This is motivated by the new paper of Smith, Myers, Kaplan, and Goodman-Strauss, wherein they define the existence of an aperiodic monotile. Clearly their tiling is not three-colorable, so we have from Appel and Haken (1977) that its chromatic number is 4. What is not clear to me, however, is how one could algorithmically construct such a coloring. Any suggestions would be much appreciated!