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Iterating Fractals

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Author: Barry Eitel

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

Problem:

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

Materials:

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

Procedure:

  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?
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