Lemniscate (Mandelbrot Set)

A curve on which points of a Map $z_n$ (such as the Mandelbrot Set) diverge to a given value $r_{\rm max}$ 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 $\vert z_n\vert<r$ 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, Mandelbrot Set

References

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