MA-351 Homework 4
Tuesday, Nov 18, 10:15am, in class.
Solutions may be submitted in person in class,
or you may email an ASCII text,
Maple Worksheet (.mws),
html,
or postscipt/pdf-formatted document to me.
Note my office hours on my
schedule.
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Please list all strings with 4 left and 4 right parentheses where the
parentheses are balanced. Then for each string give a unique full
(= all non-leaf vertices have 2 children) binary tree with 4 non-leaf
and 5 leaf vertices.
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Please consider the following variant to Fibonacci's rabbits' problem.
Each pair of rabbits takes one month to mature.
Once mature, the pair has one or two pairs of rabbits after every month
of gestation. Therefore, it takes a newly born pair 2 months
to produce offspring. The number of pairs is produced
alternatingly: first one pair, then two pairs then one pair, then two pairs, etc.
An additional twist is that the pairs only live 5 months,
i.e., die after the second litter of 2 pairs.
Please give a L-system [note the correct spelling:
A. Lindenmayer, J. Theoret. Biol., vol. 18, 1968, pp. 280-315]
that models the growth and show the first 7 generations of applying your rules.
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DMM §3.6, Problem 13, page 168.
Note that your coloring also needs to include the
country "11" surrounding countries 1-10.