This paper reinterprets a simple model of growth and fluctuations across many economies to allow explicitly characterizing the dynamically evolving corss-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. Our 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 falls to overturn these characterizations.