The Mandelbrot set has its origin in complex dynamics, a field first investigated by the French mathematicians Pierre Fatou and Gaston Julia at the beginning of the 20th century. The fractal was first defined and drawn in 1978 by See more

Main cardioid and period bulbs
The main cardioid is the period 1 continent. It is the region of parameters $${\displaystyle c}$$ for which the map
$${\displaystyle f_{c}(z)=z^{2}+c}$$
has an attracting fixed point. It consists of all parameters of … See more

Multibrot sets
Multibrot sets are bounded sets found in the complex plane for members of the general monic univariate polynomial family of recursions See more

The Mandelbrot set is widely considered the most popular fractal, and has been referenced several times in popular culture.
• The Jonathan Coulton song "Mandelbrot Set" is a tribute to both the fractal itself and to the man it is … See more

The Mandelbrot set is a compact set, since it is closed and contained in the closed disk of radius 2 around the origin. A point $${\displaystyle c}$$ belongs to the Mandelbrot set if and only if $${\displaystyle |z_{n}|\leq 2}$$ for all
The See more

For every rational number $${\displaystyle {\tfrac {p}{q}}}$$, where p and q are relatively prime, a hyperbolic component of period q bifurcates from the main cardioid at a point on the edge of the cardioid corresponding to an internal angle of See more

There exist a multitude of various algorithms for plotting the Mandelbrot set via a computing device. Here, the most widely used and … See more