Math stuff

Thus the contagion or epidemic being modeled is of a disease that only lasts one period and can be passed along or passed back and forth between cells. With a mutation rate of say 0. But it is quite random which block of locations will lock in as successful neighborhoods.

This is used in all the spreadsheets below. There is a sweet spot between the crystalline order quickly reached with no mutation and the chaos of too much mutation.

The model consists of cells each of which can be "sick" or "well" 1 or 0. Indeed the "two" parents could be the same string cloning. A model string of 10 0s and 1s is randomly chosen and is fixed throughout the run.

With a mutation rate of say 0. Above that a certain portion of the population keeps reinfecting each other. A cell can be infected by one of its four neighbors east, west, north, and south with a probability P. Hit the F9 key to run it.

If exactly two neighbors are alive, then the cell remains in its present state in the next generation. Mutation is introduced only for the two members reproducing by crossover.

Equilibrium Random Start Bead Game: The key trick in any spreadsheet with circular references and iterations is the iteration counter.

The following spreadsheet just introduces iteration counters. Mutation is introduced only for the two members reproducing by crossover. Eventually the red or black balls will dominate and drive out the others.

There is an initially random population of a fixed number of members 6 in this case that evolve using selection, mutation, and crossover. There are two offspring produced by combining the string to the left of randomly chosen crossover point on one parent with the string to right of the crossover point on the other parent.

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Math stuff
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Wolfram MathWorld: The Web's Most Extensive Mathematics Resource