Are You a Math Genius?
The original picture is by an artist who wrote an influential math book containing the duplication of the cube problem, epicycloids, and Archimedean solids, among other things. The warping method is a conformal map of some kind. An animation of some conformal maps is shown below.
Conformal map
Wolfram SpikeyPuzzles provided by Wolfram Research, Makers of Mathematica