The Smooth Power of the "Neandertal Method"

TL;DR

This paper introduces a simple, efficient algorithmic method for transforming Euclidean wallpaper patterns into Circle Limit-style images using conformal maps, emphasizing mathematical soundness, aesthetic quality, and computational speed.

Contribution

It presents the 'Neandertal Method,' a straightforward, parallelizable approach for pattern transformation that outperforms more complex methods in speed and simplicity.

Findings

The method is mathematically sound and produces aesthetically pleasing patterns.

It can be efficiently parallelized on GPUs for fast computation.

The approach is simpler and faster than existing complex methods.

Abstract

We describe an algorithmic method to transform a Euclidean wallpaper pattern into a Circle Limit-style picture \`a la Escher. The design goals for the method are to be mathematically sound, aesthetically pleasing and fast to compute. It turns out that a certain class of conformal maps is particularly well-suited for the problem. Moreover, in our specific application, a very simple method, sometimes jokingly called the "Neandertal Method" for its almost brutal simplicity, proves to be highly efficient, as it can easily be parallelized to be run on the GPU, unlike many other approaches.