Journal Article
Analysis of shape grammars: continuity of rules

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.

Title
Publication TypeJournal Article
Year of Publication2021
AuthorsHaridis A, Stiny G
JournalEnvironment and Planning B: Urban Analytics and City Science
Pagination1-21
Type of ArticleResearch Article
KeywordsContinuity, design process, emergence, Shape Grammars, topology
Abstract

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.

Refereed DesignationRefereed