MAT 331 Homework Exercises. Week 11 (Dec 2, 99).
- #31 (exp. 12/9)
- 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 t2 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 tutle describes after 10 and after 100 seconds.
- #32 (exp. 12/9)
- Consider the recursively defined sequence
Sn = Sn - 12 - 4Sn - 1 + 6
for n1, with S0 = 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.]
Finally rewrite the recursive procedure adding option remember and
see the difference in terms of computational speed.
- #33 (exp. 12/9)
- Draw a fern like the one in page 4:12 of the
notes. (It doesn't need to look as good, but your aesthetic effort will
be rewarded.)
- #34 (exp. 12/9)
- 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.]
- #35 (exp. 12/9)
- Write a procedure that draws the n-th
approximation of a fractal of your choice (not the snowflake!) and
calculate its box-counting dimension. Note the similarity between this
question and the third project.
Translated from LaTeX by MAT 331
1999-12-09