  We consider a particle system on $Z^d$ with finite state space and
interactions of infinite range. Assuming that the rate of change is continuous
and decays sufficiently fast, we introduce a perfect simulation algorithm for
the stationary process. The algorithm follows from a representation of the
multicolor system as a finitary coding from a sequence of independent uniform
random variables. This implies that the process is exponentially ergodic. The
basic tool we use is a representation of the infinite range change rates as a
mixture of finite range change rates.
