Periodicity and growth in a lattice gas with dynamical geometry
We study a one-dimensional lattice gas ``dynamical geometry model" in which
local reversible interactions of counter-rotating groups of particles
on a ring can create or destroy lattice sites.
We exhibit many periodic orbits and show that all other solutions have
asymptotically growing lattice length in both directions of time.
We explain why the length grows as $\sqrt{t}$ in all cases examined.
We completely solve the dynamics for small numbers of particles with
arbitrary initial conditions.
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