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 Set## Explore 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 Lemniscate## Cite this as:

Weisstein, Eric W. "Mandelbrot Set Lemniscate."
From *MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/MandelbrotSetLemniscate.html