Logistic map zoom to magnification ×1,000,000,000
Автор: Logicedges
Загружено: 2012-05-17
Просмотров: 43813
Описание:
Zoom into the complete logistic map bifurcation diagram from which the Feigenbaum constant, δ = 4.669 201…, is calculated. The universal Feigenbaum constant indicates the rate at which branches of the tree split ("How to calculate .." is at https://sites.google.com/site/logiced... ).
The animation is of the complete logistic map starting across its full range (a = -2 to +4).
The graph is drawn by repeating the simple calculation: a × x × (1 - x)
which gives a new value of x. More than 1000 successive values of x are plotted vertically, against a set value of a, plotted horizontally.
The Feigenbaum constant, δ, is a universal constant (= 4.669 201 609 102 990 671 853 203 821 578 … ) and is deeply connected to many natural processes that display chaotic dynamics. There is also a related constant, the second Feigenbaum alpha constant, α = 2.502 907 … .
Further information at http://sites.google.com/site/logicedg...
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