Saturday, November 13, 2010
After coming across a TED talk by Benoit Mandelbrot on Pat's blog, I had fractals on the brain and I eventually returned to an old problem of trying to construct the dragon fractal in Sketchpad. The construction of the dragon fractal was first described to me as follows: start with a line segment. Rotate it 90 degrees about one endpoint. Rotate the figure 90 degrees about its endpoint, always using the newest endpoint as the pivot. Repeat. This I tried several times in Sketchpad. I could do it one iteration at a time using the rotation, but I could not utilize the "iteration" construction because I couldn't figure out what iterated to what. If you would like to wrestle with this part of the problem, stop reading and give it a try.
It may in fact be possible to describe the iteration in terms of the rotation definition of the curve, but eventually I gave up and consulted the internet, where I quickly found this nice page by Shannon Umberger. I learned that the dragon fractal has another definition that is far simpler to employ in the statement of an iteration rule. After that, I started to poke around with some other fractals. In GSP, once you define an iteration rule, you can change the number of iterations using the + and - keys.
Posted by Nate