Homework 8

Homework 8: Due Friday 8 March

Please hand in all work on separate paper -- please don't hand in your work on the photocopied worksheets.

Lesson 2: Complex Linear Iteration

Lesson 3: The Squaring Rule

3
4
5
6 Optional

For the next several exercises, you'll need a computer to make Julia and Mandelbrot sets for you. Here are some java applets you can use.

http://math.bu.edu/DYSYS/applets/M-set.html. Lets you click on the M-set and get the corresponding Julia set.
http://math.bu.edu/DYSYS/applets/M-setIteration.html. Will let you see what happens to the orbit of 0.
http://aleph0.clarku.edu/~djoyce/julia/explorer.html

Lesson 4: Julia Sets of Quadratic Iterations

3
4 (Don't actually do the computation. Look at the shape of the Julia set instead.)

Lesson 5: The Mandelbrot Set

Write a paragraph or two in you own words in which you explain what a Julia set is and what the Mandelbrot set is. Rather than giving a formal definition, it might be easier to give directions describing how they're calculated.

[Dave] [Chaos and Fractals] [Homework Page] [COA]

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