the whole is greater than the sum of its parts.

3, Fractals

Mandelbrot set

“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.

Five stages in the evolution of a Menger sponge. Credit: Niabot Wikimedia (CC BY 3.0).

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.

A Sierpinski Triangle outlined by a fractal tree.

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.