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"That their main business was not put into the mind knowledge which was not there before, but to turn the mind's eye towards light so that it might see for itself." ...Plato's advice to educators(429-347BC)

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Fu-Kwun Hwang
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 « Embed this message on: June 13, 2010, 02:13:14 pm » posted from:Taipei,T\'ai-pei,Taiwan

The logistic map
The logistic equation was first proposed by Robert May as a simple model of population dynamics. This equation can be written as a one-dimensional difference equation that transforms the population in one generation, xn, into a succeeding generation, xn+1.
xn+1 = 4 r xn (1-xn)
Because the population is scaled so that the maximum value is one, the domain of x falls on the interval [0; 1].
The behavior of the logistic equation depends on the value of the growth parameter, r. If the growth parameter is less than a critical value r<0.75.., then x approaches a stable fixed value. Above this value for r, the behavior of x begins to change. First the population begins to oscillate between two values. If r increases further, then x oscillates between four values. Then eight values. This doubling ends when r > 0.8924864... after which almost any x value is possible.
Author : Francisco Esquembre and Wolfgang Christian.
Text and original idea from the Open Source Physics project manual
Date : July 2003

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 « Embed this message Reply #1 on: December 11, 2019, 10:22:23 am » posted from:,,Satellite Provider

I know it's too hard to understand. But the knowledge in the body.
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"That their main business was not put into the mind knowledge which was not there before, but to turn the mind's eye towards light so that it might see for itself." ...Plato's advice to educators(429-347BC)