Mathematik – Creatgraphy

Approximation of the Mandelbrot set

dots of complex numbers in green are not part of the Mandelbrot set. Each Iteration eliminates new complex numbers. The brighter the color, the higher the iteration until $n>2$ .

The Mandelbrot set is a set of complex numbers, generated with the sequence $z_{n+1}=z_n^2+c$ , where $c\in\mathbb{C}$ and $z_0=0$ . The complex numbers in the set fulfill the following equation

$\forall n\in\mathbb{N} : ||z_n||_\infty \leq d\in\mathbb{R}$

In some cases, $d$ is defined as $d=2$ , therefore the computation is much simpler.

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