M.C. Escher

Maurits Cornelis Escher (1898–1972) was a Dutch graphic artist renowned for his mathematically inspired woodcuts, lithographs, and mezzotints. His work explores impossible constructions, mathematical concepts such as tessellations, symmetry groups, infinity, and the nature of space-time. Escher had no formal training in mathematics but collaborated with crystallographers and mathematicians to refine his understanding of geometric structures.

Key Themes & Techniques

• Tessellation: Interlocking tilings using birds, reptiles, fish, and demons Tessellation.
• Impossible Objects: Structures that violate Euclidean geometry or physical laws, such as Waterfall, Relativity, and Ascending and Descending.
• Perspective & Infinity: Distorted viewpoints and recursive scaling, notably in Circle Limit series.
• Duality: Interchangeable positive and negative space.

Major Works

• Day and Night (1938)
• Drawing Hands (1948)
• Waterfall (1961)
• Relativity (1953)
• The Print Gallery (1956): A lithograph depicting a fish-eye view of a harbor scene viewed from a building corner, featuring a recursive loop where the viewer looks at a print of the scene they are in.

Mathematical Connections

Escher’s work has profound implications for Geometry, Topology, and Complex Analysis. While he approached these subjects intuitively, later mathematicians formalized the underlying structures.

Conformal Mapping in The Print Gallery

• The creation process of The Print Gallery involves a complex geometric transformation known as a conformal map.
• Specifically, the image utilizes a logarithmic spiral inversion to achieve the circular perspective and recursive central hole.
• For a detailed breakdown of how Complex Analysis explains this transformation: M.C. Escher’s Print Gallery: Complex Analysis and Conformal Mapping.

References

• M.C. Escher’s Print Gallery: Complex Analysis and Conformal Mapping — 3Blue1Brown explanation of the logarithmic mapping used in The Print Gallery.