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Standard Lyapunov logistic fractal with iteration sequence AB, in the region [2, 4] × [2, 4]. Generalized Lyapunov logistic fractal with iteration sequence AABAB, in the region [2, 4] × [2, 4]. Generalized Lyapunov logistic fractal with iteration sequence BBBBBBAAAAAA, in the growth parameter region ( A , B ) in [3.4, 4.0] × [2.5, 3.4], known as Zircon Zity . 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 .