The Golden Spiral

 

What turns on many mathematicians as well as artists?

The Golden Spiral does.

It was derived from the “Golden Ratio” of 1:1.618 – aka, the “Golden Mean” and “Divine Proportions.” Simply explained, it’s the ratio that results from dividing a line into two parts so that the longer part divided by the smaller part is equal to the whole length of the line divided by the longer part.

The Golden Ratio first appeared as popular concept in the art and mathematics of ancient Greece. Some claim it’s been around even longer than that. Based on the irrational number Phi, the Golden Ratio served as a foundation for geometry, painting, music, design, architecture, and, in modern times, the Fibonacci sequence – a mathematical concept that seems to account for the many “fractal” shapes we see in nature, especially in such forms as the nautilus shell, coastlines, flowers, and the shape of the cosmos itself. Scientific research even suggests that the pleasing qualities of the human face emerge from these divine proportions.

Some artists and mathematicians point to the prevalence of the Golden Ratio in nature as an evidence of its intrinsically aesthetic qualities. It’s almost as if the beauty of the ratio is built right into the fabric of the universe and how the human mind appreciates it. Some thinkers even believe that the Golden Ratio constitutes the essence of what we humans consider “beauty.”

 

Beyond the Math

All of that is the good news. The not-so-good news is that you need to be a mathematician to really understand the mathematics of the Golden Ratio and how the Golden Spiral is derived from it. When you check out any article that describes this mathematical geometry, your head will probably start spinning before you get past the first paragraph. I wouldn’t be surprised if you had to read my “simply stated” description of the ratio several times before it made sense. At some point, most of us will have to take it on faith that there indeed is a mathematical basis for the golden ratio and the spiral that emerges from it.

I want to side-step all that math, and even the assumption that Mother Nature uses it as her basic tool in designing the universe as we know it. When push comes to shove, I’d say that the math approximates nature. After all, we’re continually discovering that Nature doesn’t strictly follow our concepts of her. She’s always a bit more elusive and mysterious than that. As with all great ideas, the Golden Ratio could very well be the product of cultural thinking – in this case, a cherished aesthetic concept in the traditional western world.

 

Visualizing the Spiral

In this article, I’d like to focus specifically on the golden SPIRAL rather than the ratio. Not as much is written about the spiral. In fact, if you search for information about the spiral, you’ll probably end up reading something about the ratio.

When you work with the spiral in composition, you can forget about all that complex math. Just imagine the nautilus shell. In the case of the shell depicted above, the spiral is a bit squat in the lateral dimension. That’s OK. If there’s one thing I’d like to emphasize, it’s the idea that you can work with spirals of different lengths and shapes. Don’t get too obsessed with the exact dimensions of the mathematically “perfect” spiral.

Now take a look at the two drawings of the Golden Spiral on the right. One of them illustrates how the spiral relates to the Golden Ratio composition of squares that has served artists well for centuries. If you can memorize this classic geometry, good for you! That will come in very handy when doing photography. If not, don’t be dismayed. Just imagine the other drawing of the spiral all by itself. Try to burn that shape into your memory so it can serve as a mental template when constructing compositions.

The dimensions of the spiral, as revealed by the box around it in the drawing, roughly correspond to the 2:3 dimensions of the conventional SLR camera image. That 2:3 proportion has dominated camera design over the years because it closely approximates the Golden Ratio. When placed in the horizontal position, this “landscape” view resembles the wide field of vision through which we humans see the world with our two eyes. That fact might partly explain why we like the Golden Ratio. It's because that's the way we humans were designed to see.

The Psychology of the Spiral

The sensations and emotions we associate with the Golden Spiral make it so appealing. It entails circularity, which is always enticing to the human psyche, along with the feeling of movement that spirals inward towards some fixed destination in the distance or at the heart of the scene, or outward into the mysteriously expansive space that lies outside the frame of the image. The spiral is the connection between inner and outer.

