# Another Jump Into Fractals

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). 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):

An IFS Fractal

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):

Apophysis Fractal #1

Apophysis Fractal #2

## 4 thoughts on “Another Jump Into Fractals”

1. I know this is an old post,but I’m very curious to know how the black and white fractal was created with the IFS software. I have been tinkering with it but can’t seem to come up with anything that ornate.

• William,
The IFS software has samples that you can tweak and learn from. It’s rather difficult to come up with ornate ones from scratch, but if you look at the samples’ parameters, you can get some good starting points. Thanks for stopping by!

• I’ve come up with a few nice looking spirals, but I’m still very interested in your example here. How did you get the spiral to straighten out and change direction? Any chance you remember your transformations?

• William,
You’re in luck, I actually saved the file. Here are the parameters:
T1: 0.5 0.5 (blank) 0.68 0.68 3
T2: 0.8 0.8 45 (blank) (blank) 10

Make sure you Run Infinite Iterations