Analysis of shape grammars: continuity of rules

TL;DR

This paper investigates how to analyze the continuity of rule applications in shape grammars by using shape topology and continuous mappings, providing a characterization to distinguish suitable mapping forms and an algorithmic approach.

Contribution

It introduces a method to determine appropriate mapping forms for continuity analysis in shape grammars using shape topology theory.

Findings

Provides a characterization of suitable mapping forms for continuity analysis.

Shows how to compute shape topologies algorithmically.

Highlights the importance of retrospective analysis of rule continuity.

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 as a computation moves forward, part-structures for shapes can be defined retrospectively by analyzing how the rules were applied. An important outcome of this is that rule continuity is not builtin but it is "fabricated" retrospectively to analyze the 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 using 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 intrinsic properties of shape topologies and continuous mappings provide an effective method of computing topologies algorithmically.