As self-aware and introspective creatures, we humans feel drawn to that spiraling inward sensation. As creatures who sense the power of forces higher and bigger than ourselves, we also become hypnotized by the feeling of spiraling outward into realms that transcend our individuality.

If you think about how we experience spirals in the real world, you’ll discover some of the possible meanings and emotions we might attach to compositions using this design. Water spirals as it goes down funnels and drains. Wind and tornadoes spiral as do kites, planes, and birds descending downwards. Some staircases spiral - hence the irresistible “spiraling stairs” shot. Across different cultures, the spiral symbolizes balance, growth, birth, expansion, contraction, change, evolution, surrender, release, letting go, connectivity, union, journeying, development, constant movement, and infinity – because it goes on and on.

The spiraling sensation looks especially graceful, elegant, and dramatic when working in that classic 2:3 field of view. As you elongate the spiral shape, its movement seems to accelerate rapidly inward while approaching the heart of the spiral, or rapidly outward as you fly off into the space beyond the image frame. When you compress the spiral towards a more square shape, as in the images of the nautilus shell and the staircase, the movement feels more even, regular, and contained.

For the spiral to work effectively, its path carries your eye to important features of the image that rest near its delightfully curving line. In some cases, that path is obviously at work in a composition. In other cases, the spiraling effect can be much more subtle. Unconsciously, we sense it’s mysterious presence, which then quietly generates all those sensations and ideas we associate with it.

The Rule of Thirds

Especially when using that traditional 2:3 ratio, the Golden Spiral does roughly correspond to the rule of thirds, with the heart of the spiral near one of the “power points” of the rule of thirds grid. However, the rule of thirds is a much less sophisticated composition than the Golden Spiral. There is no intrinsic sensation of movement in it, nor a feeling of inner and outer, nor the magic of those special proportions.

Beware of websites or articles about the Golden Spiral that try to illustrate this composition with a drawing of the spiral superimposed on a scene that really doesn’t look like a spiral at all. They are forcing the concept. Usually such images illustrate the rule of thirds rather than the Golden Spiral.

Shooting the Golden Spiral

When you’re out shooting, try to see the Golden Spiral in the scene around you. Unlike painters, you can’t create it from nothing. You have to be able to spot the potential for it. It’s not easy. In your imagination, try to superimpose the spiral shape over your environment. If you do see a possibility, shift your viewpoint and camera angle in order to refine the spiraling effect.

Take a look at the photo of the trees. The negative space of the sky forms a rather nice beginning to the Golden Spiral that then transitions into the cluster of tree branches resting at the core of the spiral. While this composition works fairly well, it would be considerably improved if there was something in particular at the heart of the spiral – perhaps a bird. Any object that lies at the core of the spiral easily becomes the central subject of the image because all the movement of the photo either radiates from that object or converges onto it.

Now take a look at the street scene below. Here the Golden Spiral is more subtle, almost subliminal. The eye moves along the curving path created by the car in the foreground, the sign of the car hanging on the building, the stop light, the “Selby Avenue” sign, the sweeping branches of the tree in the background, the man in the background, and the woman walking her dog at the heart of the spiral. I decided to process this photo in a painterly style in order to create a classic feeling for a modern street scene.

 

Cropping to the Spiral

In some photo editing programs, like Photoshop, you'll have access to a tool that provides overlays of the Golden Spiral to help you crop the image to that magical design - and other types of compositions as well, including the rule of thirds. Play with that tool. It will help you spot the spiral even in images where it otherwise might have eluded you. You can see how the spiral overlay compares to the other types of overlays, such as the rule of thirds. If the theory is correct that the Golden Ratio exists everywhere in nature, then there must be a Golden Sprial somewhere in your shot. But don't always count on that. Some images might have no spiral at all. Others might contain it in a smaller area of the shot. If you find it, crop to reveal it. And don’t worry about getting that supposedly perfect proportion of 2:3 or 1:1.618 (to be exact). Even less than “golden” spirals will make for an interesting composition.

 

If you liked this article, I'd also recommend these:

Geometric and Organic Patterns
Circular Compositions
Movement in Photographs