Mandelbrot Set Lemniscate


A curve on which points of a map z_n (such as the Mandelbrot set) diverge to a given value r_(max) at the same rate. A common method of obtaining lemniscates is to define an integer called the count which is the largest n such that |z_n|<r where r is usually taken as r=2. Successive counts then define a series of lemniscates, which are called equipotential curves by Peitgen and Saupe (1988).

See also

Count, Lemniscate, Mandelbrot Set

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Peitgen, H.-O. and Saupe, D. (Eds.). The Science of Fractal Images. New York: Springer-Verlag, pp. 178-179, 1988.

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Mandelbrot Set Lemniscate

Cite this as:

Weisstein, Eric W. "Mandelbrot Set Lemniscate." From MathWorld--A Wolfram Web Resource.

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