Definition:Mandelbrot Set/Definition 1

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 $c \in M$ the sequence:
 * $\tuple {0, \map {T_c} 0, \map { {T_c}^2} 0, \ldots}$

is bounded.

Also see

 * Equivalence of Definitions of Mandelbrot Set