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Plotting the logistic map bifurcation diagram (feigenbaum plot) with Javascript and canvas.
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Feigenbaum bifurcation plot

The logistic map

The logistic map equation

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:

First attempt to visualize a fraction of the feigenbaum diagram Feigenbaum Plot (with errors)

Feigenbaum bifurcation (logistic map) Plotting the Feigenbaum bifurcation

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

Zoom in a little bit more into [3.563,3.6] Plotting the Feigenbaum bifurcation

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)


  • 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


  • HTML5 Canvas
  • HTML5 WebGL
  • PlotBoilerplate.js


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