The nature of design: the Fibonacci sequence and the Golden Ratio - Cleveland Design (2024)

by Jonathan Cleveland | Sep 24, 2020 | Expertise

The nature of design: the Fibonacci sequence and the Golden Ratio - Cleveland Design (1)

The great thing about being a graphic designer in the Boston area is having the opportunity to take in all the nature that presents itself in New England this time of the year. The sunflowers in my garden are tall, strong and they seem to keep the hope alive that summer is not quite over. But the best thing about the sunflowers is the incredible seed formation that bursts from the center of the flower. It’s nature at its best but also math at its best—it’s the Fibonacci sequence in action.

What is the Fibonacci sequence?

The Fibonacci sequence is one of the most famous formulas in mathematics. Each number in the sequence is the sum of the two numbers that precede it. So, the sequence goes: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, and so on. It’s been called “nature’s secret code,” and “nature’s universal rule.” Just take a look at the pattern it creates and you can instantly recognize how this sequence works in nature like an underlying universal grid. A perfect example of this is the nautilus shell, whose chambers adhere to the Fibonacci sequence’s logarithmic spiral almost perfectly. This famous pattern shows up everywhere in nature including flowers, pinecones, hurricanes, and even huge spiral galaxies in space. But the Fibonacci sequence doesn’t just stop at nature. In graphic design, we refer to it as the Golden Ratio. It can be applied to everything from logo design, print design and website design.

What is the Golden Ratio?

The Golden Ratio is a design concept based on using the Fibonacci sequence to create visually appealing proportions in art, architecture, and graphic design. The proportion, size and placement of one element compared to another creates a sense of harmony that our subconscious mind is attracted to.

To use or not to use

As designers, there are no rules when it comes to creating an aesthetic or an effective design for a project. Sometimes we find that the Golden Ratio works perfectly in application, while other times we come up with a great idea that doesn’t necessarily follow the rules. There is an ongoing debate among graphic designers, mathematicians and scientists about whether the Golden Ratio in relation to design is a myth. But there is plenty of evidence, not only in nature but in created design, that proves the ratio to be a solid tool for us designers. It can be a helpful when creating a grid for a layout, finding the perfect cropping for a photo, or figuring out sizes for type hierarchy when featuring content, just to name a few. Overall, it’s an interesting way to look at great design through a mathematical lens and we think it’s fascinating to identify where and how it is used in the world around us.

Intrigued? Here are some great examples of the Golden Ratio in action.

The nature of design: the Fibonacci sequence and the Golden Ratio - Cleveland Design (2)

The nature of design: the Fibonacci sequence and the Golden Ratio - Cleveland Design (2024)

FAQs

What is the nature of design the Fibonacci sequence and the golden ratio? ›

The Golden Ratio is a design concept based on using the Fibonacci sequence to create visually appealing proportions in art, architecture, and graphic design. The proportion, size and placement of one element compared to another creates a sense of harmony that our subconscious mind is attracted to.

What is the relationship between the golden ratio and the Fibonacci sequence? ›

The Golden Ratio is a relationship between two numbers that are next to each other in the Fibonacci sequence. When you divide the larger one by the smaller one, the answer is something close to Phi. The further you go along the Fibonacci Sequence, the closer the answers get to Phi.

What is the golden ratio design in nature? ›

One of the most remarkable occurrences of the Golden Ratio in nature is seen in the formation of spirals. Examples include the patterns found in sunflowers, pinecones, and seashells. These spirals exhibit a consistent growth rate, adhering closely to the Golden Ratio.

What is the Fibonacci sequence and how does it relate to nature? ›

In trees, the Fibonacci begins in the growth of the trunk and then spirals outward as the tree gets larger and taller. We also see the golden ratio in their branches as they start off with one trunk which splits into 2, then one of the new branches stems into 2, and this pattern continues.

How to use the Fibonacci sequence in design? ›

How To Use It. If you look at the Fibonacci Sequence and consider them as possible section, margin and font sizing it should be clear that it can structure your entire design. The smaller range of the sequence (8, 13, 21, 34, 55) is perfect to decide margins, line heights and font sizes.

What is the golden ratio in design? ›

Take a square and multiple one side by 1.618 to get a new shape: a rectangle with harmonious proportions. If you lay the square over the rectangle, the relationship between the two shapes will give you the Golden Ratio.

How is the Fibonacci sequence used in architecture? ›

The principles of the Fibonacci sequence has been used by countless artists and architects since the Renaissance in proportioning their works to approximate the golden ratio with the belief that this proportion is aesthetically pleasing based on its harmony, proportion, and mathematical order.

How is the Fibonacci sequence used in real life? ›

We observe that many of the natural things follow the Fibonacci sequence. It appears in biological settings such as branching in trees, phyllotaxis (the arrangement of leaves on a stem), the fruit sprouts of a pineapple, the flowering of an artichoke, an uncurling fern and the arrangement of a pine cone's bracts etc.

Where is the golden ratio used in real life? ›

Golden Ratio is one of the most common mathematical ratios in nature. We see this ratio everywhere from majestic landscapes like the Pyramids of Giza and the Mona Lisa to modern-day logos such as Twitter and Pepsi. Golden ratios are unique because of their golden proportion.

What is the golden ratio of the human face? ›

It is suggested that a face is perceived as more aesthetically pleasing when its width is about 1.618 times the width of the mouth. This application of the golden ratio helps to create a sense of balance across the facial features, making the face appear more proportionate and visually appealing.

What is the formula for the golden ratio in nature? ›

Golden ratio is a special number and is approximately equal to 1.618. Golden ratio is represented using the symbol “ϕ”. Golden ratio formula is ϕ = 1 + (1/ϕ). ϕ is also equal to 2 × sin (54°)

Why is golden ratio beautiful? ›

Others think that we tend to perceive a face more aesthetically appealing when it features the Golden Ratio because the human eye can process it faster and that causes our brain to feel 'pleased'. The Golden Ratio is not just observed in humans, but it is actually used in architecture and art work as well.

How does the Fibonacci sequence relate to the golden ratio? ›

The essential part is that as the numbers get larger, the quotient between each successive pair of Fibonacci numbers approximates 1.618, or its inverse 0.618. This proportion is known by many names: the golden ratio, the golden mean, ϕ, and the divine proportion, among others. So, why is this number so important?

Why is the Fibonacci sequence so important? ›

The Fibonacci sequence is important for many reasons. In nature, the numbers and ratios in the sequence can be found in the patterns of petals of flowers, the whorls of a pine cone, and the leaves on stems. As the sequence continues, the ratios of the terms approach a number known as the golden ratio.

What are the five examples of the Fibonacci sequence? ›

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181. … and so on.

What is the Fibonacci sequence and why is it important? ›

The sequence of numbers, starting with zero and one, is a steadily increasing series where each number is equal to the sum of the preceding two numbers. Some traders believe that the Fibonacci numbers and ratios created by the sequence play an important role in finance that traders can apply using technical analysis.

Does the Fibonacci sequence turn out to be the key to understanding how nature designs? ›

Guy Murchie Quotes

The Fibonacci Sequence turns out to be the key to understanding how nature designs... and is... a part of the same ubiquitous music of the spheres that builds harmony into atoms, molecules, crystals, shells, suns and galaxies and makes the Universe sing.

How is the Fibonacci sequence used in art? ›

Fibonacci Spirals

In classical art, this spiral's proportions are often used to guide the placement of elements within a composition, leading the viewer's gaze along an aesthetically pleasing path.

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