(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 a painting by M.C. Escher: some Dutch mathematicians have found what the transformation is and explained it in (almost) layman terms.
In this particular case the image is twice repeated. In the parameterization discussed here, this is a (1,2) spiral
This image was done in The Gimp and transformed with MathMap.