Circle Limit I

Escher originally called this print “Smaller and Smaller II”.
 
Circle Limit I is based on hyperbolic geometry. Escher claimed to have never understood the mathematics behind it, but with the help of H.S.M. Coxeter (a Canadian Professor) he was able to create hyperbolic graphs and ultimately the “Circle Limit” tessellations. Escher loved how cleanly the increasingly tiny figures represented an infinite plane and at the same time created a smooth border. In essence, hyperbolic geometry encapsulated infinity. He had previously expressed frustration that his tessellations could fill a plane infinitely, but to put them on paper either meant he had to create false borders, such as the men fading at the edges of Encounter, or simply end the tessellation along an edge, like Sun and Moon.
 
The block for CLI is actually 1/3 the size of the final image. It is printed three times to create the whole.