Category:Definitions/Multibrot Sets

This category contains definitions related to Multibrot Sets.
Related results can be found in Category:Multibrot Sets.

Let $n \in \Z$ be an integer such that $n > 2$

The multibrot $n$ set $M_n$ 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:

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

Then $c \in M_n$ if and only if the sequence:

$\tuple {0, \map {T_c} 0, \map { {T_c}^2} 0, \ldots}$

is bounded.