  The increasing number of crimes in areas with large concentrations of people
have made cities one of the main sources of violence. Understanding
characteristics of how crime rate expands and its relations with the cities
size goes beyond an academic question, being a central issue for contemporary
society. Here, we characterize and analyze quantitative aspects of murders in
the period from 1980 to 2009 in Brazilian cities. We find that the distribution
of the annual, biannual and triannual logarithmic homicide growth rates exhibit
the same functional form for distinct scales, that is, a scale invariant
behavior. We also identify asymptotic power-law decay relations between the
standard deviations of these three growth rates and the initial size. Further,
we discuss similarities with complex organizations.
