This paper reinterprets a simple model of growth and fluctuations across many economies to allow for the explicit characterization of the dynamically-evolving cross-economy distribution of income. Such a framework provides a more natural, revealing study of the convergence hypothesis. The data show limited intra-distribution mobility in incomes across economies and thus, little convergence. The analysis uncovers some `convergence club'-like dynamics, and reveals the wide diversity in growth experiences across countries. Conditioning on physical capital investment, secondary school enrolment, and a dummy for the African continent fails to overturn these characterizations.