We’ve just completed Week 8 of the Fall semester, so it’s time for the next update on my Mathematics and Digital Art class! As I had mentioned before, the major difference this semester was starting with Processing right from the beginning of the semester.

It turns out this is making a really big difference in the way the class is progressing. The first two times I taught the course, I had students work in the Sage environment for the first half of the semester. The second half of the semester was devoted to Processing and student projects.

Because students only started to learn Processing at the same time they were diving into their projects, they were not able to start off with a Processing-based project. As it happened, a few students actually incorporated Processing into their final projects as the second half of the semester progressed, but this was the exception, not the rule.

But last week, we already started making movies in Processing! Starting simply, of course, with the dot changing colors.

This was a bit easier to present this time around, since we already had a discussion of user space vs. screen space earlier in the semester. So this time, I could really focus on linear interpolation — the key mathematical concept behind making animations.

Next week will be a Processing-intense week. I’ll delay some topics — like geometric series — to a little later in the course so we can get more Processing in right now. The reason? I really think many students will involve Processing in their final projects in a significant way. I want to make sure they have enough exposure to feel confident about going in that direction for their final projects. I’ll let you know what happens in this regard in my next update of Mathematics and Digital Art.

Now for some examples of student work! For the assignment on iterated function systems, students had three different images to submit. The first was a Sierpinski triangle — I asked students to create an image simultaneously as close to *and* as far away from a Sierpinski triangle as possible. The idea was that a viewer should recognize the image as being based on a Sierpinksi triangle, but perhaps only after staring at it for thirty seconds or so.

This is Sepid’s take on the assignment. On many of her pieces, she experimented with different ways to crop the final image. This has a significant effect on the image’s final appearance.

This is Cissy’s submission for the Sierpinski triangle. In this piece (and the others submitted for this assignment), Cissy remarked that she really enjoyed experimenting with color. I commented that I thought color choices were among the most difficult decisions to make as far as elements of a work of digital art are concerned.

The second piece was to involve only two affine transformations. This is often a challenge for students, but there really is an enormous variety of images that may be created using just two transformations. In addition, one of the transformations needed to involve a rotation by a non-trivial angle (that is, not a multiple of 45°), and students needed to submit a picture of their calculations as well.

One student was trying to create an image that looked like an animal footprint. She remarked that she did consider a different color palette, but in the end, preferred to go with monochromaticity.

Interestingly, Terry also used a simple color palette. She remarked that it was challenge to use just two transformations — and because of this minimalist requirement, decided to go with a minimalist color palette. In addition, her resulting fractal reminded her of birds, so she set the fractal against a white moon and gray sky.

For the third submission, there were no constraints whatsoever — in fact, I encouraged students to be as creative as possible. There was a *very* wide range of submissions. One student was fairly minimalistic, using a highly contrasting color palette.

Jack’s piece was also fairly minimalistic. I should remark that we took part of a lab one day for students to do some online peer commenting; Jack (and others as well) remarked that he used the advice of another student to improve an earlier draft of his piece. In particular, he adjusted the stroke weight to increase the intensity of the colors.

Tera based her work on the Sierpinski triangle, but *also* included reflections of each of the three smaller components of her version of the Sierpinski triangle. She remarked that the final image reminded her of a snowflake, or perhaps a Christmas sweater.

Alex’s inspiration came from *The Great Wave off Kanagawa*, by Katsushika Hokusai.

First, he created the fractal image, experimenting with various color combinations. When he was satisfied with his palette, he added the boat and the white circle to suggest a black moon. A rather interesting approach!

As you can see, I’ve got quite a creative class of students who are willing to experiment in many different ways. It’s interesting for me, since there is no way to predict what they’ll create next! I look forward to seeing what they create when they really dive deeply into Processing and begin making animations.

In the next update, I’ll report on how students involve Processing in their project proposals. In addition, they will have submitted their fractal movie projects by then, so there will undoubtedly be many interesting examples of student work to exhibit. Stay tuned!

It sounds like an interesting class, Vince.

I have always been interested by the strong emphasis mathematics has on computer graphics.

Your blog post has certainly deepened my curiosity!

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