O God, I could be bounded in a nutshell and count
myself a king of infinite space
-William Shakespeare (Hamlet)

INFINITY: One of Escher's ambitions was to represent infinity in a confined space, and in doing so, he employs hyperbolic geometry. That is, on a hyperbolic plane, points infinitely far way are thought of as within a circle, which is the hyperbolic world. Geometric form is consistent within the plane, but the distances are distorted. The circumference is infinitely far away from the center, and one might consider the perpective change when looking upon a shpere to understand how the distance becomes increasingly more distorted as we move from center to circumference. Circle Limit III is an excellent example of this kind of representation.

#434 Circle Limit III 1959
woodcut in five colors

Escher also represents infinity from the reverse direction, using a mathematical procedure known as inversion. Inversion represents all points in two-dimensional space in a circle such that as a point in space gets farther from the circle's circumference, the corresponding point in the inversion circle approaches the center much the way an asymptotic line approaches a limit. Escher basically inverts equiangular spirals, which we see here:

$423 Whirlpools 1957
woodcut in three colors

# 440 Larix [Apple] 1961
Wood engraving 3 x 3"