Circle Limit IV (Heaven and Hell) - M.C. Escher

A classic woodcut by M.C. Escher, this piece uses hyperbolic geometry to create an infinite tessellation of winged figures.

M.C. Escher created this work in 1960, utilising the principles of hyperbolic geometry. The composition is a woodcut that demonstrates the concept of a circle limit, where figures decrease in size as they approach the edge of the circular frame. This specific piece, often referred to as Heaven and Hell, features a tessellation of winged creatures that morph between angelic and demonic forms.

The arrangement relies on a Poincaré disk model, a method for mapping infinite hyperbolic space onto a finite circular area. Escher was inspired by the work of mathematician H.S.M. Coxeter, whose papers on hyperbolic tilings provided the theoretical framework for this series. The butterflies or winged figures are arranged in a radial symmetry, creating a sense of infinite regression toward the centre of the print.

Visually, the work is defined by its stark contrast and precise linework. The figures are locked together in a repeating pattern, where the negative space of one creature forms the body of another. The colour palette is restrained, focusing on black, white, and muted tones of red and ochre to define the boundaries of the tessellated shapes. This print is a clear example of the intersection between artistic practice and geometric theory, showing how rigid mathematical rules can produce complex, organic-looking results. The viewer is drawn into the centre of the circle, where the figures become smaller and more condensed, suggesting an infinite continuation beyond the physical limits of the paper.