The Mandelbrot set is a two-dimensional set with a relatively simple definition that exhibits great complexity, especially as it is magnified. It is … See more

Main cardioid and period bulbs
The main cardioid is the period 1 continent. It is the region of parameters $${\displaystyle c}$$ for … See more

Multibrot sets
Multibrot sets are bounded sets found in the complex plane for members of the general monic … See more

The Mandelbrot set has its origin in complex dynamics, a field first investigated by the French mathematicians Pierre Fatou 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 … See more

For every rational number $${\displaystyle {\tfrac {p}{q}}}$$, where p and q are relatively prime, a hyperbolic component of period q … See more

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