We have used Lempel-ZIv Algorithm, based on the Kolmogorov complexity, to calculate the number of different patterns in the time series generated by the logistic map and it varies for different number of iterations, but it has something like the saturation value.
Hello Gordan. I have been giving the "logistics equation" as an example in one of my lectures. We try to do the calculations of the equation on the excel platform. After we did the calculations we graph the values with scatter graph tool. With the initial value of x0=0,4, r=2 and 4000 iterations we obtain a "sweeper" like graph. Thats all what we do but we don't do any further tests. I add an example excel file. Regards. Have a good day.
I made calculations long time ago. However what I remember is that the track is depending in the initial point. Books generally assume x_0=0.5. For other starting points the function behaves differently.
I have found the answer in the paper by Kaspar and Schuster (attached below). They say that "This indicates a pattern selection process which leads to a stable dynamical equilibrium which is probably characterized by a dynamical kink structure with a conserved number of kinks."
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