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.Comment: 23 pages, 6 Figures, 6 Tables. Research Report, 2020, MIT. Preprint of Journal Article (2021

Making grammars: From computing with shapes to computing with things

Recent interest in making and materiality spans from the humanities and social sciences to engineering, science, and design. Here, we consider making through the lens of a unique computational theory of design: shape grammars. We propose a computational theory of making based on the improvisational, perception and action approach of shape grammars and the shape algebras that support them. We modify algebras for the materials (basic elements) of shapes to define algebras for the materials of objects, or things. Then we adapt shape grammars for computing shapes to making grammars for computing things. We give examples of making grammars and their algebras. We conclude by reframing designing and making in light of our computational theory of making

Principles for the definition of design structures

Different kinds of design structure are created and used in engineering design and development processes. Function structures, design grammars and bills of materials are common examples. However, there is a lack of clarity regarding distinctions and similarities between different kinds of structure and systematic ways to articulate them. This paper brings together research on product structuring and shape computation to inform the specification of principles for the definition of design structures. The principles draw together findings reported in the computational geometry and product definition literature with research from a range of companies and industry sectors that encompasses enterprise and process structures. The potential value of the principles to computer integrated manufacturing and through-life support is demonstrated through application to four case studies

Shapes, structures and shape grammar implementation

Shape grammars are a generative formalism in which dynamic changes to shape structure plays a vital role. Such changes support ambiguity and emergence, and as a result shape grammars are often used as the basis for proposed developments in supporting shape exploration in computer-aided design. However, the general implementation of shape grammars remains an unsolved problem, and a common solution is to adopt a fixed structure. This paper explores the consequences of assuming a fixed structure, via analysis of a simple shape grammar, often used as a benchmark problem to illustrate advances in shape grammar implementation. With reference to the combinatorics of words, it is proved that adopting a finite fixed structure limits the capability of a shape grammar. The paper concludes with a discussion exploring the implication of this result for shape grammar implementation and for design descriptions in CAD

The Critic as Artist: Oscar Wilde’s Prolegomena to Shape Grammars

Shape grammars include Wilde’s aesthetic (critical) method—I can calculate with shapes as in themselves they really are not. Embedding makes this possible with schemas and rules that are “superb in [their] changes and contradictions”

ARTIFICIAL INTELLIGENCE AND AESTHETICS

Firschein et al. [1] describe some products that can be expected to result from research in artificial intelligence. One of these products is "creation and valuation systems " which the