(help my city!)
Conformal mappings are great: it's a very powerful branch of mathematics, which basically says you can deform almost any 2D object and transform it into something else while keeping the shape of objects the same (on a small scale). Hence this picture: you see no holes, no obvious distortion, but this image cannot be real. This trick is inspired by apainting by M.C. Escher: some Dutch mathematicians have found what the transformation is and explained it in (almost) layman terms.