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bifurcation 1 bifurcation 2 basis: bifurcation
pictorial representation of a population groth model.
let P = new population, p = old population,
r = growth rate
the model is:
P = p + r * fn(p) * [1 - fn(p)].
3 parameters: filter cycles, seed population,
and function.
bifurcation 3 bifurcation 4 The wonder of fractal geometry is that such complex forms can arise from such simple generating processes. A parallel surprise has emerged in the study of dynamical systems:
that simple, deterministic equations can yield chaotic behavior, in which the system never settles down to a steady state or even a periodic loop. Often such systems behave normally up to a certain level of some controlling parameter, then go through a transition in which there are two possible solutions, then four, and finally a chaotic array of possibilities.