  We develop a "multifocal" approach to reveal spatial dissimilarities in
cities, from the most local scale to the metropolitan one. Think for instance
of a statistical variable that may be measured at different scales, eg ethnic
group proportions, social housing rate, income distribution, or public
transportation network density. Then, to any point in the city there
corresponds a sequence of values for the variable, as one zooms out around the
starting point, all the way up to the whole city -- as if with a varifocal
camera lens. The sequences thus produced encode in a precise manner spatial
dissimilarities: how much they differ from perfectly random sequences is indeed
a signature of the underlying spatial structure. We introduce here a
mathematical framework that allows to analyze this signature and we provide a
number of illustrative examples.
