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Computer Programs + Simulations

Index:
|> Forest Fire Simulation
|> Small-World Network Simulation
|> References


Follows are a few simulation examples we've implemented using the Windows .NET framework. The projects include running, executable software that can be downloaded below. The simulaitons should work on any PCs running Windows-XP and Windows-Vista, which possess the .NET framework as part of the system.

<| Forest Fire Simulation [11.2008]

This program simulates a fire spreading through a 2-D grid of trees. Trees which are "on-fire" will set off trees on adjacent nodes during successive time-steps, and the fire will spread throughout the grid. The trees occupy grid cells at random, with a selectable probability density.

The results are highly-nonlinear and non-intuitive. For low tree-densities, the fire quickly burns out, but at intermediate densities the fire burns patches of trees exhibiting characteristic "fractal" patterns (as shown, right). Then, above some critical tree-density, the fire quickly spreads to burn essentially all trees in the grid. Of note, the range of tree-densities from few-burned to all-burned is extremely narrow, and the curve relating %trees-burned to tree-density is highly-nonlinear ("S"-shaped curve in diagrams).

This simulation has some relationship to other situations involving random distributions of active-nodes which can "infect" neighboring nodes, including "real" forest fires, the spread of epidemics, spread of "memes", etc.

See next page for more details about the Forest Fire Simulation.

<| Small-World Network Simulation [11.2008] - program status: works, some bugs exist.

This program simulates signal flows in random, ordered, and so-called small-world [ordered with random cross-connections] networks.

See next page for more details about the Small-World Network Simulation.

<| REFERENCES

  • How Nature Works, The Science of Self-Organized Criticality, by Per Bak (1996).

  • Self-Organization in Biological Systems, by Scott Camazine and 5 others (2003) - semi-theoretical coverage of self-organizing systems in biology. Includes multiple chapters with extensive descriptions of computer simulations, eg, pattern formation in bacteria, fish schooling, termite mound building, trail formations in ants.

  • Signs of Life, How Complexity Pervades Biology, by Ricard Sole + Brian Goodwin (2000) - popular introduction to complexity theory. Includes a few algorithms, useful for initial attempts at simulating systems with emergent (unexpected) characteristics. Eg, genetic networks, edge of choas, fractal cities, market crashes.

  • "Collective dynamics of 'small-world' networks", by Duncan J. Watts & Steven H. Strogatz (1998), Nature, v.393:440-442.

  • © www.robotrambler.com, Dec 2008, updated July 2009