Math 331, Fall 2002: Problems 21-24

**21.**- (
*expires 11/22*)*[No Maple]*Compute the box counting dimension of the fractal in the figure below: **22.**- (
*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 degrees, where 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. **23.**- (
*expires 11/22*) Consider the recursively defined sequence

for , with . 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. **24.**- (
*expires 11/22*) By using only`TurtleCmd`, draw a random walk of 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