A one-dimensional lattice gas is a system of particles, each attached to one of a finite number of binding sites around a circle. Time advances in discrete steps; at each time step the particles may hop from one site to a neighboring one, and nearby particles may interact with one another. I will discuss a novel lattice gas model in which the interaction of adjacent particles can create new binding sites or remove existing ones. Although the basic interactions are time-reversible, numerical simulations show an irreversible tendency for the number of sites to grow with time, roughly as . I will explain this behavior, exhibit other solutions of the model in which the motion of the particles and the number of sites are periodic in time, and point out remaining open research problems. This is based on joint work with Karin Baur and David Meyer.