A growth model, in which the morphology of the clusters grown depends
on temperature and disequilibrium, is presented. The model is a modifi
ed version of Kadanoff's pedestrian model. Sticking, rearrangement and
evaporation compete with rates appropriate to the inverse temperature
betaJ and to the disequilibrium beta DELTAmu. The relation between th
e simulations and the continuum thermal model is discussed, and the de
pendence of growth morphologies on the anisotropy epsilon is stressed.
As temperature and disequilibrium increase the clusters become more a
nd more branched. The same occurs to a lesser extent, for given temper
ature and disequilibrium, as time goes by. For 4 < betaJ < 5 a fairly
well defined tip-splitting transition takes place from a dendritic to
a dense branching morphology. The model correctly describes the behavi
our of the growth velocity upsilon of a dendrite as a function of time
. After a transient decrease, upsilon tends to a constant value. The m
odel may be relevant for understanding domain growth in a lipid monola
yer.