How (and why) to take a logarithm of an image

Summary by Krater

An explanation of the complex mathematics behind M. C. Escher's print The Print Gallery, showing how conformal maps and complex logarithms recreate its infinite self-similar loop.

From the video

Answers: How does M.C. Escher's Print Gallery work mathematically?

• The Print Gallery by M.C. Escher
• Conformal maps
• Complex logarithms
• Droste effect
• Mesh warp technique
• Complex exponential function

What it concludes

• M. C. Escher's lithograph The Print Gallery features a self-similar Droste effect with a scaling factor of 256.
• The mesh warp technique allows an artist to map a straight reference image onto a warped grid to create complex distorted scenes.
• Conformal maps preserve angles locally, meaning small squares remain approximately square after transformation.
• The complex exponential function maps vertical lines to concentric circles, turning periodic vertical strips into a continuous tube.
• The natural logarithm acts as the inverse of the complex exponential, turning circle points into vertical lines and creating the infinite nesting of the Print Gallery.