SimuLab 18: Percolating Forests
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: 

2. Choose a tree density, here called p, with a value of 0.500
by using the mouse to click on the numbers. This means that the
probability is onehalf that a given square will have a tree on
it; the same as the probability that a coin flip will be heads.
3. Click on Go and see what happens. A picture of the forest
appears on your screen, with trees shown in green. A fire starts
burning on the left side of the forest and spreads toward the
right. As each tree burns it turns red, then the ashes left behind
turn blue.
4. There is a helicopter in this game that we will use later on
to try to stop the fire from spreading. For now, though, just
watch the forest burn. Don't move the mouse or click it until
the fire burns out.
5. How far does the fire spread across the forest? Does it percolatethat
is, does it reach the opposite side of the grid?
6. Grow and burn more forests using a tree probability of 0.500.
Do any of these forests have fires that percolate? Carry out at
least 10 trials, and note in your lab book what percent of your
trials produce fires that percolate.
7. Repeat the experiment using tree probability p = 0.600. Burn
10 or more forests. What fraction of these p = 0.600 forests have
a fire that percolates?
8. Repeat the experiment using tree probability p = 0.700. Burn
10 or more forests. What fraction of these p = 0.700 forests have
a fire that percolates?
9. Stop and think. Do you notice a significant change in the number
of fires that percolate between probabilities p = 0.5 and 0.7?
Guess: Will the number of fires that percolate be radically different
for p = 0.3 than for p = 0.5? Will the number of fires that percolate
be radically different for p = 0.9 than for p = 0.7? Try a few
at these lower and higher values of p to check out your guesses.
The tree probability p at which approximately half of the fires percolate is called the critical probability. Below the critical probability, the fire is unlikely to percolate, spread across the forest. Above the critical probably the fire almost always percolates.



Now let's go back to the Blaze program and test your skills
as a forest ranger!
2. Your job is to maneuver your helicopter and drop water to stop
the spread of the fire. The helicopter moves toward the position
where you place the cursor and drops water when you click the
mouse button. Any tree that you dump water on does not burn. The
idea is to wet trees ahead of the fire and to stop its spread.
Are there certain placessocalled tree bridgeswhere you can
wet just one or two trees and cut off the fire easily?
3. When the fire is finished burning, your score flashes on the
screen. The score depends on the number of trees you saved, and
the quantity of water used; your score decreases the more water
you use to stop the fire. If your score is 0, you were not able
to stop the fire from spreading. Try again!
