Chaos, Fractals, and Dynamical Systems
Assignment #8
due Monday, December 6th

Read 15.1, 15.2, 16.1, skim 16.2 and 16.3, read 16.4

p. 218

1.  ade   Answers should be in the form x + iy.
2.  abde
3.  abde
5.  abcd
9  (just show that -1 + i is on a 2-cycle, and use the Fractal Microscope on the appropriate Julia set to determine whether the cycle is attracting or repelling)

Use the Fractal Microscope to finish Experiment 16.5 on p.238-9.  Remember that to get to the Julia set applet, you have to select "Show me the Julia set" at the first screen, then click somewhere in the picture to get to the Julia set.  Write a one-paragraph essay as described in the Results section.

Go to my Julia Quilt page.  The idea is to make lots of little Julia set pictures and get an idea of how they change as c changes--a sort of catalog of Julia sets.  The Julia sets pictured are for the x and y values indicated on the table.  Use the Fractal Microscope to generate 32x32 pixel pictures of the Julia sets for the 8 squares where your initials appear, and email me the pictures.