Mandelbrot

The Mandelbrot set () is a two-dimensional set with a relatively simple definition that exhibits great complexity, especially as it is magnified. It is popular for its aesthetic appeal and fractal structures. The set is defined in the complex plane as the complex numbers $c$ for which the function $f\_c(z)=z^2+c$ does not diverge to infinity when iterated starting at $z=0$, i.e., for which the sequence $f\_c(0)$, $f\_c(f\_c(0))$, etc., remains bounded in absolute value.
This set was first defined and drawn... more