In mathematics Lyapunov fractals (also known as Markus-Lyapunov fractals) are bifurcational fractals derived from an extension of the logistic map in which the degree of the growth of the population, r, periodically switches between two values a and b.

A Lyapunov fractal is constructed by mapping the regions of stability and chaotic behaviour in the a-b plane for a given periodic sequence of as and bs.