Our world is, roughly, spherical. Since we are a traveling species we have developed different ways of figuring out where we are on that sphere, and where we are going. One of the most basic things we have done is created imaginary lines of latitude and longitude that run around our sphere. The lines of latitude and longitude cross each other at right angles, making a grid. We use them to measure how far we are from equator and poles (latitude) and how far we are from zero longitude (a line running from pole to pole through the old Royal Astronomical Observatory in Greenwich, England).
Once we know where we are on that grid we know where we are in relation to everywhere else. Even more interesting – if we keep traveling across the lines of that grid in one direction we’ll end up spiralling our way around the globe, and the circles we travel in will keep getting smaller and smaller as we get closer to the poles. Those spiralling lines are called loxodromes.
In “Spherical Spirals” Escher used the concept of loxodromes. His spirals travel around his sphere, crossing the lines of the grid he created around it, always at the same angle. As they get closer to the ‘poles’, those spirals get smaller and smaller.
But he used bands, not lines – and we can see them both inside and out. And he used colour and shading to define inside and outside, closer and further away. It creates the illusion of being able to see the sphere in three dimensions, when all we can really see is two dimensios.
Our brain tells us what we’re looking at looks like a solid object. But it’s an illusion.
M. C. Escher, Spherical Spirals
Loxodrome Animation by Karl Benarik shared under Creative Commons Attribution-Share Alike 3.0 Unported License.