Lesson Scenario - Far Far Away (AgentSheets)

Basic Model:

Description

This is a basic model that simulates a forest fire and the effects of a single spark on the whole population of trees. A spark begins with one tree and spreads to the others after each iteration (time step). The user can adjust the probability that a tree will catch on fire if the conditions for fire spread are met. The model can be used to understand random chance in relation to fire spreading in a forest as well as the actual dangers and uses of fires.

Background Information

The spread of fire in a forest is often times the result of a compilation of factors that essentially make the movement random. As a spark starts in a forest, the trees surrounding it have a certain probability of catching on fire. With increased proximity to other trees-such as can be found in the middle of the forest-comes a quicker promulgation of flames. On the other hand, if the fire begins in the corner of the forest, it initially comes into contact with fewer trees; therefore, not as many trees are likely to burn.

Science/Math

The fundamental principle behind this model is HAVE = HAD + CHANGE. For each time tick, the following things happen:

1. The trees that have been sparked begin to burn
2. The flames spread to surrounding trees
3. The green trees turn to red
4. Red trees turn to black

The red trees in this simulation represent the CHANGE and intermediate state of the equation. Burning trees are the result of the fire interacting with the green trees to produce burned trees.

Teaching Strategies

In order to allow students to best understand this model when using it, ask them to come up with hypotheses to these questions:

1. What would be the initial effect of adding a spark to a tree in the forest?
2. In what way would the fire spread between the trees (exponentially, linearly, etc.)?
3. How would random chance have an effect in the spread of fire in a forest? Is this realistic?
4. 4. In real-life situations, what are some factors that would prohibit the spread of fire in a forest?

These hypotheses should be formed before using the simulation so that the students may test them.

Implementation:

How to use the Model

This model has a few parameters that can be changed in order to affect the outcome of the simulation.

1. The "burnprob" attribute changes the probability that any specific tree will catch on fire if there is an adjacent flame.
2. The user may choose the location(s) for the initial spark(s) in the forest. These will be the starting points for the forest fire.

These parameters are changed by accessing the Simulation Properties from AgentSheets. The numbers of green, red, and black trees are also found in the simulation properties, but they are counts and cannot be directly changed. The initial conditions are taken into account when the simulation is first run. Outcomes from changing these variables may be observed in graph form by clicking on the variable to plot and clicking the "Plot" button in the Simulation Properties. In order to run the simulation, click the green triangle in the bottom left hand corner of AgentSheets. The fire will begin to spread as prescribed by the preset variables. The number of green, red, and black trees at the current time of the simulation may be observed by looking at the Simulation Properties and the graph of each variable. For more information about Agentsheets, reference the Agentsheets tutorial at: here.

Learning Objectives:

1. Understand the random chance that goes into the spread of the forest fire and the probabilities of it spreading to a specific tree.
2. 2. Understand the effect of each parameter on the spread of the forest fire over time.

Objective 1

Students should pay attention to the different outcomes that result from changing the number and position of initial sparks as well as the change that the burnprob variable has on the number of burned trees. With a lower burn probability, the trees are much less likely to catch on fire from a nearby tree. The number of black trees at the end of the simulation should be much greater with a higher burn probability. Therefore, burnprob and total number of trees burned have a direct relationship. Ask the following questions in order to guide the students' discovery:

1. Start the simulation with one spark and a 1.0 burn probability. Rerun the same simulation with one spark and a 15.0 burn probability. What effect does the higher burn probability have on the number of trees burned? Why is that the case?
2. Run the simulation with one spark in every corner and a 15.0 burn probability. What differences do you see from the simulation with one spark? What explanation can you give for this outcome?
3. Graph the number of red (burning) trees. Is this number in the simulation affected by the burn probability at all? Explain.

Objective 2

This objective focuses on the graph of green, red, and black trees over time. Have the students plot those three variables through the Simulation Properties. The graph of the number of green trees should always be inverse sigmoidal with a beginning point of the number of trees-560 in the given model-and a lower limit of 0. The number of black trees should be sigmoidal with a lower limit of 0 and an upper limit of how many trees are burned. The graph of the rate at which trees catch on fire should be parabolic with the peak at the center time of the simulation. The students should explore these graphs and seek to understand the outcomes. Ask the following questions to guide the students:

1. Run the simulation with a 100.0 burn probability and one spark in the center of the forest. What does the graph of green trees look like? The red trees? Why do the graphs have these shapes?
2. What does the peak of the red tree graph signify? Can you see this visually when running the simulation?
3. What do the upper and lower limits of the black and green trees signify? Can you see this visually when running the simulation?
4. If the burn probability is changed to 2.0, do the graphs have the same shape? Why or why not?
5. Place two sparks across from each other in the forest and run the simulation with a 100.0 burn probability. How does the peak of the red trees over time differ from the graph taken with one spark? Do the slopes of the green and black trees over time differ when two sparks are in the system? Explain.

Extensions:

Extension 1

Have students research the positive and negative uses of fires. Specifically focus on surface fires. While forest fires are often seen as a dangerous threat to the ecosystem, in actuality, surface fires and other wildfires of this kind are beneficial to the forest. Balance has mostly been restored through surface fires-and now prescribed burns-that allow more diverse habitats for animals and burn out underbrush (which was a potential hazard for more dangerous fires). Ask the following questions:

1. Are fires always bad for forests? How can fires potentially be beneficial?
2. Why do you think trees might have evolved to benefit from forest fires?
3. How is our model not a perfect representation of actual forest fires?

Extension 2

In the Fire Model, the fire is started by a single spark and spreads to other trees based on proximity and exposure to the fire. Ask students to think of other factors that could play a role in starting and spreading forest fires. This could include factors like lightning, wind, temperature, humidity, topography, forest density etc. The following questions will help to direct students in their thinking and researching.

1. What could the "spark" represent in the Fire Model? Explain your choices.
2. What factors influence the spread of fire in the model? In real life forest fires, what other factors could have an influence? How?
3. Research the three conditions that must be met in order for there to be a fire. How are might all three of these be met in a forest?

Related Models:

Dominant Recessive Sampling

The Dominant Recessive Sampling Model will allow students to further understand randomness contained within a predictable system. With genetics, if the recessive allele has a certain frequency, one can attempt to find this number by counting the number of individuals with the recessive alleles in a given population. As the number increases, the actual allelic frequency will begin to appear. Even though the allele passed on to someone's offspring is random, specific frequencies are possible. The Fire Model resembles the Dominant Recessive Sampling model, since the spread of fire is random, but it is governed by a set of variables that allow the spread to be predicted. Supplemental Materials:

The Game of Life

In order to fully understand how a variable might have unforeseen consequences as a model progresses, students should study The Game of Life. It is an adaption from Conway's Game of Life and iteratively determines which cells are "dead" or "living" based on their neighbors. Governed by a set of specific mathematical rules, the populations either die off or reproduce based on surrounding populations. Like in the Fire Model, certain variables are preset before running the simulation, and each variable will have an effect on the population.