Standard Lyapunov logistic fractal with iteration sequence AB
Generalized Lyapunov logistic fractal with iteration sequence AABAB
In mathematicsLyapunov 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. Image File history File links Download high resolution version (640x640, 162 KB)Lyapunov logistic fractal with iteration sequence AB. By Blotwell. ... Image File history File links Download high resolution version (640x640, 162 KB)Lyapunov logistic fractal with iteration sequence AB. By Blotwell. ... Image File history File links Download high resolution version (640x640, 194 KB)Lyapunov logistic fractal with iteration sequence AABAB. By Blotwell. ... Image File history File links Download high resolution version (640x640, 194 KB)Lyapunov logistic fractal with iteration sequence AABAB. By Blotwell. ... Main article: History of mathematics The evolution of mathematics can be seen to be an ever increasing series of abstractions. ... The Mandelbrot set, named after its discoverer, is a famous example of a fractal. ... The logistic map is a polynomial mapping, often cited as an archetypical example of how complex, chaotic behaviour can arise from very simple non-linear dynamical equations. ...
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.
The term fractal was coined in 1975 by Benoît Mandelbrot, from the Latin fractus or "broken".
Fractal geometry is the branch of mathematics which studies the properties and behaviour of fractals.
Fractal geometry was also used for data compression and for modelling complex organic and geological systems, for example the growth of trees or the development of river basins.
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