## Watch it grow complex!

Introduction

Why study fractals?
fractals, anyway?

Fractal Properties
Self-similarity
Fractional dimension
Formation by iteration

For Teachers
Teachers' Notes
Teacher-to-Teacher

Fractals on the Web
The Math Forum

Other Math Lessons
by Cynthia Lanius

Here's another look at the fractal after 4 paper-folds, what the book calls the First Iteration.

What would the fractal look like after another paper-fold? Let's try it and see.

Take the fractal you made and fold it back together as before, then fold once more, five times in all. Unfold and compare to the Second Iteration below.

If you folded the paper again, it would look like this:

If you could fold the paper again, it would look like this:

If you could fold the paper about 50 times, it would look like this:

But of course, you can't fold the paper 50 times, so you let the computer take over the paper-folding process. A computer can't fold paper!?! No, but it can simulate the process.

Next: Look at the real first iteration.