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kdilliplan's picture

The Game of Life, Ants and Oil Percolation

            After fooling around with the MIT version of the Game of Life and Langton’s Ant, I made a few observations and answered a few questions I had from the first time I looked at the models.  To begin with, yes, the ant can build a road in a direction other than the one we saw in class.  The road has the same appearance, but it can build it heading down/left, down/right, up/left and up/right, and with a simple application of road blocks, it can build them in all four possible directions in the same run.  My other, somewhat trivial question was whether I could beat the record of five-cell beginning state in the Game of Life and create a beginning state that created a longer sequence of seemingly random shapes.  I ultimately created a nine-cell pattern that ran for a minute and 40 seconds before settling into a set of repeating patters.  The original five-cell pattern only lasted 37 seconds.

            After playing with the models we’d looked at in class, I went on to exploring the NetLogo models.  I’m taking a class on soils right now, and so I looked at the oil percolation model because I thought it would tie in nicely.  In this model, you set the porosity of the soil as a percent, and then allow the “oil” to move through it.  The “oil” can move downward diagonally to the left or right or move nowhere at all, depending on the porosity of the soil and the associated probability.  At a porosity of 65.0% or lower, the “oil” will eventually stop percolating, but at any porosity above 65.0%, the “oil” will percolate indefinitely. 

            Based on these three models, I’ve noticed a few patterns.  There seem to be three basic operations any of these models can exhibit: continuous random change, finite patterns of change, or complete extinction.  The more complex the system, the more combinations of patterns can be seen.  For example, the Game of Life showed patterns that began with random change and then lapsed into either finite patterns or complete extinction.  With the percolation model, no finite patterns developed.  There was either continual random change or eventual extinction.  I think a defining characteristic of systems that can exhibit all three patterns is the ability to modify (as opposed to merely respond to) the environment.  The Game of Life and Langton’s Ant both modify the environment, while the oil percolation model does not.  The Game of Life and Langton’s Ant show lots of different and surprising outcomes, but the percolation model either runs continually or stops.  There is also the issue of probability and randomness.  We agreed as a group to leave off talking about randomness until later, but after playing around with these models, I am especially curious as to what its role is.


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