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