Since Renaissance times some of our greatest thinkers have grappled with the scientific and mathematical formulas behind what we consider to be beautiful or aesthetically pleasing. For many of us, science and math couldn’t be further from our minds when we create art. Some of us even become twitchy when these subjects are mentioned but if we can put aside the psychological damage inflicted by certain high school teachers, the math and science of art and nature is a fascinating subject, and one that may just change the way you observe the things around you.
The Fibonacci Sequence and The Golden Ratio provide us with the mathematical formulas behind some of the patterns we see reflected in the world around us. Renaissance mathematicians believed that you could apply these formulas to your art to create works that were more aesthetically pleasing and many of these ideas have gone on to form basic compositional rules that artists are still taught today. We thought a crash course in both might spark a few ideas about how you can use some of these principles into your own art and design. Alternatively, you could just use your new found knowledge to astonish your mates next time you’re down the pub
The Golden Ratio: Ancient Greek mathematicians we’re captivated by the Golden Ratio which was showing up all over the place in their studies of Geometry. There was a lot of chin rubbing and wonderment. But things really started to heat up when a fellow named Luca Pacioli described the Golden Ratio as ‘the divine proportion’. He wrote a long manuscript on mathematical and artistic proportions called De divina proportione which was illustrated by none other than Leonardo da Vinci. The work inspired artists and architects to experiment with incorporating these proportions and principles in their own work.
A rectangle created using the Fibonacci Sequence and a Fibonacci Spiral
The Fibonacci Sequence: Fibonacci was an Italian mathematician who conducted an experiment about breeding patterns in rabbits which resulted in a series of numbers called the Fibonacci Sequence. Each number in the sequence is the sum of the previous two numbers so the beginning of the sequence looks like this: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233 … The higher the numbers go, the closer two consecutive numbers of the sequence divided by each other will approach the Golden Ratio. And as it turns out, although not identical, spirals created by using the Golden Ratio or the Fibonacci Sequence are very similar.
If we’re just about to lose you at this point, this video does a pretty amazing job of demonstrating how the Golden Ratio and the Fibonacci Sequence are reflected in nature. It’s pretty cool stuff.
The Golden Ratio can be used to create a golden triangle, golden rectangle and golden spiral. Each of the links in that previous sentence will take you to a page which shows you how to draw up the shape. Once you have a basic grasp of these shapes, you can begin to visualize how you may be able to use them for compositional guidance. We’ve also included a bunch of links below which explain how you can put these principles into practice when it comes to creating your own art. If you manage to incorporate the proportions of the Golden Ratio into your work, you’re following in the footsteps of artists including Leonardo Da Vinci, Salvador Dali and Piet Mondrian. Not bad company hey!
Further Reading and Inspiration:
- Foundations of Design – Part 1: The Math And Science
- The Golden Ratio vs The Rule Of Thirds
- The Golden Ratio
- The Lazy Rule Of Thirds
- Fibonacci numbers in popular culture
- A lesson on Fibonacci from Tool (rawk + math = awesome m/)
- Fabulous Fibonacci and His Nifty Numbers (From Mensa for Kids)
- Golden Ratio in Art and Architecture
- Composition And Golden Ratio Variations (By Anton Gorlin)
- Creating Art Using The Golden Ratio (Digital Arts Online)
- Golden Section and Photography
- Golden Spiral design template for Illustrator
- Composition In Portraiture
- Composition Guides In Lightroom
We’d love to hear from artists who have studied (or taught) Fibonacci, The Golden Ratio or any related subjects on composition or the science and math behind aesthetic beauty. If you have links or resources you’d recommend or books you’ve lost yourself in, we’d love to hear about them. If you’ve incorporated any of these ideas in your work, please post them in the comments below. And if this inspires you to experiment in your own work, we’d love to see the results!
The Science and Math Behind Great Art and Design was written by Natalie Tyler.
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