Math 331, Fall 2002: Problems 21-24

(expires 11/22)    [No Maple] Compute the box counting dimension of the fractal in the figure below:

Image SelfSimFractalThree

(expires 11/22)     Suppose that a turtle is moving with constant velocity 1 unit/sec. The turtle is told, every second, to steer right by an amount equal to $t^2$ degrees, where $t$ is the time (in secs). (For example, after the first step, it turns right 1 degree, then after the second, turn right by 4 degrees, and so on.) Draw the curve the turtle describes after 10 and after 100 seconds.

(expires 11/22)     Consider the recursively defined sequence

S_n = S_{n-1}^2 -4 S_{n-1} + 6

for $n \ge 1$, with $S_0=5$. Implement this in Maple using both a recursive and a non-recursive procedure. [Hint for the computation of the non-recursive formula: complete the square.]
Bonus: rewrite the recursive procedure adding option remember and see the difference in terms of computational speed.

(expires 11/22)     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.]

MAT 331 2002-11-13