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I am curious about how to describe the stability of a graph using some form of bona fide statistical analysis.

I unfortunately have very little statistical background.

The data come from a Computer Science research project I am working on. We are attempting to use simulated cellular automata to arrange themselves in specific shapes. We have a "fitness function" that determines how "well" it fits the shape. The closer the function gets to 0, the better.

We evaluate the fitness at step 100 of the simulation as the measure of how "good" the automaton is.

Now, we are attempting to classify the automaton, and I am trying to determine stability. We have run the simulations for 1000 steps and evaluated the fitness at each step. We can therefore plot a graph of fitness vs time.

We don't much care if the graph varies widely in the first steps, but after step 100 we want it to remain stable.

Currently I have made it work so that it calculates the standard deviation, and then counts how many steps pass until the fitness passes out of the range of 1(or a fraction of) standard deviation/s above and below the fitness value at step 100. That count is then it's stability 'score'.

However, I am concerned that the nature of these automata will skew the standard deviation.

For instance:

>>I have one gene that reaches a good value at step 100 and then promptly dies off completely (thus sending his fitness back up to maximum for the remaining 900 steps) and making him rather un-useful, and in a way, 'unstable'.

>>Another gene "blinks" on and off at each step - also unstable, he alternates between minimum and maximum fitness values at each step.

Are there any methods in statistics that would help in evaluating their stability?

Also, as my statistics is pretty shaky, a method that is common-sense-y would score bonus points. Or is the method I am using an acceptable one?

Thanks

Laura

2nd yr BSc (Physics, Mathematics, Computer Science)

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# Statistics of Stability?

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