  We propose a new model of cluster growth according to which the probability
that a new unit is placed in a point at a distance $r$ from the city center is
a Gaussian with mean equal to the cluster radius and variance proportional to
the mean, modulated by the local density $\rho(r)$. The model is analytically
solvable in $d=2$ dimensions, where the density profile varies as a
complementary error function. The model reproduces experimental observations
relative to the morphology of cities, determined via an original analysis of
digital maps with a very high spatial resolution, and helps understanding the
emergence of vehicular traffic.
