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Crystallization by particle attachment (CPA) is a frequently occurring mechanism of colloidal crystallization that results in hierarchical morphologies^{, , –}. CPA has been exploited to create nanomaterials with unusual properties^{, –} and is implicated in the development of complex mineral textures^,. Oriented attachment^,—a form of CPA in which particles align along specific crystallographic directions—produces mesocrystals that diffract as single crystals do, although the constituent particles are still discernible^,. The conventional view of CPA is that nucleation provides a supply of particles that aggregate via Brownian motion biased by attractive interparticle potentials^{,, , –}. However, mesocrystals often exhibit regular morphologies and uniform sizes. Although many crystal systems form mesocrystals^{, , , , , , , –} and individual attachment events have been directly visualized, how random attachment events lead to well …