Feigenbaum Constants

The Feigenbaum constants are two related mathematical constants, both discovered by the physicist Mitchell Feigenbaum in 1975, that describe universal patterns in the behavior of certain nonlinear dynamical systems as they transition into chaos through a process called period doubling. The first Feigenbaum constant, approximately 4.6692, is the limiting ratio between successive intervals between the parameter values at which period doubling occurs in a one parameter family of maps, such as the logistic map, and the second, approximately 2.5029, describes the ratio of widths of successive branches of the resulting bifurcation diagram. Remarkably, both constants are universal, in the sense that the same values arise for a broad class of unrelated mathematical functions that share the same qualitative shape, a discovery that helped establish the field of chaos theory as a genuine area of mathematical physics rather than a collection of unrelated curiosities.