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Math 331, Fall 2004, Due Monday, Nov 15
- 1.
-
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 turtle describes after 10 and after 100 seconds.
- 2.
-
Consider the recursively defined sequence
Sn = Sn-12 -4 Sn-1 + 6 for ,
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.]
Extra credit: rewrite the recursive procedure adding option remember and
see the difference in terms of computational speed.
- 3.
-
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.]
- 4.
-
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.]
- 5.
-
Write a TurtleCmd procedure that draws the n-th
approximation of a fractal of your choice (not one saw in class) and
calculate its box-counting dimension.
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Moira Chas
2004-11-08