Escher’s Infinity Loop Unveiled: Four Rectangles, Elliptic Curves, and a Self-Referential Image

A Hackaday piece explains how MC Escher’s 1956 drawing creates a Droste-like, self-referential loop by using four differently scaled, interconnected rectangles. Building on work by B. de Smit and H. W. Lenstra Jr. (2003) and popularized via a 3Blue1Brown video, the technique can be modeled by treating the scene as an elliptic curve over the complex numbers, allowing the central void to be filled with a coherent, endlessly looping transformation rather than remaining blank.