Perhaps one of the first lessons graphic designers learn in a Swiss-based degree program is the Fibonacci sequence, in which we inevitably think to ourselves, “If I had wanted to do math, I would have pursued a different career.” To our surprise, the ratio derived from this mathematical sequence has a significant bearing on aesthetics. The ancient Greeks considered it to be the most beautifully proportioned ratio. It is known by many names, including the golden ratio, divine proportion, divine section, the golden mean and the golden number. Beginning with zero and 1, each subsequent number in the sequence is determined by the sum of the two preceding numbers: 1, 1, 2, 3, 5, 8, 13, etc. A visual translation of this sequence results in the golden ratio, illustrated below, providing an iconic spiral you might recognize. The golden ratio was the driving force behind the grid system in Swiss Style compositions – including those by Josef Müller-Brockmann, one of the pioneers of Swiss Style – and is commonly used today in logo, product and layout design. The advantages of the ratio are numerous, including a well-balanced composition and the ability to lead the viewer’s eye around the page following the sweeping arc of the spiral.
So where did this sequence come from? Some of you are probably ahead of me: It originated in nature. Take a look at the head of a sunflower and you’ll notice beautifully balanced spirals originating from the center. The sequence is found everywhere in nature, from the growth of a cell to a hive of bees to a pine cone or a nautilus shell. If you’re anything like me, you find this simply mind-blowing. How can such a dynamic, unpredictable world contain the same specific sequence of numbers across diverse flora and fauna? It’s almost hard to believe, in which case this video might be enough to convince you.
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These organisms are not aware of the sequence and don’t purposely arrange themselves to follow the numbers. Rather, they grow in the most efficient way possible, which happens to be the Fibonacci sequence, an emergent principle. The leaves on certain plants are staggered around the stem at 137.5 degrees (derived from the Fibonacci sequence) relative to the preceding leaf, which maximizes their exposure to sunlight, as seen in this video. The seeds in a sunflower are staggered in double spirals around the center, which allows it to pack in as many seeds as possible. In Life’s Principals, this would be an example of “Fit Form to Function: Select for shape or pattern based on need.” The organisms that employ this sequence don’t do so because it looks pretty. They do so because it provides advantages for them to live more efficiently with less energy expenditure.
It’s important to note that nature makes mistakes. You may stumble across a pine cone or pineapple with spirals that add up to be numbers that differ from the Fibonacci sequence. In these cases a disturbance has taken place to bump the sequence from its original path. Here we see another Life’s Principle in action: “Maintain Function Following Disturbance.” Though something has knocked the original sequence off course, plants overcome the disturbance and settle into a different but stable pattern.
Enough about nature – back to design. The use of the golden ratio can be seen in much more than just graphic design. It’s thought that the pyramids were constructed using the ratio, as well as the Parthenon and Notre Dame. The “Mona Lisa” owes at least some of its beauty to the ratio. It can be found in the stock markets and foreign currency exchange, and even the proportions of human DNA (and I find myself back to nature again).
What does it look like when you emulate the ratio in a bit of biomimicry for more than just beauty and divine proportions? An MIT team applied the ratio to a concentrated solar plant in which mirrors direct sunlight to a central tower where water is boiled to release steam that activates a turbine and produces electricity. Arranging the mirrors like a sunflower so that they’re turned 137.5 degrees (a “golden angle”) respective to their neighbors decreased land usage by 20 percent and increased the overall efficiency of the plant by eliminating the shadows cast by mirrors onto neighboring mirrors. Fitting form to function allowed the team to optimize the packing of mirrors for a more efficient and ultimately cost-effective design. Read the full case study at AskNature.org.
We often use the golden ratio in our designs to achieve pleasing aesthetics. Looking at the history of the sequence and why it exists, perhaps we can challenge ourselves to use the ratio not only for aesthetics, but also for function with the ultimate goal of creating life-friendly products and designs. But why stop there? By inserting “fitting form to function” into the scoping phase of our work, we could open up countless possibilities in which nature can fuel innovative, life-friendly designs.