Visual Calculating Aesthetic Value: Formal Models of Description and Evaluation for Aesthetic Systems

Abstract

This dissertation presents research on visual calculating with shape grammars, that bridges gaps between seeing as an open-ended aesthetic process and mathematical formality in computing methods in architecture and other areas of design. The work extends across two areas of research.

First, by taking as background developments in “mathematics of shapes”, it introduces new approaches to the structural description and geometric computation of form. A framework is developed for working with point-set free topological descriptions and for analyzing structural properties of computations, such as the continuity of rules involving incompatible shape descriptions. Further, it introduces a new approach to studying “construction lines” and “registration marks” as point-line arrangements with their own algebraic, geometric, and combinatorial properties. In addition to individual contributions to the area of mathematics of shapes, this work illustrates a broader methodological direction for linking architecture and design with mathematics and computing, whereby visual observation and spatial intuition in the former are the starting point for developments in the latter.

Second, as part of a recent direction toward assimilating aesthetic theory into visual calculating, an aesthetic evaluation system is developed for producing aesthetic responses related to the form of aesthetic objects. While the system is formulated in general terms, it uniformly assimilates aesthetic responses that are based on formal notions of unity (order) and variety (complexity/diversity), measured individually or in terms of some ratio that interrelates them. Expanding on the topic of aesthetic value systems, the last part of the dissertation discusses the role of aesthetic value judgements in educational programs connecting computing with design areas and why they are a necessary component in any pursuit for models of human-level “general” intelligence.