SimuLab 16: Modeling a Scattered-Seed Forest

 You need the Blaze program to complete this SimuLab. You can download it to your computer or use it online in a Java applet. Download Blaze: Java Mac OS 7.x Windows 95/98/NT/2000

Now play Blaze, the computer game of forest management and fire fighting. Here is how the game works. You are responsible for growing and harvesting trees on a plot of land. The more trees you harvest, the higher your income. Unfortunately, your forest is located in a high-risk fire region; when the forest is grown, a blaze begins along the left edge. The more trees survive the fire, the more your profit.

The Blaze program allows you to select the density of tree growth, the probability, labeled p, that a tree will grow on each site. In the preceding activity, you flipped a coin, so the probability was one half, or p = 0.5. In Blaze you can select the value of p between 0 (no trees) and 1 (a tree on every site). You can also select the dryness of the forest, which determines how fast the fire spreads.

What value of p, the tree probability, should you use? If you plant trees at low probability, trees will usually be separated from one another (low density), so the fire will not spread. As a result, not many trees will burn, but you won't harvest many trees either, since there are not many trees altogether. On the other hand, if you use a high tree probability, the trees will typically be next to one another (high density), fire will spread across the forest, and again you won't have much of a harvest. The trick is to find a particular tree density (a particular probability p) that gives you the chance for a large harvest but allows you to control the spread of fire.

In addition to controlling tree density, you can fight the fire by dumping water on individual trees. Your job is to maneuver your helicopter and drop water to stop the spread of the fire. The helicopter moves to the position where you place the cursor and drops water when you click the mouse. Any tree that you dump water on does not burn. The idea is to wet trees ahead of the fire to stop it from spreading. You have a limited amount of water to dump on the forest.

When the fire has burned out, your score is shown in the lower right of the screen. The score depends on the number of unburned trees and the dryness of the forest.

 Q7.4: If you are using these materials in a classroom setting, as many class members as possible should try the Blaze program, selecting different tree probabilities and dryness settings in order to win the highest score. Get the whole class together and discuss your results. Who got the highest score? Did this person have a strategy, or did it just happen? Was there more than one winning strategy? Go back to the game and test the strategies. Does the strategy work for other players? If there is more than one strategy, which one is best?

 Q7.5: What is the largest tree probability p at which you can keep the fire from reaching the opposite side (right side) of the forest, no matter how effective your strategy? Do you "run up against a wall'' at some value of p, finding it impossible to keep the fire from crossing the forest for higher values of p?

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