A new method of analyzing rule continuity in computations with shape grammars is presented. By building on recent results in topology for shapes in algebras $U_i$, the paper provides, (1) a general formulation of continuous rule applications based on the continuity of the mappings that describe these rule applications, (2) conditions that a mapping must satisfy to be suitable for analyzing rule continuity, and (3) procedures for computing continuous topologies in a given computation.