*What do you plan to investigate?* The relationship between the
number of lightning strikes necessary to completely burn a forest and
the density of the forest.

*Why did you choose to study this?* To see the relationship
between forest densities and destruction of them due to lightning
strikes.

*How will you conduct your investigation?* Introductory research
on Forestry Management Techniques followed by student predictions,
hypotheses, and activities culminated with the data collection and
analysis using the computer program "Blaze".

As the density of a forest increases, the number of lightning strikes needed to destroy the forest will decrease.

overhead transparency sheets marked off in a 12 by 12 grid

Sets of 12-sided dice

1 green and 1 brown marker

Blaze Computer Program

Fractal Dimensions Computer Program

Graphical Analysis program

LCD panel

Overhead projector

Teacher demonstrates the rules, through simulation, on how lightning strikes and travels through forests of varying densities.

**Part 1:** Use the 12 x 12 grid and markers to set up a forest
representation by flipping a coin place a tree or a rock in each grid.
What is the probability of placing a tree in a square?

Use the 12-sided dice to determine an ordered pair for the location of the lightning strikes. Mark out all trees destroyed by each lightning strike. Record the number of lightning strikes. Continue until the forest is destroyed.

Compare your data with your classmates. Record the data on the board for the entire class and make summary statements on the class data.

Predict what would happen if there was only a .25 probability of having a tree in each square. How would this impact the number of lightning strikes necessary to destroy the forest?

How could you design an experiment to test your hypothesis?

Please run this experiment and record your data.

Compare your data with your classmates by recording the data on the board for the entire class and make summary statements on the class data.

Compare the .5 data and the .25 data.

Draw conclusions about your work thus far.

**Part 2**

Using the computer program "Blaze", determine how the density of the forest affects the number of lightning strikes necessary to destroy the forest. Choose 40 for the tree size to get a 12 x 12 tree grid.

Select a probability and use random lightning to destroy the forest. Select three other probabilities to measure.

Repeat each probability setting four times. (NOTE: Save the burn pictures from each probability setting for fractal dimension analysis).

Save data about the number of lightning strikes on the data chart. Graph this data using average number of lightning strikes vs. probability. Compare your results with your classmates. Graph the class data on the board.

Determine fractal dimensions for each saved picture using the "Fractal Dimension" program. Graph fractal dimension against probability. Compare your results with your classmates. Graph the class data on the board.

1. What factors contribute to randomness in real forests?

2. Compare the shape of the lightning strikes to fractal shapes. Is there a relationship between these two factors?

3. Summarize and draw conclusions as to any relationships between forest density and the corresponding fractal dimensions. Relate this to the lightning strikes.

4. Compare and contrast these simulations and the parameters to real life situations.

5. How might this activity relate to real life forest management and fire fighting techniques?

6. How did the cluster size of the forest change with the change in probability?

**
Final Note:**

Finish this activity with a written summary of your work and complete your laboratory report with all required sections.

**
Extension 1:**

Can you calculate the greatest number of trees you can place on the grid to record the greatest number of lightning strikes?

Can you do this mathematically?

Would the rules change if you change the grid size? (i.e., even by even; odd by odd; even by odd).

**Extension 2:**
Change the tree size and repeat the experiment.

**Extension 3:**
Vary the dryness and repeat the experiment.

**
Extension 4:**
Allow the students to decide on other variables and test them.

**
Extension 5:**
Analyze the log-log graphs of lightning strikes vs. fractal dimensions.