Feigenbaum constant


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The Feigenbaum delta constant has the value


It governs the structure and behavior of many types of dynamical systemsMathworldPlanetmathPlanetmath. It was discovered in the 1970s by http://www-groups.dcs.st-and.ac.uk/ history/Mathematicians/Feigenbaum.htmlMitchell Feigenbaum, while studying the logistic mapMathworldPlanetmath


which produces the Feigenbaum tree:

Generated by GNU Octave and GNUPlot.

If the bifurcationsMathworldPlanetmath in this tree (first few shown as dotted blue lines) are at points b1,b2,b3,, then


That is, the ratio of the intervals between the bifurcation points approaches Feigenbaum’s constant.

However, this is only the beginning. Feigenbaum discovered that this constant arose in any dynamical system that approaches chaotic behavior via period-doubling bifurcation, and has a single quadratic maximum. So in some sense, Feigenbaum’s constant is a universal constant of chaos theory.

Feigenbaum’s constant appears in problems of fluid-flow turbulence, electronic oscillators, chemical reactions, and even the Mandelbrot setMathworldPlanetmath (the “budding” of the Mandelbrot set along the negative real axis occurs at intervals determined by Feigenbaum’s constant).


  • 1 http://www.research.att.com/ njas/sequences/A006890A006890, “Decimal expansion of Feigenbaum bifurcation velocity”, in the On-Line Encyclopedia of Integer Sequences (http://planetmath.org/OnLineEncyclopediaOfIntegerSequences)
  • 2 “Bifurcations”: http://mcasco.com/bifurcat.htmlhttp://mcasco.com/bifurcat.html
Title Feigenbaum constant
Canonical name FeigenbaumConstant
Date of creation 2013-03-22 12:34:25
Last modified on 2013-03-22 12:34:25
Owner yark (2760)
Last modified by yark (2760)
Numerical id 11
Author yark (2760)
Entry type Definition
Classification msc 37G15
Synonym Feigenbaum delta constant
Synonym Feigenbaum bifurcation velocity constant
Synonym Feigenbaum bifurcation velocity
Synonym Feigenbaum number
Synonym Feigenbaum’s number
Synonym Feigenbaum’s constant