On a visit to the Exploratorium this weekend, we were hanging out near the harmonograph, watching kids make really cool pictures, when the Cinema Arts Saturday Cinema program started just across the way. Since the program for this week was titled Geometry in Motion, I told the people I was with that I was going to watch. We all enjoyed the program, and each had a different favorite film. Since most of the five films shown are available to watch for free online, I thought I'd share them with you.
The first was Symmetry from the 1961 IBM Mathematics Peep Shows by Ray and Charles Eames. This one is available in a free iPad app from IBM, but unfortunately I haven't been able to find it elsewhere. It is a very short introduction to formal definitions of symmetry, defining the degree of symmetries of an object as the number of different ways it can be placed in a box that fits it exactly. This made me really want a dodecahedron box, and a dodecahedron to fit in it exactly! I'm not sure I have the construction skills and equipment to make that happen, though. I was also entertained by the cameo appearance of group multiplication tables at the end of this very short film; the reference without explanation felt similar to the jokes in kids' movies that are really aimed at parents.
The second film, Aesthetic Species Maps, is available to watch online from its creator, David C. Montgomery. This film set the tone for the rest of the program, which consisted of basically wordless art films with strong ties to geometry. Each segment was assembled from still images taken of many specimens of the same type of plant of animal, in approximately the same orientation. For me the first segment was the most interesting, because you could clearly see variation of the degree of symmetry between specimens.
The next film we saw I can't find anywhere online. It was Eights by Seth Olitzky, and it used computer animation to play with symmetrical figures in a way reminiscent of kaleidoscopes or screensavers. I stared at a lot of screensavers around the time the film was made, though, and it was more interesting than any of them.
After that we watched a more modern take on computer animated geometry shorts, Nature by Numbers. Etérea Estudios, the creator of this film, has a webpage for it with not just the movie, but also still images from it and a page explaining the mathematics behind it. I'd seen a lot of the material towards the beginning of the video before, whether as the countless fibonacci spirals that had filled my notebooks since we learned to make them in 6th grade, or more recently in this series of videos about being a plant by Vi Hart. At the end, though, I had a big surprise, as a Voronoi tessellation turned a grid of sunflower seeds into a dragonfly's wing. This was my favorite film, so I'll embed it here, too, though if it makes you curious about things, Etérea's website is a great place to start.
The final film, Rectangle & Rectangles by René Jodoin, is available from the National Film Board of Canada. This one didn't directly explore a mathematical concept as much as some of the other, but it was one of the more fascinating films to watch and is even better to watch online. It uses strobe effects and a variety of growing and shrinking rectangles to create an interesting and somewhat confusing visual experience. The Exploratorium loves to create a "Why is this happening?" moment with its exhibits, so I can definitely see why they would show this film! In the theater, I did a lot of fast blinking to try to understand the technique behind the visual effects. I'd love to have a frame-by-frame replay option for this, but the freedom to pause and rewind at will makes the streaming version nearly as good.
Thus ended the film series, and thus ends this post, although we saw plenty of other fascinating things at the museum. I hope you enjoyed these films, and I hope you get a chance to visit the Exploratorium and see some of the other stuff for yourself.
