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Q7.22: If you were the owner of a tree farm, how would
you maximize your profit by growing the largest number
of trees, while taking account of the danger of fire?
The answer depends on the number of tree bridges,
strings of trees that connect one cluster to another.
There are few tree bridges when there are few trees; this
occurs when tree probability p is low. For low p you may
not have to use any water at all: the fire just burns
itself out in isolated clusters of trees. But few trees
means low profit. So try the alternative: grow many trees
by choosing a high tree probability p. But then there
are many tree bridges, so many in fact that you may not
have time to dump water on all of them before the fire
arrives. So most of the trees burn and your profit is
low again.
What is the trick to making a high profit? What tree
density p should you use and why? (To encourage you
to actually save trees, your score in the game is based
on the number of threatened trees that you manage
to save, along with a penalty for the amount of water
used.)
Q7.23: Write an essay on the possible connection between
the microscopic molecular interactions of various concentrations
of Jell-O and the forest program Blaze at various
tree probabilities.
Q7.24: We noticed in the Blaze program that the
forest fire follows the "path of least resistance''
by spreading through a connected network of trees. In
an essay talk about systems in nature that may follow
this same principle and explain the mechanisms involved.
For example, electrons in electrical circuits follow
the path of least resistance: if a circuit breaks off
into two branches A and B where the equivalent resistance
of A is 100 times the equivalent resistance of B, the
flow of electrons through branch A will be 100 times
less than the flow through B. Hint: Thinking of how
fluids flow through sewer systems or how erosion occurs
on a beach may help get you started.
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