Iterating Fractals

Print Friendly, PDF & Email

A fractal is a geometric shape that is self-similar, meaning that the shape can be split into parts that represent the whole, by using iterating equations.


Fractals are on the cutting edge of mathematics, because deep exploration of their properties was not possible without modern technology.


This experiment will use computers to examine how the famous Mandelbrot set can be manipulated in fractals.

What You Need:

  • Computer
  • Fractal software (available free online)
  • Printer

What You Do:

  1. Download fractal-producing software on your computer.
  2. Select Mandelbrot set as the fractal formula.
  3. Change the number of iterations to 1.
  4. Print the resulting image.
  5. Go back to the options and change the number of iterations to 2, and print this image out.
  6. Repeat step 5, increasing the number of iterations (5, 10, 20, 100, 1000, etc.) and printing out each image.
  7. Now you can compare the images. What’s the effect of altering the iteration? How does the image change? Does the fractal become bigger or more complex with each iteration?

Find Fractal Software: HERE

For more great ways to teach your kids about math (including fun games and worksheets), visit!