This Paper develops a model of economic growth and activity locating endogenously on a 3-dimensional featureless global geography. The same economic forces influence simultaneously growth, convergence, and spatial agglomeration and clustering. Economic activity is not concentrated on discrete isolated points but instead a dynamically-fluctuating, smooth spatial distribution. Spatial inequality is a Cass-Koopmans saddlepath, and the global distribution of economic activity converges towards egalitarian growth. Equality is stable but spatial inequality is needed to attain it.