Dendrite morphology is necessary for the correct integration of inputs that neurons receive. The branching mechanisms allowing neurons to acquire their type-specific morphology remain unclear. Classically, axon and dendrite patterns were shown to be guided by molecules providing deterministic cues. However, the extent to which deterministic and stochastic mechanisms, based upon purely statistical bias, contribute to the emergence of dendrite shape is largely unknown. We address this issue using the Drosophila class I vpda multi-dendritic neurons. Detailed quantitative analysis of vpda dendrite morphogenesis indicates that the primary branch grows very robustly in a fixed direction while secondary branch numbers and lengths showed fluctuations characteristic of stochastic systems. Live tracking dendrites and computational modeling revealed how neuron shape emerges from few local statistical parameters of branch dynamics. We report key opposing aspects of how tree architecture feedbacks on the local probability of branch shrinkage. Child branches promote stabilization of parent branches while self-repulsion promotes shrinkage. Finally, we show that self-repulsion, mediated by the adhesion molecule Dscam1, indirectly patterns the growth of secondary branches by spatially restricting their direction of stable growth perpendicular to the primary branch. Thus, the stochastic nature of secondary branch dynamics and the existence of geometric feedback emphasizes the importance of self-organization in neuronal dendrite morphogenesis.