2017-03-25, post № 164
mathematics, PIL, programming, Python, #alpha, #chaos, #chaos theory, #delta, #Feigenbaum, #fractal, #iterations, #Mandelbrot set, #modelling, #population
Generating the famous fractal, which can be used to model populations with various cycles, generate pseudo-random numbers and determine one of nature’s fundamental constants, the Feigenbaum constant 𝛿.
The fractal nature comes from iteratively applying a simple function, with , and looking at its poles.
The resulting image looks mundane at first, when looking at , though the last quarter section is where the interesting things are happening (hence the image below only shows the diagram for ).
From 𝜆 = 𝟥 on, the diagram bifurcates, always doubling its number of poles, until it enters the beautiful realm of chaos and fractals.