Professor Robert Devaney of Boston University gave two excellent talks to our precalculus classes (consisting mostly of juniors, with a sprinkling of advanced sophomores and freshmen) on Tuesday. His talk to the college-prep classes (”Precalculus Part One”) focused on the use of geometric transformations to create fractals which in turn could become artificial but convincing landscapes in movies. This combination of pure and applied math was a stunning example of real-life applications of what appears to be a highly theoretical piece of pure mathematics.
I only wish the audience had been more consistently respectful. As Bob’s introducer, I happened to be sitting in front, where I got to see a non-representative sample of the audience. The kids near me were not only respectful but were also attentive and engaged. They were duly appreciative when the apparently random activity of the Chaos Game turned into the highly regular Sierpinski’s Triangle, and when Barnsley’s Fern emerged out of chaos. But teachers in the back of the room reported a different cohort there: kids using cell phones, sleeping, talking, etc. Since students sat where they pleased, the distribution was certainly not coincidental. But the question to me is why this audience was so extremely different from the honors math students (see next paragraph). Of course it’s easy to claim that students in honors classes are almost always better behaved than those in non-honors classes, as those who don’t want to take a subject seriously are unlikely to sign up for an honors class. And there is indeed a certain measure of truth in that observation. But it’s clearly not the whole truth. For instance, my non-honors Algebra II class is far more respectful, polite, and better behaved than my D Block Honors Geometry class. I wonder what accounts for these differences; is it merely the chance distribution of students?
The talk to the honors classes was almost entirely about the Mandelbrot Set, although it had to involve some necessary preliminaries about Julia Sets. The students were attentive and learned a lot from this presentation, including some surprising interpretations of “how to count” and “how to add.” Although I had heard almost all of this many times before, there was one important nugget that was brand new to me: how to insert sliders into Excel spreadsheets. The resulting dynamic graph became a wonderful tool for visualizing (and therefore understanding) the chaotic effect of varying a single factor when looking at the orbit as a function is iterated. I will have to try using that myself some time.
Also, as a follow-up, yesterday’s Fractal Fair was extremely successful. Almost all the projects were solid, many were excellent, and we got a lot of visitors of all ages. Stay tuned for a post on one project in particular, a spectacular children’s book on fractals. Here are a few photos, taken by the school librarian: