  The Cellular Potts Model (CPM) is a lattice based modeling technique which is
widely used for simulating cellular patterns such as foams or biological
tissues. Despite its realism and generality, the standard Monte Carlo algorithm
used in the scientific literature to evolve this model preserves connectivity
of cells on a limited range of simulation temperature only. We present a new
algorithm in which cell fragmentation is forbidden for all simulation
temperatures. This allows to significantly enhance realism of the simulated
patterns. It also increases the computational efficiency compared with the
standard CPM algorithm even at same simulation temperature, thanks to the time
spared in not doing unrealistic moves. Moreover, our algorithm restores the
detailed balance equation, ensuring that the long-term stage is independent of
the chosen acceptance rate and chosen path in the temperature space.
