M. C. Escher's spiral effect in *Print Gallery* inspired a WebGL recreation using polar coordinate transformations. The project translates Cartesian coordinates to polar space, enabling spiral animations through rotation and scaling. This mirrors the Droste effect's recursive image embedding but adds seamless transitions between nested layers.

The technical core involves converting (x,y) coordinates into radius-angle pairs, creating periodic structures. A rotation in polar space merges horizontal image rows, breaking their separation. Transforming back to Cartesian coordinates produces the spiral illusion. This method simplifies complex calculations, akin to Fourier transforms in signal processing.

WebGL shaders handle the coordinate shifts and rotations efficiently. The vertex shader maps positions to polar coordinates, while the fragment shader applies color blending for the recursive effect. The result is a smooth, infinite spiral that mimics Escher's optical illusion.

This implementation highlights how computational geometry can replicate artistic concepts. By leveraging mathematical transformations, developers can create visually striking effects with minimal code. The project demonstrates the intersection of art, math, and programming in modern digital tools.