  Holroyd and Liggett recently proved the existence of a stationary 1-dependent
4-coloring of the integers, the first stationary k-dependent q-coloring for any
k and q. That proof specifies a consistent family of finite-dimensional
distributions, but does not yield a probabilistic construction on the whole
integer line. Here we prove that the process can be expressed as a finitary
factor of an i.i.d. process. The factor is described explicitly, and its coding
radius obeys power-law tail bounds.
