Among the pre-Socratics, it was Pythagoras who hypothesized that the most basic constituent of the universe wasn't some material substance but rather numbers. The idea must have seemed strange to most of his contemporaries, but over two thousands years of research have led to the inescapable conclusion that the book of the universe really seems to be written in the language of mathematics.
One of the most famous and intriguing mathematical patterns found throughout nature is phi (also known as the golden ratio). The idea is simple: two numbers are said to be in this ratio if the sum of the two numbers to the larger of the two is equal to the ratio of the larger to the smaller (like in the rectangles above). You can also converge on this fraction by taking the ratio between any two consecutive numbers in the Fibonacci sequence (or in the Lucas series).
As the stunning animation below shows, the remarkable thing is that the Fibonacci series and the golden ratio seem to be beautifully manifested in various aspects of the natural world, from the spiral shape of the nautilus to the arrangement of petals in sunflowers and even the predatory flight of the peregrin falcon as it hones down on its unsuspecting prey.
Need more proof that the golden ratio is a thing of beauty? Behold!
And if this has whetted your appetite, take a listen to this episode on the Fibonacci sequence from In Our Time, with Melvyn Bragg.
Or you might also be interested in The Secret Life of Chaos, and how order can arise out or disorder.