A curve on which points of a map (such as the Mandelbrot set) diverge to a given value at the same rate. A common method of obtaining lemniscates is to define an integer called the count which is the largest such that where is usually taken as . Successive counts then define a series of lemniscates, which are called equipotential curves by Peitgen and Saupe (1988).
Mandelbrot Set Lemniscate
See also
Count, Lemniscate, Mandelbrot SetExplore with Wolfram|Alpha
References
Peitgen, H.-O. and Saupe, D. (Eds.). The Science of Fractal Images. New York: Springer-Verlag, pp. 178-179, 1988.Referenced on Wolfram|Alpha
Mandelbrot Set LemniscateCite this as:
Weisstein, Eric W. "Mandelbrot Set Lemniscate." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MandelbrotSetLemniscate.html