“My life seemed to be a series of events and accidents. Yet when I look back, I see a pattern.”
— Benoît B. Mandelbrot.
- Segment a cube equally (into 27 cube segments).
- Remove a segment from the centre of each face of the cube.
- Remove the segment situated at the core.
- Recursively iterate these steps over each remaining cube segment.
Voila, you have successfully constructed a Menger sponge which has a unique property of infinite surface area, yet zero volume. This is also a feature of the lungs-alveoli physiology that optimises gaseous exchange.
Fractals are geometric constructs that exhibit self-similarity across scale. Families of fractals are ubiquitous in nature and systems.
Branching shapes ripple through lush shubbery; jolts ripping through the sky; bulls & bears racing over financial exchanges. Our own brain architecture depend on these units of branching patterns facilitating the abstractions that construct our entire experience of existence.