Every January, the school where I teach has a 3-week alternative curriculum called Winterim. I teach a short course on fractals during this time. My students have just finished working on some simple Iterated Function Systems (IFS’s) using some software called, surprisingly, IFS 2.0 (free download here). I say simple, because the transforms are limited to scale changes, rotations, and translations, and the outputs are black and white. What’s fascinating about these IFS’s is that those basic transforms can create startlingly organic figures. Here’s an example of one I made using only two transforms (a scale reduction with a horizontal translation, and a scale reduction with a rotation):
You can see my students’ creations here. I am always amazed at how quickly they can figure out how to make beautiful images.
Yesterday, we downloaded and installed another IFS program called Apophysis. (Free download here, and lots of tutorials here.) The difference between Apophysis and IFS 2.0 is like the difference between a Maserati and a tricycle, even though the mathematical principles behind them are exactly the same. I’ve been messing around with Apophysis off and on for about three years now, and I have barely scratched the surface of its capabilities. Right now, we are out of school due to icy roads, but as my students and I make more fractals, I’ll be posting links to them. Anyway, here are a couple of fractals I made with it last night (click on thumbnails for full-size images):