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