MA-351 Homework 4
Thursday, Oct 30, in class.
Solutions may be submitted in person in class or put in my mailbox,
or you may email an
ASCII text,
Html,
or postscipt/pdf-formatted document to me
(kaltofen@math.ncsu.edu).
Note my office hours on my
schedule.
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Consider the formula
(a-b+c)*d/(e*(f+g)).
Please give the parse tree for this expression
according to the context free grammar for expressions given in class.
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Consider the following variant to Fibonacci's rabbits' problem.
Each pair of rabbits takes two months to mature.
Once mature, the pair has two pair of rabbits after every month.
Therefore, it takes a newly born pair 3 months to produce offspring.
An additional twist is that of the two pair one pair is barren
and cannot produce children. The system starts with one freshly
born pair of non-sterile rabbits.
Please give a Lindenmayer system that models the growth
and show the first 6 generations of applying your rules.
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Consider a fractal called the Sierpinski gasket. You start with
an equilateral triangle. Remove the equilateral triangle formed
by the midpoints of the three edges. This leaves 3 equilateral
triangles of the same size at the corners. Recur the procedure
with these triangles.
Compute the remaining area (drawn in black in the above
picture) as a fraction of
the area of the original triangle when this procedure is continued to
infinity.