Abstract: Silicate minerals grown from glasses, and rapidly cooled melts, often have non-compact branching or ‘spherulitic’ morphology. The branching patterns are observed in volcanic rocks, glasses, meteorites, slags and sometimes in shallow level intrusive rocks. Experiments, observations, theory and simulations all support the concept that the crystal morphology is the result of growth under diffusion limited conditions. We show that in a silicate melt under appropriate conditions the equations for heat transfer and chemical-diffusion reduce to the Laplace equation. This means that the temperature or chemical gradient is a steady state field. Interaction between this field and a random variable (Brownian motion of growth species) is modelled and yields complex branching objects. The growing cluster affects the field such that an in-filled structure cannot be formed. The branching structures of the model crystal are remarkably similar to those formed in nature, and to those produced in laboratory experiments, implying that the model captures the essence of the branching-growth process.