The Smooth Power of the 'Neandertal Method'

We describe an algorithmic method to transform a Euclidean wallpaper pattern into a \emph{Circle Limit}-style picture à 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.