Math 331, Fall 2004. Problem Set 8

1. Compute the perimeter and area of the snowflake.

2 Write a TurtleCmd procedure that draws the n-th

approximation of a fractal of your choice (not seen in class) and

calculate its box-counting dimension.

3. Construct a Cantor set whose box counting dimension is 1/2.

Explain a general algorithm for constructing a Cantor set with

any given box dimension 0 < d < 1

You can do this on Maple or by hand.

4.Write an IFS procedure to draw the

n-th approximation of a fractal of your choice (not one seen in class)

and compute its box-counting dimension.

5 By using only TurtleCmd, draw a random walk of n steps. (In a random walk the turtle takes a step forward, backwards, to the right, to the left, with equal probabilities, and then repeats the process.) [Check rand.]