The combined simplicity and complexity of a Mandelbrot fractal never fails to impress. The complexity is obvious as you dive deeper and deeper into the points defined by the Mandelbrot set.
But at the same time the function which defines the fractal is so simple.
$$f(c)z = z^2 +c$$
Where c is a member of the Mandelbrot set. The black in the familiar Madelbrot fractal shape represents values of c which are not part of the set.
It was my old friend Andy – or rather his Father who introduced me to them, many years ago now. Andy gave me a 3-1/2” floppy disk with a program that could generate fractals and allow you to zoom in and cycle through the colours giving a psychedelic / hypnotic effect.
Note that in the picture above it is the white areas which are not part of the Mandelbrot Set.