logistic mapping

• A fractal generated by iterating: \( x_{n+1} = \lambda x_n (1-x_n)\)
• boom and bust cycles

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If you had a Java browser, you would be able to alter the parameters of this logistic curve, and "zoom in" on interesting values of lambda.

Choose new start and end values of lambda between 1.0 and 4.0, and click "Redraw".

In particular, try 3.8 < lambda < 3.9, an "island of period three" in the "sea of chaos". All periods are present: can you find periods 5, 6 and 7?

Beware loss of precision if your values of lambda are very close together: don't necessarily trust the precise locations of bifurcation points!