Mathematical Analysis and Generation of Palladian Designs

Mathematical Analysis and Generation of Palladian Designs

DOI: 10.4018/978-1-7998-1698-0.ch003

Abstract

This chapter describes the development of a schematic “Palladian Grammar” for analysing and generating Palladian villa plans. This grammar has four stages using eleven rule sets, which start by generating initial modules and end with the application of a termination rule. Thereafter, the chapter introduces a mathematical approach to measuring and comparing the grammatical properties of selected design instances of Palladian villas. Normalised distance is used to identify the level of disparity implicit in each design instance, relative to the grammatical rule-set. