Script Monkey Blog – The Mandelbrot Set and Julia Sets.

The set of all 'C' where iterating fC(Z) -> Z2+C, starting at Z=0, does not diverge to ∞.

11th August 2021

Julia sets are either connected (one piece) or a dust of infinitely many points. The Mandelbrot set is those 'c' for which the Julia set is connected.

I have always been fascinated by geometry and fractals since first seeing the Mandlebrot set back in the Triassic period, well, the 1980's, I have written various scripts to try to reveal the hidden fractal geometry hidden around us in nature.

These geometries are incredibly simple to define, a little harder to code. The fractal below is drawn on a canvas element using WebGL. If you turn on hardware acceleration in Chrome --> Settings --> Advanced --> System, you should get super smooth results.

It is humbling to think that these mathematical entities are all around us and barely hidden from view. Once you start recognising fractal forms, you will see them everywhere in nature.

Here is a Mandelbrot set:

Click anywhere on the Mandelbrot below to see the corresponding Julia Set; each position should give different results.