page_title: Lyapunov fractal
hierarchical_section_title: Lyapunov fractal
caption_attribution_description: English: en:Lyapunov fractal for the sequence AABAB, a and b in [2,4], a as y-coordinate and b as x-coordinate. Downsampled from a 6000x6000 image. Русский: ru:Фрактал Ляпунова для последовательности AABAB, где a и b принадлежат промежутку [2,4]. a используется как x-координата, а b - как y-координата. Уменьшено с оригинального 6000х6000 изображения.
context_page_description: In mathematics, 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 given periodic sequences of a and b. In the images, yellow corresponds to, and blue corresponds to.
  Lyapunov fractals were discovered in the late 1980s by the Germano-Chilean physicist Mario Markus from the Max Planck Institute of Molecular Physiology. They were introduced to a large public by a science popularization article on recreational mathematics published in Scientific American in 1991.
context_section_description: 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 (measured using the Lyapunov exponent ) in the a−b plane for given periodic sequences of a and b. In the images, yellow corresponds to  (stability), and blue corresponds to  (chaos).
  Lyapunov fractals were discovered in the late 1980s by the Germano-Chilean physicist Mario Markus from the Max Planck Institute of Molecular Physiology. They were introduced to a large public by a science popularization article on recreational mathematics published in Scientific American in 1991.
caption: Generalized Lyapunov logistic fractal with iteration sequence AABAB, in the region [2, 4] × [2, 4].
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