Fractal algorithm basics

This post is meant to be the first in a serie about the basic working of what I now call "Fractal Growth based algorithms", including not only the "Fractal AI" I am working on, but also methods for function optimisation or even my biggest experiment, the "quantum physics simulator" showed in previous posts.

Why are those methods relevant?

I have a strong feeling that those methods could be revolutionary in several aspects and serve as a base for new mathematical tools based on the power of fractals: I think they have the power to dilute some NP problem into P, and even more interesting, into O(n), making some hard problem to become "not so hard" anymore.

Nature is made up of fractals, as Maldelbrot showed us: a tree is a fractal, the coast line is a fractal, a mountain is also a fractal, etc. but we only use fractals for drawing fractals... it is the "lovely cat generator" of modern maths.

Benchmarking a fractal algorithm

An algorithm is only "promising" until you perform some benchmarks against others similar state-of-the-art algorithms that are aimed at the same kind of problems.

Benchmarking a general AI algorithm is not easy as it is supposed to generate "intelligent behaviour" and it is not quite clearly defined, but I also develop some other fractal algorithms aimed at finding the global minimum of a real function, or "optimising" functions, and in this case, the algorithm is easily comparable with others, so here we go.