  We study a discrete-time resource flow in $Z^d$, where wealthier vertices
attract the resources of their less rich neighbors. For any
translation-invariant probability distribution of initial resource quantities,
we prove that the flow at each vertex terminates after finitely many steps.
This answers (a generalized version of) a question posed by van den Berg and
Meester in 1991. The proof uses the mass-transport principle and extends to
other graphs.
