LogisticMap

The LogisticMap model shown using Vergil, the Ptolemy II schematic editor:

This model shows a polynomial mapping described by the equation: x(n+1) = rx(n)(1-x(n)) which was originally introduced as a demographic model where x(n) is a number between 0 and 1, and represents the population at year n and r is a positive number, and represents a combined rate for reproduction and starvation.

It is often cited as an archetypal example of how complex, chaotic behavior can arise from very simple non-linear dynamical equations:

For more details, see http://en.wikipedia.org/wiki/Logistic_map