6. Patterns in Nature (part one)

The idea that we can bring the seemingly effortless elegance of the wild into the constructed world is something I’m excited to pursue in a lot of different ways.  One of those ways is the direct inspiration of the beautiful visual patterns you see in nature.  For a long time people have been studying natural patterns and geometries, searching for relationships and meaning that sometimes go deep into philosophy and mysticism.  Many interesting things have been discovered with some really fun implications for a designer.  In fact, I didn't realize what a fascinating and complex topic this is until I got into it, and I've struggled to keep the discussion brief.  I’d like to start by talking about the Golden Ratio, in part to answer the question I seem to always get – “Why do you have a spiral in your back yard?”

The Golden Ratio

Early in Architecture school we learn about the idea of proportion, especially how it is used in the western Classical styles of architecture (mainly Greek and Roman). The basic idea is that the ratio of the length of one line to another can be repeated for different size elements in a building to visually unify the pieces.  Classical designers, going back to Pythagoras, Euclid and others, believed that certain proportions commonly found in nature could be applied to buildings to give them the same harmonious relationships.

One of the oldest and most well-known proportioning systems is the Golden Ratio, which is said to be found throughout nature, including certain proportions of the human body.  It is therefore called “Golden” because it is believed to be an especially harmonious and aesthetically pleasing proportion, and it can be found in the design of quite a few famous Classical buildings, such as the Parthenon in Athens.

The definition of the Golden Ratio is quite simple: divide any line segment so that the proportion of the smaller part to the larger part equals the proportion of the larger part to the whole.  This ratio equals 1.618…(a repeating decimal) which is called Phi.  Place the line segments perpendicularly and you generate a Golden Rectangle, and if you take a square out of the rectangle you get another Golden Rectangle in an infinite progression, as shown in the diagram below.  The exciting part to me is what comes next: if you draw an arc within each square as they get smaller and smaller, you generate a spiral which looks a lot like spiral forms you see in nature, such as shells.  There is the classic example of the Nautilus shell, but also certain animal horns, hurricanes, even our own galaxy are said to have a similar form.  I haven't researched this deep enough to say that all these phenomenon have exactly these proportions, but there is clearly some level of similarity.

The Fibonacci Sequence

Related to the Golden Ratio is the Fibonacci Sequence of numbers.  This sequence is used to model natural patterns from the arrangement of leaves on a stem to the spiral arrangement of a pine cone, and even rumored to be used in stock market predictions.  The series starts with 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144… where the sum of each pair of numbers equals the next number.  If you take the ratio of one number to the next it increasingly approximates the Golden Ratio, and if you draw a series of squares using each number you can generate a very similar spiral.  It is said that Fibonacci first developed this number series to model the population expansion from a pair of rabbits, but from there it has been found to be useful in an amazing number of things, for example musical scales and frequencies.  I won’t be able to get much further into it this time, but these numbers will crop up again when we talk about branching patterns and fractals.

So, from this cursory discussion you can see that there is a lot going on with the Golden Ratio and the Fibonacci Sequence, and it has inspired me to use the Golden Rectangle and spiral in my designs.  As a child raised in the realm of science I won’t go so far as to assert what Francis Ching describes as “The belief that certain numerical relationships manifest the harmonic structure of the universe,” but now that I have a Golden Rectangle in my backyard, I’m getting direct experience with it and will let you know just as soon as the galactic harmony is objectively evident!

References:

Architecture: Form, Space and Order, by Francis D.K. Ching

Patterns in Nature, by Peter S. StevensShapes, by Philip Ball

Sacred Geometery, by Miranda Lundy

On Growth and Form, by D’Arcy Thompson

Sacred Geometry – Philosophy and Practice, by Robert Lawlor