Reading: pg. 297-352
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?
Maintainer: leader@rose-hulman.edu.