The Geometry Of Plants

We were asked by culinary art extraordinaires Bompas & Parr to contribute to their upcoming book Tutti Frutti with Bompas & Parr and Friends. We explored the architectural qualities and patterns within plants, fruits and vegetables, through the Fibonacci sequence and the Golden Ratio.


Patterns are something you come across every day. They are everywhere you go and in everything you do – you even eat, drink and think them… but it’s unlikely they demand too much of your attention. The closer we look at the fascinating and infinite world of pattern the deeper we can hope to go about understanding the wonders of world and what’s in it.

But where to begin? Perhaps the soundest place to start this somewhat daunting voyage of discovery is to take a bite sized chunk at the patterns that abound in the natural world.  Zooming in even closer for an up-close examination into the mysterious geometry of plants…

So looking around, you might imagine that branches and leaves are arranged at random, haphazardly. The reality is, however, that the points at which every branch, leaf, stem, bud or seed emerge, have all been set out with fixed laws and miraculous measures.  Despite the astonishing smorgasbord of the many different flora and fauna that surround us many have creepily closely comparable features whether viewed under the microscope or from afar. Take for example – the Romanesque broccoli – Such refined regularity in nature was and in many cases still is taken as evidence of God’s guiding hand. And understandably so in fact  – for most observers ruminating for any length at it’s beautifully orchestrated florets, their spontaneous spiralling and tactful repeated twirling could have mesmerising results.

"God sleeps in the minerals, awakens in plants, walks in animals, and thinks in man"
Arthur Young

Our logical reasoning of the manmade world however informs us that “making a pattern requires a patterner”. When we construct an architectural pattern, it is through considered planning and execution, with each individual element carefully laid in place. Our experience from human technologies thus only goes so far in explaining nature’s creation – such questions duly arise  “surely there must be a master at work? What ho’ this higher helping hand?! Which creative genius would have such patience to concoct such a magnificent form? And more fundamentally.. why?! Like staring up at the sky at night, delving into the world of pattern in plants can have humbling and resonating results – sparking philosophical ruminations on life, death and the universe….

And it could all begin at the local grocery shop.  As the naturalist Joseph Banks once mused over patterns found in nature  “ Compared to this what are the Cathedrals or palaces built by men! Mere models or playthings, as diminutive as his works will always be when compared with those of nature.  What now is the boast of the architect! Regularity, the only part in which he fancied himself to exceed his mistress, Nature, is here found in her possession, and here it has been for ages undescribed.”

So back down to earth and with higher powers aside “when the forces of nature have conspired to produce a pattern without, we must presume, any blueprint or foresight or design” how can we systematically dig beneath the surface of this mysterious world of natural growth and form? The answer it would appear lies with some simple, and very fundamental mathematics.  So – if Pattern comes from the Latin pater, meaning father, while the word matter derives from the Latin mater, meaning mother – who exactly is the daddy?  And how on earth do we find him…? perhaps we need a paternity test…

"How can we systematically dig beneath the surface of this mysterious world of natural growth and form? The answer it would appear lies with some simple, and very fundamental mathematics"

Setting off on our geometrical expedition in search of our natural father zooms us straight back in time to 13th century, Italy to Italian mathematician, Leonardo of Pisa who was more famously known as ‘Fibonacci’. Fibonacci  - aka the poster boy of the numerical system – famously drew a new and excited audience to the wonders of mathematics with his weighty 600 page, handwritten (ouch!) compendium in which he cited a sequence – so simple it’s almost baffling. Here each number is created by adding together the previous two – starting 1 1 2 3 5 8 13 21 – a pattern that continues to infinity. The search for an explanation of the persistent occurrence of Fibonacci’s numbers in nature has gone on for over three centuries – and the sequence occurs so frequently in nature that although not impossible – it’s a challenge to find a plant or fruit structure that does not conform to it.  There’s even music in the mathematics – although popularised by Fibonnaci, this sequence of recursive growth originally dates back to 1200 BC in Ancient India where it was used as a method of counting music and rhythm.

Venturing forth, – as these ratios of consecutive numbers get progressively closer to a single number: 1.618034 to the first six decimal places It would be impossible to go any further before next encountering the almighty Golden Ratio – a number so imbedded into the fabric of the universe us that it has haunted human culture for thousands of years. some of the greatest mathematical minds of all ages have spent endless hours over this simple ratio and its so-called mystical properties. “ Where there is matter, there is geometry.” Said Kepler, Johannes, But this fascination is not confined just to the maths room. Biologists, artists, musicians, historians, architects, psychologists, and even mystics have pondered and debated the basis of its ubiquity and appeal. In fact, it is probably fair to say that the Golden Ratio has inspired thinkers of all disciplines like no other number in the history of mathematics. Also known as the divine section it has long been considered to have almost mystical properties – even so far as being entwined with our DNA, this figure is supposed to represent an ‘ideal’ proportion that many people instinctively prefer and has been often used for the proportions of classical architecture – the Parthenon is said to be proportioned this way. Even our own bodies conform to this rampant ratio.

So does any of this actually matter? Why should we even care? Musing more deeply about what’s growing in our garden or sitting on the end of our fork can have small but powerful results.

“Mathematics, rightly viewed, possesses not only truth, but supreme beauty — a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show,” Bertrand Russell

An awareness of these fascinating numerical sequences has the power to transform even the mundane operations of the humble brussel sprout into the magnificent musings of matter and the universe. Through understanding pattern further we can begin to dig a little deeper into the inner workings of the cosmos – a powerful learning tool that can drive forward our man-made designs and innovations – much can be learned from the inner workings of the natural world.

“Copying nature is one thing and understanding nature is another. Copying nature can be simply a form of manual dexterity that does not help us to understand, for it shows us things just as we are accustomed to seeing them. But studying the structures of nature, observing the evolution of forms, can give everyone a better understanding of the world we live in.” Bruno Munari, artist and designer

Pattern is a universal language that connects us all – it shapes the world around us. Without mathematics there is no art.” Said Luca Pacioli but art is only the beginning… understanding more about how spontaneous pattern formation occurs has the power to unite many disparate fields –from science to sociology, architecture to anthropology, music to mechanics – engineering to environmentalism.. and beyond. Most importantly – being more aware of the world around us and our collective connectivity can generate a good dose of much needed empathy. Being more aware, considering the bigger picture can remind us that we are all part of a greater whole and perhaps by that token this might positively shape the way we engage with our environment and each other.

“The kind of attention we bring to bear on the world changes the nature of the world, we attend to, the very nature of the world in which those functions would be carried out, and in which those things would exist. Attention changes what kind of thing comes into being for us, in that way it changes the world” Iain McGilchrist, psychiatrist, doctor and author

The voyage of discovery is by no means over… 

With thanks to Philip Ball