Fractals & Chaos Recap for 9/26

We discussed Ivars Peterson’s Ants in Labyrinths at the start of class, noting some interesting passages and talking about questions we had. In particular, I made a note to remember the part towards the beginning, where Peterson suggests an interesting problem with measuring a particular coastline:

Finer and finer scales reveal more and more detail and lead to longer and longer coastline lengths. On a world globe, the eastern coast of the United States looks like a fairly smooth line that stretches somewhere between 2000 and 3000 miles. The same coast on an atlas page showing only the United States […] seems more like 4000 or 5000 miles. […] A person walking along the coastline, staying within a step of the water’s edge, would have to scramble more than 15,000 miles to complete the trip.

This is an important idea. Remember it! We’ll be revisiting it later in the course.

The rest of our time in class was spent working on our fractal designs in FractaSketch. Don’t forget the expectations for the soon-to-be-announced Fractal Art Show! I expect from each of you one entry in three of the following categories:

  • Fern
  • Tree (or shrubs, bushes, weeds, etc.)
  • Spiral
  • Realistic (other natural phenomena)
  • Artistic (patterns, designs, etc.)

Again, each student will be submitting three entries, each falling in a separate category. You are welcome to submit more designs if you would like, but they will be placed in a separate “Additional Works” category.

Please feel free to work on your designs outside of class and transfer them to the laptops we’ve been using in class.

Homework: Read On Being the Right Size, an essay written by biologist JBS Haldane in 1926. We will discuss this reading tomorrow. As you read, ask yourself this classic question from the Internet: “Which would you rather fight: one horse-sized duck or 100 duck-sized horses?”

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