A fractal is a recursive element: "fractals can be any type of infinitely scaled and repeated pattern." (http://rsb.info.nih.gov/ij/plugins/fraclac/FLHelp/Fractals.htm)
Also useful for this discussion are the terms "nonlinear" and "stochastic."
"a nonlinear system is any problem where the variable(s) to be solved for cannot be written as a linear combination of independent components"
"A stochastic process is one whose behavior is non-deterministic in that a state's next state is determined both by the process's predictable actions and by a random element. Stochastic crafts are complex systems whose practitioners, even if complete experts, acknowledge that outcomes result from both known and unknown causes. Classical examples of this are medicine: a doctor can administer the same treatment to multiple patients suffering from the same symptoms, however, the patients may not all react to the treatment the same way. This makes medicine a stochastic process.[1] Additional examples are warfare, meteorology and rhetoric, where success and failure are difficult enough to predict that explicit allowances are made for uncertainty."
Why are fractals important?
Fractals provide a way of successfully mapping extremely complex systems. Non
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