Mandelbrot Set Algorithm

The Mandelbrot Set image that we’ve grown to know and love (well, I’ve grown to know and love) is generated using a very simple set of rules, much in the way that the broccoli plant uses simple rules to generate it’s seemingly complex structure.

In fact, it is one of the simplest set of rules that you could possibly imagine for a mathematical system, and not only that, but the exact same set of rules that govern the growth of that broccoli plant also govern the formation of this fractal as I will demonstrate in the next section.

Here is the algorithm or set of “rules” that are used to generate all the beautiful Mandelbrot Set images that you have seen so far. As you can see, it is a very simple algorithm with very few steps involved. It's always been a wonder to me how such a complex object with its infinite beauty can arise from so few lines of code.