Feigenbaum fractal

A Feigenbaum fractal is any bifurcationMathworldPlanetmath fractal produced by a period-doubling cascade. The “canonical” Feigenbaum fractal is produced by the logistic map (a simple population model),


where μ is varied smoothly along one dimensionMathworldPlanetmath. The logistic iteration either terminates in a cycle (set of repeating values) or behaves chaotically. If one plots the points of this cycle versus the μ-value, a graph like the following is produced:

Note the distinct bifurcation (branching) points and the chaotic behavior as μ increases.

Many other iterations will generate this same type of plot, for example the iteration


One of the most amazing things about this class of fractals is that the bifurcation intervals are always described by Feigenbaum’s constant.

Octave/Matlab Code to generate the above image is available \PMlinktofilehereoctave_feigen.zip.


  • “Quadratic Iteration, bifurcation, and chaos”: http://mathforum.org/advanced/robertd/bifurcation.htmlhttp://mathforum.org/advanced/robertd/bifurcation.html

  • “Bifurcation”: http://spanky.triumf.ca/www/fractint/bif_type.htmlhttp://spanky.triumf.ca/www/fractint/bif_type.html

  • “Feigenbaum’s Constant”: http://fractals.iuta.u-bordeaux.fr/sci-faq/feigenbaum.htmlhttp://fractals.iuta.u-bordeaux.fr/sci-faq/feigenbaum.html

Title Feigenbaum fractal
Canonical name FeigenbaumFractal
Date of creation 2013-03-22 12:34:18
Last modified on 2013-03-22 12:34:18
Owner akrowne (2)
Last modified by akrowne (2)
Numerical id 6
Author akrowne (2)
Entry type Definition
Classification msc 37G15
Synonym Feigenbaum tree
Defines logistic map