What You Need to Know About Spirals

Spirals are present everywhere in art and in the world around us, from the form of the sea snail to stars in the galaxy. Most spirals have a logarithmic shape. This means that just like fractals they keep repeating themselves on a smaller scale. A small part of a spiral looks just like the bigger part. If a snail shell keeps growing, it will retain its shape as it is getting bigger. Spirals appear everywhere, even in the places that are not very obvious such as the circular arrangements of florets in a sunflower or a flowing fluid in the bathtub.

Spirals are very special because they are often not just scrolling shapes. They start with large curves and become increasingly coiled as they move closer to their centre. This is very different from a spiral that you can create by, say, rolling up a garden hose. When you do create spirals in your daily life, the widths of the elements remain the same. This is an important distinction.

Archimedes first described the coiled-hose spiral in his book On Spirals. In the real world, this spiral typically comes from rolling some rope or another element.

The snail shell is very different because it is based on a logarithmic spiral. One of the most important properties of this spiral is that it remains the same in shape no matter how large or tiny it is. It is yet another example of a self-similar structure that attracts artists so much.

There are more differences between the Archimedean spiral and the logarithmic spiral. The Archimedean spiral can only get so small because the coil does not change its width as the circles become smaller and smaller. When a logarithmic spiral gets close to its centre, the coils get much narrower and the curvature becomes tighter. If you zoom to the centre of a snail shell, you’ll see that curve that looks exactly like the curve that you see when you zoom out.