7.2 - What Do You Think?

 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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