feigenbaum-plot's Introduction

Feigenbaum bifurcation plot

The logistic map

when plotted gives a peek into deterministic chaos. Whilst lambda resides inside the range ~[0..3.2] everthing seems fine and the recursive definition of the function gives (more or less) convergent series, the situation changes for values beyond ~3.2, and for values larger than 3.6 the result becomes (pseudo) chaotic, als the number of accumulation points increases.

Numberphile postet a really nice video about this function/map and the two Feigenbaum constants ... for those who are new to this topic: https://www.youtube.com/watch?v=ETrYE4MdoLQ

First attempt to visualize a fraction of the feigenbaum diagram

Feigenbaum bifurcation (logistic map)

Closer look into a bifurcation point near [3.563,3.6]

Zoom in a little bit more into [3.563,3.6]

I made a high resultion plot (13776x924 pixels) which took my machine about an hour to compute.

Download Hi-Res plot here

This file is about 40MB large:

plot range [3.2 to 3.83]
500 iterations per sample
sample size 0.1 (10 samples per pixel, makes 137.760 samples for lambda)
plot (y axis) is scaled up from [0,1]
x(0) is 0.2 (this value does not seem to have any affect at all after some iterations)

Find a live demo here (better have a quick machine)

Changelog

2018-12-30
- Added a rectangular selector tool (to select sub plot areas).
2018-12-29
- y was plotted inverted.
2018-12-28
- Removed the 'plotScale' param (in favour of 'normalizeToMin' and 'normalizeToMax').
- Added the balanced binary tree collection to increase performance.
2018-12-22
- Added some equations.
2018-12-11
- Replaced the plotting engine by the PlotBoilerplate.
- Calculated the first hi-res plot <3
2018-10-23
- Init