Spreading of Fire

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Spreading of Fire
www.werc.usgs.gov

• Angela Shiflet
• Wofford College
• SC07
• November 10, 2007

http//www.wofford.edu/ecs/
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Background

• Inspiration
• "Fire!!" and "A Better Fire!!
• http//www.shodor.org/interactivate/activities/fir
  e1/index.html
• http//www.shodor.org/interactivate/activities/fir
  e2/index.html
• Woffords Emphasis in Computational Science
• Applying computer science mathematics to
  science problems
• Modeling and Simulation
• No prerequisites
• Software
• Mathematica, Maple, MATLAB
• Python or other programming language

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Cellular automaton simulation of spreading of
fire in classes

• Variety of classes
• CS1, CS2, computer graphics, modeling
  simulations
• Variety of assignments
• With or without graphics
• Team work
• Students love
• graphics animations
• creativity problem solving
• real-world type applications
• Particularly women

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With animation

• Grid of trees (green)
• For simplicity, surrounded by empty ground
  (yellow)
• Tree on fire in middle (red)
• (n25p55.mov)

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Without animation

• Vary probability of a tree adjacent to burning
  tree catching fire from 0 to 100
• Plot
• Explain

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Simulation algorithm for fire(n, probCatch)

• spread
• Function for updating rules of each cell
• fire parameters
• n
• Size ( rows or columns) of internal grid
• probCatch
• Probability of tree catching fire from neighbor
  burning tree

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Grid

• n-by-n array
• Possible cell values
• EMPTY (0)
• TREE (1)
• BURNING (2)
• Initially
• Empty border
• Trees inside
• 1 burning tree in middle

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Simulation Programfire(n, probCatch)

• initialize forest
• grids ? list containing forest
• do as long as a burning tree is in forest
• forest ? applySpread(forest, probCatch)
• Append forest to grids

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Applying spread to each cellapplySpread(mat,
probCatch)

• Applies spread(site, N, E, S, W) to each internal
  cell in grid
• Returns new grid

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Updating Rulesspread(site, N, E, S, W) function

• If site is EMPTY, remains EMPTY
• spread(EMPTY, N, E, S, W) returns EMPTY
• Burning tree burns down in 1 time step
• spread(BURNING, N, E, S, W) returns EMPTY
• If site is TREE and a neighbor is BURNING,
  sometimes tree burns

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Variations

• Random trees on fire
• Different rules
• Lightning
• 2 time steps to burn
• Wind
• Probability of catching fire proportional to
  number of neighbors on fire

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Other grid-based applications

• Spread of disease in society
• Attack of HIV on immune system
• Foraging
• Movement of ants
• Cloud formation
• Mushroom fairy rings

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Introduction to Computational Science Modeling
and Simulation for the Sciences

• Angela Shiflet George Shiflet
• Princeton University Press, 2006
• Cellular automaton simulations systems dynamics
  modeling
• www.wofford.edu/ecs/
• shifletab_at_wofford.edu

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