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 .
The rules in a shape grammar apply in terms of embedding to take advantage of the parts that emerge visually in the appearance of shapes. While the shapes are kept unanalyzed throughout a computation, their descriptions can be defined retrospectively based on how the rules are applied. An important outcome of this is that continuity for rules is not built-in but it is "fabricated" retrospectively to explain a computation as a continuous process. An aspect of continuity analysis that has not been addressed in the literature is how to decide which mapping forms to use to study the continuity of rule applications. This is addressed in this paper in a new approach to continuity analysis, which uses recent results on shape topology and continuous mappings. A characterization is provided that distinguishes the suitable mapping forms from those that are inherently discontinuous or practically inconsequential for continuity analysis. It is also shown that certain inherent properties of shape topologies and continuous mappings provide an effective method of computing topologies algorithmically .
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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 rules in a shape grammar apply in terms of embedding to take advantage of the parts that emerge visually in
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appearance of shapes. While the shapes are kept unanalyzed throughout a computation, their descriptions can be defined retrospectively based on how the rules are applied. An important outcome of this is that continuity for rules is not built-in but it is "fabricated" retrospectively to explain a computation as a continuous process. An aspect of continuity analysis that has not been addressed in the literature is how to decide which mapping forms to use to study the continuity of rule applications. This is addressed in this paper in a new approach to
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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
analysis, which uses recent results on shape topology and continuous mappings. A characterization is provided that distinguishes the suitable mapping forms from those that are inherently discontinuous or practically inconsequential for continuity analysis. It is also shown that certain inherent properties of shape topologies and continuous mappings provide an effective method of computing topologies algorithmically