# Homework #7

1. (Refer to pg. 298-301 of the text.) Write a program which implements the chaos game for the Sierpinski gasket (marker points (0,0), (1,0), (.5,cos(pi/6))). Demonstrate your program. (Submit both the code and the demonstration.) Comment.

2. (Refer to pg. 298-301 of the text.) Write a program which implements the chaos game for the Sierpinski gasket (marker points (0,0), (1,0), (.5,cos(pi/6))) with a 2/3 probability of choosing (0,0) and a 1/6 probability for each of the other two markers. Demonstrate your program. (Submit both the code and the demonstration.) Comment.

3. (Refer to pg. 298-301 of the text.) Write a program which implements the chaos game for the Sierpinski carpet. Demonstrate your program. (Submit both the code and the demonstration.) Vary the probabilities; comment.

4. What are the advantages and disadvantages of using IFS codes for image compression?

5. Use several examples to show that an affine map Ax+b contracts or dilates areas by a factor of |A|. Is |A| the contractivity factor s? Verify in each case that |A| is equal to the product of the eigenvalues of A. How does this show up in the action of the Hutchinson maps for the Sierpinski triangle, Sierpinski carpet, and Cantor set?