Definition:Mandelbrot Set/Definition 2

Definition
The Mandelbrot set $M$ is the subset of the complex plane defined as follows:

Let $c \in \C$ be a complex number.

Let $T_c: \C \to \C$ be the complex function defined as:


 * $\forall z \in \C: \map {T_c} z = z^2 + c$

Then $M$ is the set of points $c$ for which the Julia set of $T_c$ is connected.

Also see

 * Equivalence of Definitions of Mandelbrot Set