Quantum to Cosmos 2009

In 2009, the Perimeter Institute in Waterloo, Ontario celebrated their ten-year anniversary by hosting Quantum to Cosmos, a large science-themed festival. The event consisted of talks, panels, live music performances, a large science exhibit, a film festival, and probably many other things besides. As someone who has worked on academic outreach activities from within the university, I can only envy the scope and excellence of their efforts.

I was lucky enough to have been invited to give a talk as part of the festival. I spoke on some of my favourite examples of mathematical art, including two-dimensional patterns, origami, and geometric sculpture. You can view the talk in the embedded player above, or visit the festival's page for the talk. I can't offer the complete slides from the talk for download, since I received special permission to reproduce many of the images from their owners. However, you can download this redacted PDF of the slides (warning: 50MB!), in which most of the images that aren't mine have been replaced by relevant URLs. I hope that's useful.

The audience seemed to enjoy the material, and some of them expressed an interest in finding out more about some of the art and science in the talk. So I've created this web page, in which I collect links to all the art and artists I refer to. I'll also use the page as a repository for errata; if you spot an error in the talk, please let me know and I'll post it here. I tend to work without a net in talks like this one, meaning that I might have recalled details incorrectly.

My goal is not to turn this page into a portal for mathematical art. That's a lot of work, and would require ongoing effort to maintain. So I'll include a few extra links from people who contacted me before or after the talk, but please don't send me more links that you want to see included.

Thanks again to my hosts at the Perimeter Institute for the invitation, and for the excellent support before and during the talk.

Two-dimensional patterns

• Patterns in neolithic Croatian earthenware -- an example of just how far back in time our love of patterns goes.
• Patterns on bronze-age Spanish pottery
• David Wade's Pattern in Islamic Art: an excellent photo archive of geometric patterns from the Islamic world.
• Nic McPhee's CC-licensed flickr set of photos from The Alhambra
• Two examples of the Moroccan Zellij style of Islamic star pattern design, both from fountains: one from Steve & Jemma Copley, and another as part of a set of Islamic patterns by Mike Eddie Jousiffe.
• My work on Islamic star patterns.
• Escher's Relativity in lego, by Andrew Lipson. (It's very hard to get permission to show Escher's art, but this made a great substitute.)
• Jos Leys's gallery of Escher tilings. See also his page of hyperbolic Escher patterns.
• My work on computer-generated Escher tilings.
• I wrote a book that could help you learn tiling theory: Introductory Tiling Theory for Computer Graphics. You might also want to get a copy of Tilings and Patterns by Grünbaum and Shephard. This book has been out of print for a number of years, but it looks like Dover will be re-releasing it at the end of 2009 (hurray!).
• I showed some aperiodic Islamic star patterns I had constructed. Those appear only in my PhD thesis. Other great examples of art in this style can be found on the web pages of Jean-Marc Castéra and Jay Bonner. See also the recent paper by Lu and Steinhardt on quasiperiodicity in Islamic art.
• Roger Penrose's description of the discovery of his aperiodic tilings, together with an image of his "chicken tiling", can be found in this original Pentaplexity paper.
• Doug Dunham has done a huge amount of work on understand and generating hyperbolic Escher patterns. There are many papers and talks to browse on his site.

Origami

• It was fun to be able to show a Bizarro comic, published just days before my talk, on the subject of origami. Thanks to Dan Piraro!
• I showed a large number of images by Robert Lang. Lang is one of the world's most well-known contemporary origami experts, particularly when it comes to the mathematical and computational methods that underlie origami.
• Robert's TreeMaker software is a free package that anyone can use to design crease patterns for complex origami sculptures.
• One of my favourite designs in Brian Chan's Attack of the Kraken, from the 2006 Origami USA Convention. Gilad Arahoni has a large gallery of amazing origami from many artists (including himself) on his web page.
• Recent computer graphics work by Tomohiro Tachi is producing some lovely new designs. See also his flickr page.
• I showed examples of modular origami by etringita and Darkmuse. You can find lots of instructions for making modular origami online, or look for books by Rona Gurkewitz.
• Goran Konjevod's Pureland Origami creates a variety of lovely forms based only on systems of intersecting pleats.
• Joel Cooper also uses pleats to create sculptural works such as human forms.

Geometric sculpture

• There are many sculptors whose work I'd love to have shown. On the opening slide for this section, I slipped in an example of the work of Rinus Roelofs.
• As an historical example, I showed carved stone balls from prehistoric Scotland.
• George Hart is an extremely talented and creative sculptor who works in many different materials. Be sure to look through his sculpture gallery.
• I love the work of Bathsheba Grossman. She sells lovely metal sculptures in various sizes directly from her website.
• I also suggest you take a look at the work of Vladimir Bulatov.

Other artists and links

• If you're interested in contributing to the world of mathematical art, or participating in events, I'll take this opportunity to promote two things I'm involved with. First, check out the Bridges Conference. It's a wonderful annual gathering of artists, scientists and educators interested in mathematical art. I also work on a scholarly journal devoted to the topic, the Journal of Mathematics and the Arts.
• You might also want to look into the ISAMA organization and its conference.
• If you don't have a programming background, one reasonable way to get into mathematical art via computers is to learn Processing.
• Sculptor Helaman Ferguson.
• I got some great ideas from a blog post by Edmund Harriss in his blog Maxwell's Demon. Edmund has created some lovely art himself, and includes links on his blog to other artists worth reading about.
• Sculptor Max Bill is worth reading about. See in particular his essay The Mathematical Approach in Contemporary Art.
• I didn't get a chance to talk about Carlo Séquin, or his long, fruitful collaboration with sculptor Brent Collins.
• Certified Genius Erik Demaine has done all kinds of great work on mathematical art. See, for example, his work on curved origami sculpture.
• I always love looking at Ulrich Mikloweit's beautiful paper polyhedral sculptures.
• While preparing my talk, I became aware of the static and video work of local artist Laura De Decker. She created the video that accompanied the performance by the Penderecki String Quartet at the Q2C Festival. She also pointed me to artist Bill Ralph.
• After the talk, James Gavreau and Anna Pantchev alerted me to some of their work, which was until recently on display at a gallery in Toronto.
• See the work of Kenneth Huff.
• I love the computer-based art of Jared Tarbell.
• One question that arose at the talk was about what sites I can recommend. Obviously, this page is a way to answer that question. In addition, here are some blogs I read regularly that have at least some content related to mathematical art:
  • bit-player
  • dornob
  • Information aesthetics
  • KrazyDad
  • Maxwell's Demon
  • SpaceCollective