An n-state Potts lattice gas Hamiltonian is constructed whose partition function is shown to reproduce in the limit n→0 the generating function for the statistics of either lattice animals or percolating clusters for appropriate choices of potentials. This model treats an ensemble of single clusters terminated by weighted perimeter bonds rather than clusters distributed uniformly throughout the lattice. The model is studied within mean-field theory as well as via the ε expansion. In general, cluster statistics are described by the lattice animal's fixed point. The percolation fixed point appears as a multicritical point in a space of potentials not obviously related to that of the usual one-state Potts model.