The Golden Spiral is a mystical shape that is an absolute in both abstract mathematics and chaotic nature. It was first discovered by Phythagoras, a failed Greek messiah and mathematical cult leader in the 5th century B.C.
The spiral is derived via the golden rectangle, a unique rectangle which has the golden ratio. When squared, it leaves a smaller rectangle behind, which has the same golden ratio as the previous rectangle. The squaring can continue indefinitely with the same result. No other rectangle has this trait.
When you connect a curve through the corners of these concentric rectangles, you have formed the golden spiral. The Phythagoreans loved this shape for they found it everywhere in nature: the Nautilus Shell, Ram's horns, milk in coffee, the face of a Sunflower, your fingerprints, our DNA, and the shape of the Milky Way.
This photography compositional tool based on the golden ratio, and is called the golden spiral (image from the Wikipedia article). This is probably the most pleasing of all composition rules, if used properly. It's the reason that spiral staircase photos and photos of snail shells are so appealing. But it's not limited to those contexts. It's also another way to look at photos that utilize the golden triangle. And it's always another tool that you can use.
How to use it in photography…
First, when taking a picture, imagine placing the Fibonacci spiral on top of the scene you’re shooting. Then, the idea is to position the most important element of your shot—perhaps a person’s eyes—not at the overall center of the image, but at the off-centered eye of the Fibonacci spiral. It’s simple, but this technique really does make for more interesting pictures—search the web for examples and see for yourself.
This trick of using the golden ratio to lay out your image is related to the well-known “rule of thirds” you hear me talking about. The idea here is to divide your image into thirds both horizontally and vertically, and then to place important elements at the intersections of these lines. The rule of thirds is really just a simplified version of the golden ratio method—after all, it’s a lot easier to mentally picture dividing an image into thirds rather than a Fibonacci spiral.
Either way, if you follow this rule when taking your pictures, your friends will soon be begging you to teach them your secrets—and now you know the math to do it!