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
A physicist is a scientist who specializes in the field of physics, which encompasses the interactions of matter and energy at all length and time scales in the physical universe.
Physicists generally are interested in the root or ultimate cau ...
from the
Max Planck Institute of Molecular Physiology. They were introduced to a large public by a
science popularization article on
recreational mathematics
Recreational mathematics is mathematics carried out for recreation (entertainment) rather than as a strictly research and application-based professional activity or as a part of a student's formal education. Although it is not necessarily limited ...
published in
Scientific American
''Scientific American'', informally abbreviated ''SciAm'' or sometimes ''SA'', is an American popular science magazine. Many famous scientists, including Albert Einstein and Nikola Tesla, have contributed articles to it. In print since 1845, it ...
in 1991.
Properties
Lyapunov fractals are generally drawn for values of ''A'' and ''B'' in the interval