The ratio called phi is quite remarkable, especially given how ubiquitous it appears to be present throughout nature at all scales. In fact, phi can be seen as one of the fundamental scaling ratios of nature, as we’ll examine below. To fully appreciate phi, lets first become familiar with some of its basic characteristics:

Phi as a number is 1.618033… (an irrational number). It can be seen as both the ratio of 1.618… to 1, or .618… to 1

It is a self-similar scaling ratio, meaning that each iteration of a sequence of phi-based objects is in the same proportion of those both before it and after it (e.g. .618 — 1 — 1.618)

One way of deriving phi is through the Fibonacci Sequence, a series of numbers that are based on the simple repeating equation of a+b=c, b+c=d, etc. Starting from zero and one:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610…

As you progress through this series and divide adjacent pairs of numbers you approach an increasing accuracy of phi (e.g. 610/377=1.61803713528)

As such, these numbers — which themselves are found present in how nature manifests form — are foundational to observing the presence of the phi ratio from the perspectives of both quantity and scale

Four primary ways in which phi can be most readily observed are

As a spiral (found in shells, plants, water and air vortices, galaxies)

As a ratio of quantity (found in plant seed heads)

As a ratio of scale (found in human body, animals, plants)

As angles of both rotation and scaling (found in plants and other phenomena)

Phi provides an optimal efficiency in the organization and interaction of energy and matter (which will be explored further below)