  We study the continuum opinion dynamics of the compromise model of Krause and
Hegselmann for a community of mutually interacting agents, by solving
numerically a rate equation. The opinions are here represented by bidimensional
vectors with real-valued components. We study the situation starting from a
uniform probability distribution for the opinion configuration and for
different shapes of the confidence range. In all cases, we find that the
thresholds for consensus and cluster merging either coincide with their
one-dimensional counterparts, or are very close to them. The symmetry of the
final opinion configuration, when more clusters survive, is determined by the
shape of the opinion space. If the latter is a square, which is the case we
consider, the clusters in general occupy the sites of a square lattice,
although we sometimes observe interesting deviations from this general pattern,
especially near the center of the opinion space.
