  We present a hydrodynamic lattice gas model for two-dimensional flows on
curved surfaces with dynamical geometry. This model is an extension to two
dimensions of the dynamical geometry lattice gas model previously studied in
one-dimension. We expand upon a variation of the two-dimensional flat space FHP
model created by Frisch, Hasslacher and Pomeau, and independently by Wolfram,
and modified by Boghosian, Love, and Meyer. We define a hydrodynamic lattice
gas model on an arbitrary triangulation, whose flat space limit is the FHP
model. Rules that change the geometry are constructed using the Pachner moves,
which alter the triangulation but not the topology. We present results on the
growth of the number of triangles as a function of time. Simulations show that
the number of triangles lattice grows with time as the cube root of the number
of time steps, in agreement a mean field prediction. We also present
preliminary results on the distribution of curvature over a typical
triangulation for these simulations.
