Synaptic clusters on dendrites are extraordinarily compact computational building blocks. They contribute to key local computations through biophysical and biochemical signaling that utilizes convergence in space and time as an organizing principle. However, these computations can only arise in very special contexts. Dendritic cluster computations, their highly organized input connectivity, and the mechanisms for their formation are closely linked, yet these have not been analyzed as parts of a single process. Here, we examine these linkages. The sheer density of axonal and dendritic arborizations means that there are far more potential connections (close enough for a spine to reach an axon) than actual ones. We see how dendritic clusters draw upon electrical, chemical, and mechano-chemical signaling to implement the rules for formation of connections and subsequent computations. Crucially, the same mechanisms that underlie their functions also underlie their formation.