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 n$ \ge$1, 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.



 


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1999-12-09