Fifth homework set
Due at the beginning of class on Thursday, Mar 3. No late homework will be
accepted.
Fold your homework paper vertically and PRINT your name on the outside.
1. Suppose C is a Cantor set consisting of N = 2 pieces scaled by r. Find the
v

Second homework set
Due at the beginning of class on Thursday, Feb 11. No late homework will be
accepted.
Fold your homework paper vertically and PRINT your name on the outside.
1. Find IFS rules for this fractal. For reference, the fractal is enclosed in

Sixth homework set
Due at the beginning of class on Thursday, Apr 7. No late homework will be
accepted.
Fold your homework paper vertically and PRINT your name on the outside.
1. Suppose we build a randomized gasket with these scalings:
(
1/2 with prob 1/

Third homework set
Due at the beginning of class on Thursday, Feb 18. No late homework will be
accepted.
Fold your homework paper vertically and PRINT your name on the outside.
1. Can this fractal be generated by an IFS with 1-step memory (forbidden
pairs

Eighth homework set
Due at the beginning of class on Thursday, Apr 21. No late homework will be
accepted.
Fold your homework paper vertically and PRINT your name on the outside.
1. How many N = 4 (each neighborhood consists of 4 cells) binary (each cell i

Fourth homework set
Due at the beginning of class on Thursday, Feb 25. No late homework will be
accepted.
Fold your homework paper vertically and PRINT your name on the outside.
1. Compute the exact values of the similarity dimension of this fractal.
2. U

Second homework set solutions
r
0.5
-0.5
0.25
0.25
1.
s
0.5
0.5
0.25
0.25
0
0
0
90
0
0
0
90
e
0
1
0.5
0.25
f
0
0.5
0
0.75
2. Inspecting the IFS with memory images with length 2 address squares superimposed, we see that for (a) the forbidden length 2 addre

Seventh homework set
Due at the beginning of class on Thursday, Apr 14. No late homework will be
accepted.
Fold your homework paper vertically and PRINT your name on the outside.
1. (a) Show that x = 3/4 is a fixed point of L(x) = 4x(1 x).
(b) Show that x

Ninth homework set
Due at the beginning of class on Thursday, Apr 28. No late homework will be
accepted.
Fold your homework paper vertically and PRINT your name on the outside.
1. Show that c = 2 and c = i are Misiurewicz points for zn+1 = zn2 + c, and
sh