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Geometry

Swirled Series: The Result

Early in November, Daniel Piker (aka @KangarooPhysics) suggested that a group of people could get together online, and each create a short segment of animation, arranged so that all the start and end frames are identical. We could then assemble all the segments into one long loop and enjoy each …

Swirled Series

This fall, as a creative outlet during a challenging teaching term (and as a distraction from the general mess of the world), I began posting weekly looping animations on Twitter, under the hashtag #swirlysquaresunday. The idea was to find creative expression under a tight set of aesthetic constraints: a looping …

Mathematical Animated GIFs

I’m freshly back from a weekend in Toronto, where I was participating in the Winter meeting of the Canadian Mathematical Society. I don’t normally attend math conferences, but this time around I was invited to a session entitled “The Art of Mathematics”, and it seemed natural to join in. As …

Andromeda Reimagined

I first learned of Burning Man from The Happy Mutant Handbook, a book of mayhem and counterculture that called out to me one day from a bookstore shelf. I’ve never participated in the festival, and probably never will, but I know many people who have and I suppose it has …

Escher-like Spiral Tilings

The artist M.C. Escher drew many lovely tilings, which he called “regular divisions of the plane”. He worked hard to ensure that his tilings were of lifelike animal forms such as birds and fish. He filled notebooks with hand-drawn sketches of tilings, many of which later found their way into …

A Molecular Near Miss!

I’m thrilled to report that I’m a co-author of the article “An ultra-stable gold-coordinated protein cage displaying reversible assembly“, which was recently published in Nature. This work is the result of an exciting collaboration between biochemists, physicists, structural biologists, mathematicians, and others (including yours truly, a computer scientist!), spread over …

Hexagonal Cross Stitch

At least year’s Bridges Conference in Stockholm, I attended a short presentation by Susan Goldstine about “self-diagramming lace”. As motivation for the new work she was presenting, Susan referenced her paper from the year before on what she calls “symmetry samplers”. Samplers are an old tradition in fibre arts. A …

The Tactile libraries

I developed a new open-source software library for manipulating isohedral tilings, based on the work I did on this topic during my PhD. The library is available in C++ and Javascript, and I offer a few fun automated and interactive demo programs that anybody can use to play with isohedral tilings.

Heesch Numbers, Part 4: Edge-to-Edge Pentagons

This post is the fourth and final one in a series about Heesch numbers. ¬†Part 1 was a general introduction, and would be a good starting point if you’re unfamiliar with the topic. Part 2 covered exhaustive computations of Heesch numbers of polyominoes and polyiamonds, and likely isn’t needed to …