Fractals use bionic numbers to offers a glimpse into how Nature forms patterns such as galaxy spirals, mountain ranges, trees, and blood vessels. The algorithms that recreates Nature is so pervasive that some call it "Thumbprint of God". The method goes by different names: engineers call it feedback and programmers call it recursion. It is very simple: given a function, take it's output and feed it back into the input. Such a simple act can account for the seeds of diversity in the world.
The most popular fractal is the Mandelbrot Set. The Mandelbrot Set are those additive seeds C whose trajectories
remain bounded. Without bionic numbers, we would not have this arithmetic. We would not have the Mandelbrot Set. We would not have this glimpse into the formation of our world.