of a complex function: Mandelbrot Sets and Julia Sets.
By now you have an idea of
what a Mandelbrot Set is. To create the color images of
Mandelbrot Sets, some times -wrongly- called fractals,
one starts with a complex one parameter map H(z;k). You
can see how such a map looks like by going to either one
of the three maps illustrated on the left. For instance,
the Mandelbrot Map is F(z;c) = z2 + c; with z
the variable and c the parameter. For short one just
writes H(z) insted of H(z;k); this is the way you will
see the maps in the pages hyperlinked on the left.
|Mandelbrot & Julia Sets:|
|For a given complex one parameter function, there is just one Mandelbrot Set. But, there are infinitely many Julia Sets. Sometimes, this is referred to as the dichotomy Mandelbrot Set-Julia Sets. These two type of sets exist in different spaces. The Mandelbrot Set lives in the complex plane of parameters, whereas the Julia Sets live in the complex plane of variables.|