to use the boundaries from the tiling instead of a rectangular crop.
Next up is this beauty designed by Mark Newbold and fabricated by Serena Mylchreest in 1996, described at dogfeathers.com/quilt/penrose.…. P3 tiling, uneven boundary.
The description says "This was before Serena knew about 'paper piecing'" so I emailed Serena to learn how it was made...
She wrote back: "The Penrose quilt that I made for Mark was done so long ago that I'm not sure how I made it. I do remember it was machine stitched and involved quite a bit of swearing. If I were doing it today I would use paper piecing to keep the fabric from stretching."
I'm really impressed that she was able to get that precise a result without any stabilization! 😲
Next we have this 1997 quilt by Evelyn Judson entitled "Deconstruction," described at evelynquilts.com/PenroseTiles.h…. P3 tiling, rectangular border.
Artist description: "Baby Blocks gone insane."
I like the patchwork colors!
This one designed by Vaughn Nelson, pieced by Beth Nelson, and quilted by Alisha Nelson Miller is entitled "Light Zero" and was done in 2006. Described at the Texas Quilt Museum: texasquiltmuseum.org/virtual-galler…. P3 tiling, rectangular. I'm guessing EPP, but you'd have to ask a Nelson.
FWIW, the write-up does say "Piecing of the Penrose tiles was difficult because of their numerous Y-seams."
This huuuuuuge P3 quilt was made by Tanya Scharaschkin. Finished in 2009, written up at toroidalsnark.net/tvspenrose.html. Notable because of size and 100% hand-sewn – no machine sewing at all!
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Next up are two by Amy Qualls. "Penmanship" was finished in 2010: domesticat.net/quilts/penmans…. If you look closely at the pic, you can get an idea of the size - I'd guess about 4' square or so. Also P3 but unlike some of the previous ones it's rhombus-centered, not star-centered.
It is gorgeous and HUMONGOUS. (Photo from Qualls' site)
Next up are four (!) Penrose quilts from Andrew Krizman. First, this xmas tree skirt from 2014 notable due to its star shape and pattern highlighting the Penrose tiling matching rules. Still P3 but not obviously so. dunawi.blogspot.com/2014/06/penros…
Then a more recognizably P3 quilt from 2014 that is a clear shout-out to Mylchreest's 1996 work. In fact Krizman calls these "Mylchreest stars". I really like the arcs quilted onto the yellow rhombi. dunawi.blogspot.com/2014/10/penros…
This one from 2015 combines some more intricate machine piecing of the patches with EPP to bring them together. dunawi.blogspot.com/2015/09/penros…
And most recently, this one from last year highlights the ring shapes that appear in the P3 tiling. I like the interlocking detail between the blue and green rings. dunawi.blogspot.com/2020/04/penros…
This one on Etsy by Amy Krasnansky (date unknown) might be my favorite, composition-wise. It combines aspects of both the P2 and P3 tilings at multiple scales and I love the color scheme.
Here's one from 2018 by textiledreamer. It's a quick 40cm x 40cm entry into what seems to be an annual friendly quilt competition among a quilting group. P3 tiling. It does a great job turning an ugly fabric into very pretty stars! textiledreamer.wordpress.com/2018/04/01/cha…
The rest I found had less in the way of write-ups or descriptions, just images found from blogs, Pinterest, or image searches. I'll just drop whatever info I have along with a link for each one.
Flickr user Cris Crawford, dated 2011 and entitled "Pluto Star". I really like the composition and the color wheel effect! flickr.com/photos/1679723…
Flickr user a_kendra, dated 2012. It's a rare sighting of a P2 tiling – you can clearly pick out the kites (blue/green/opal) and darts (orange/brown). flickr.com/photos/4133183…
Then there's about a gazillion quilts out there that resemble Penrose's P1 tiling but aren't. These are "millefiori quilts" or more specifically the "La Passacaglia Quilt". You can buy templates to make one but it looks way too fiddly for my taste. amazon.com/Passacaglia-Qu…
These lookalikes often exhibit five-fold symmetry but don't adhere to the tiling rules that guarantee the aperiodic nature of true Penrose tiling, like this nice 2003 example from cosman.nl/slide_en.php?p…
Update: this quilt sold less than 10 minutes after I tweeted it out. Good grab, savvy shopper!
And finally here's my 2021 Penrose tiling quilt once again:
It's pretty distinctive even among the many examples I dug up!
Features P2 tiling vs the predominantly P3 majority. And the composition is not radially symmetrical, so it draws they eye all over. Also notable are clear outlines for kites/darts.
Whereas most are hand-sewn using EPP, mine is machine-sewn using FPP. By making modules or blocks based on half-tiles I'm able to find long straight seams to join it all together.
The seams are chosen and sequenced by a program I wrote that builds a binary space partitioning tree (BSP tree) out of a collection of half-darts and half-kites of various sizes.
<derail> If you're a coder (as many of my followers are) you may recognize BSP's as the data structure used for the renderer in the original Doom (1993) video game. See fabiensanglard.net/doomIphone/doo… or @fabynou's excellent "Game Engine Black Book: Doom" for more details! </derail>
I'm especially pleased with my final results because I never made a single quilt before January 2021!
I learned to sew during the pandemic to relieve @EmmmilyGZ from mask fabrication duty and my first few attempts at piecing were almost comically bad...
Commonalities between the write-ups that I posted above seem to be that A) Penrose quilts push quilters to grow and learn new skills, and B) if you make one Penrose quilt, it's not unlikely that you'll make a second one, or at least some other fussy geometrical abomination.
So be sure to stay tuned to this twitter feed for more future Needlessly Complex™ quilting projects.
OK, logging off now, Laverne is yelling at me that the thread is too damn long! /FIN
PS: if you want to follow my Penrose quilt project from the very beginning, start here:
For many geometric problems, if they're simple to solve in the Euclidean plane, there's also a simple solution on the sphere.
Others are MISLEADINGLY SIMPLE on the plane and yet SURPRISINGLY THORNY on the sphere.
Here's a little story about the second kind of problem... 🧵
SETUP: We have two points p1 and p2, and two tangent directions u1 and u2. We want to construct a pair of arcs (segments of circles) of equal radius that pass through the given points with the given directions, and that are also tangent to each other, like this:
(Yes, this is a spline problem. I LIKE SPLINES, OKAY? DEAL WITH IT.)
Anyways, the first thing we're going to do is construct the two lines passing through p1 & p2, perpendicular to u1 & u2 respectively. Let's call them ℓ1 and ℓ2:
As the vast majority of US colleges and universities have announced plans to reopen in the fall with substantial on-campus attendance, let's take a moment to imagine what might happen this fall term... (THREAD)
There will be large outbreaks at some schools and surrounding communities attributable to student gatherings (this is already happening BTW). There will be outbreaks among facilities and dining staff who – unlike some lucky faculty – won't be given the option to work remotely.
A few institutions will escape the worst of the pandemic with no mass infections. In some cases this will be due to effective preparation; in others it will be sheer dumb luck.
ML is like pesticide, can be super handy but maybe think twice about using it on people
In case anyone wants to engage more deeply than this shitpost, let me refer you to a few others who have considered this more thoroughly and written about it more eloquently than me: