2023-05-08 7 min read

Notes, 2023-05-08

Notes, 2023-05-08
A Penrose tiling pattern, showing local deformation from left to right but maintaining its aperiodic and tessellation qualities. Image via Richard Welberry.

Although I’m not really the kind of programmer that knows any math, or the kind of artist that makes anything visual, I’ve always been fascinated by geometric patterns. Like any first year art student, I was obsessed with MC Escher’s repeating (and spooky) mutating forms. Among other motifs, Escher created tiling patterns made up of familiar shapes (a squirrel, a fish, a person) that fill a plane with no overlaps or gaps. This kind of tiling is called a tessellation. Lots of shapes can be tessellated. Think of a piece of graph paper: in geometry we might say that it is tessellated with square tiles, which are arranged edge to edge in a repeating pattern, and are therefore periodic. Triangular and hexagonal tiles can also be used to create periodic tessellations, but where it really gets interesting is aperiodic tessellations, in which the tiles are rotated and flipped as they spread across space, leading to a pattern that never repeats itself. Only a few shapes have been found that can do this; the most famous aperiodic tessellations are the Penrose tilings, which seem to morph and evolve as they propagate.

Roger Penrose developed his three original tilings in the 1970s; two of them use two tile shapes each, and the other uses six tiles. Since then, mathematicians thought that it might be impossible to create an aperiodic tessellation with only one type of tile, which was dubbed the “einstein problem” (“einstein” translating to “one stone” in German). Recently, however, a team of researchers discovered a single tile that can be aperiodically tiled, which they call a “hat” tile, and my mind is racing with possibilities. The shape can have rotational and reflective symmetry, which feels odd: it's hard to imagine a pattern made out of familiar shapes like rhombuses and triangles fitting together in a way that never repeats. There are a few variations of the 13 sided shape, and I’ve been playing with this tool to explore how they work. Aperiodic tilings might seem like just a fun geometric quirk, but they have been useful in understanding quasicrystals, which lack a regular repeating pattern and therefore have unique material properties. Beyond creating great visual art, I’m excited to see what material science discoveries this work can lead to.

-lee wilkins

The most clicked link from last week's issue (~6% of opens) was a film about Mohawk ironworkers. In the Members' Slack, we're planning a Toronto meetup on 2023-05-11. If you're in the GTA, join us!

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  • There is a beautiful, ornate fire station a few blocks away from my home. The other day on a whim, I knocked on the door and ended up getting a private guided tour from an elderly volunteer. They had a demo set up of how the telegraph and fire systems were connected throughout Montreal in the early 1900s, and the hardware design was stunning! The electromechanical systems all had visibly moving wheels and cams, set inside ornately designed metal frames. Early fire alarms used a complex system of telegraph wires and indicators called Gamewell Fire Alarm Boxes. A fire alarm could be pulled in  fireboxes set up on street corners, which were connected via telegraph wire to a fire station or watch tower, and the location of the pulled alarm would be indicated at the station by a number or light. A printed ticker-tape would be then used to pinpoint the location in the city. This video shows a beautiful example of how the system works together. I also love this YouTube channel, which details all kinds of vintage fire alarms.
  • FTDI is a popular brand name of adapters that are used to connect serial devices to USB. USB is commonly used for consumer applications, and serial connections such as RS-232 are often used for industrial applications. If you want to load firmware from your laptop onto a microcontroller, it’s likely that you will need an adapter, and FTDI is generally the go-to brand for this task. In 2014, in an attempt to curb the overwhelming number of fake FTDI chips on the market, they released a driver update that bricked any device that had an FTDI-cloned chip. The company tried a similar tactic in 2016 in an attempt to stop hardware clones.


I recently watched The Colour of Ink, which follows artist Jason Logan as he produces a series of custom inks for artists around the world. Logan makes inks out of basically anything, but one of my favorites is a simple, brilliant and unexpected blue that is made by soaking copper in vinegar to produce copper oxide. In fact, copper oxide was used in the very first synthetic pigment, Egyptian Blue, which was made from a mixture of silica, lime, copper, and an alkali. The recipe for Egyptian blue was lost for thousands of years, so most European painters used an expensive ultramarine blue (made from crushed lapis lazuli) until Prussian Blue was developed in 1706. Prussian blue is remarkable not only for its long-lasting color fastness, but also for its use as a medical treatment for people who have ingested thallium or radioactive cesium. It is also known as “Engineer’s Blue” (used for marking metal during the hand scraping process we described a few weeks ago) and is also a household item for whitening fabrics.

One of the more magical things about the inks Logan creates in The Colour of Ink is that they aren’t necessarily replicable, and often are more focused on a conceptual element rather than the specific color output. In particular, he explores different types of black inks, each of which he describes ephemerally rather than quantitatively. One of these black inks was made for the Japanese artist Koji Kakinuma out of a magnetic rock called magnetite, which is harvested from Ontario lakes. This got me thinking about the Ostwald color system, which explores color wavelength, purity, and luminance. There are a ton of ways of describing color, but I really appreciate Logan’s commitment to qualitative assessment.


My friend Tricia is an artist who makes paper embedded with debris collected from specific places, which she uses to make abstract maps. She invited me and a group of artists to her studio to see what we would create. Paper can be made from just about any fibrous material which can be wetted and then pressed into a fine sheet, and it can be embedded with anything that can be held within the fibers. I brought with me a broken multimeter to see if I could embed it into paper somehow. It didn’t work, but was a great exercise.

One thing that fascinated me about the deconstruction process was the beautiful array of concentric arc-shaped conductive traces on the board underneath the knob on the front of the multimeter. These are called encoders, and are used to tell what position a knob is at. In contrast to incremental encoders, which use digital logic to measure how far something has turned, absolute encoders like the one I had have a unique pattern of traces at every position. While some absolute encoders use binary numbers to determine their position, another similar system called Gray code is also often used. Gray code looks similar to binary, but only one number changes with every increment. For example, in binary, 1 is “0001”, 2 is “0010”, but in Gray code 1 is “0001”, and 2 is “0011”, making it easier to increment because we only need to change one digit in the sequence, rather than two in binary.


  • Carthusian monks have brewed Chartreuse, a legendary liqueur, since 1737. It is based on a secret from 1605 that is fabled to be an “elixir for long life,” containing at least 130 herbs, plants, and flowers as imagined, apparently, by medieval alchemists. Today, the only people who know the full recipe are three monks, and two of them only know half the recipe. In 2022 a growing shortage of the liquor became evident, but it's only recently that the monks confirmed that they’ve been limiting production to focus on their religious duties.
  • Norton Space Props is a unique LA business and a well-known source for sci-fi props. What makes Norton so amazing, though, is the fact that most items there are legit aerospace paraphernalia. This treasure trove of artifacts has been used by designers and artists to create tons of movie and TV sets. Even more interesting, though, is the fact that many startups in the rapidly growing space industry have begun to buy up their discarded components in order to reverse engineer them to get an edge on their competitors. Somewhat related to space junk, I love this zine about poop on the moon.


I’m obsessed with explaining the basics of electronics, because I feel like they are taken for granted in the learning process. I love to see videos like this deep dive into resistors, that goes over everything from how a resistor is put together to when you’d likely need one. Although most through-hole resistors look similar, made of either resistive wire, carbon film, or metal oxide, some of my favorites are liquid resistors, which are often used in large induction motors. I also like this explainer on how to make your own resistors, if you’re in a pinch.


Thanks as always to Scope of Work’s Members and Supporters for making this newsletter possible. Thanks to Kyle, Tricia, and Alex for discussions on encoders, ink, and paper that inspired me to think more about everyday things.

Love, lee

p.s. - I’d love to hear about your favorite geometry – please send me an email if you want to talk about it!

p.p.s. - We care about inclusivity. Here’s what we’re doing about it.

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