The history of the golden ratio is the history of our attempt to understand and diagram the beauty of the natural world.
We see this ratio in spiral-shaped shells, notably the chambered nautilus. We see it in the growth of pine branches, the breaking of a wave, and even the proportions of the human body.
We don’t know why we see it with such frequency. Whatever the evolutionary origin and purpose of it, it’s imprinted on our brains as a sign of beauty, of strength, of something well made.
Artists and photographers use this formula with less precision and much success. If you’ve ever heard of the “rule of thirds” for composition, that’s an application of the golden ratio. Dividing an image – a canvas, a frame – in to thirds gets an accurate enough division into the golden ratio.
So how exactly do designers translate the beauty of the chambered nautilus into a balanced logo?
Creating Your Own Golden Ratio
The proportional map is created first. Most designers make this once and keep it on hand. It starts with a rectangle with one side 1.618 times longer than the other. For example, if a rectangle has one edge that is 100 pixels long, the other edge should be 162 pixels long.
When a square is placed inside this rectangle, nestled against three edges, the remaining empty space will be another rectangle with sides in a ratio of 1:1.618.
A square placed within this rectangle will again leave leftover another rectangle….
And so on.
Circles placed within the squares will have diameters in a pattern mathematicians will recognize.
Take the smallest circle and give it a diameter of 1 unit. If you add that diameter to itself, you will get the diameter of the next largest circle: 2. If you take the second circle and add the smallest circle’s diameter to it, you’ll get the diameter of the third circle: 3. If you take the diameter of the third circle and add the diameter of the previous circle, you get the diameter of the next circle: 5. These numbers increase in this way: 1, 2, 3, 5, 8, 13… with the next number in the sequence being the sum of the two previous.
This is referred to as the Fibonacci sequence.
When you create a spiral within this shape, going corner to corner, you can see the blueprint for the shell of the nautilus.
The Golden Ratio in Existing Logos
Okay, math done.
What good is this to us now?
Now we have a set of shapes created in proportion that are pleasing to the eye and can be used to balance out graphic art. You can scale them up, scale them down, move them, duplicate them – as long as they are kept in proportion to one another.
The Apple logo is a straightforward example of this in action. By taking proportional circles, we can use them as guides to see how the Apple logo uses curves guided by the golden ratio. The main apple shape takes its curves from the largest circle, and the bite out of the apple is proportionally smaller.
That bite could have been any size, but putting it in proportion makes it visually pleasing.
The leaf at the top of the apple uses the same curves as the bite cutout, and the bumps at the top and bottom of the apple also follow the proportions of the golden ratio.
More simple is the logo for National Geographic, which is just a single rectangle in the proportions of 1:1.68.
How Do I Use This for my Own Logo Design?
So how does this work in practice when designing a logo?
I usually start with a rough sketch of an idea. For this post, I created the brand Light Touch Media, with the idea that I’d make a butterfly logo. I roughed it out, happy enough with the concept and colors.
It’s okay, but it’s not so balanced.
So I bring in my circles, fitting them in the curves of the butterfly and adjusting the narrow and flared corners of my shapes to follow the circles. I check the white markings on the butterfly as well, making sure they are sized correctly.
The overlaps, where the colors merge, I want to be spaced according to the ratio as well – as much as possible.
I get one side right and mirror it, nudging the wings into a position I like, following the proportions as best I can without getting more than two colors overlapping at a time and without leaving any white space between the wings.
By comparison, the first one now looks really awkward.
I’m much happier to place this one beside the company name and use it as a logo.
You can use the golden ratio to manage both negative and positive space. In this example of another branding I created, you can see I’ve used squares and circles to guide where corners hit, and control the width of the negative space between the frosting swirls as well as the curves of the frosting itself.
Again, I started with a roughed-out design, and then adjusted all my curves to follow the proportional circles.
The basic shape is good. I want to add a flower, and place it at the intersection of some of the circles, keeping it sized proportionally itself.
I didn’t over-worry using the golden ratio within the flower itself, but was content to trace a plumeria blossom. I think they’re beautiful enough without me correcting their math.
Colors adjusted, I’m happy to place this with its brand name and complete the logo.
Designers call these forms beautiful, and they are. But really what they are is natural. They look familiar to us – balanced, comforting, strong – like the natural world around us. It’s a way to bring the outside in, and make your logo a natural component of your business.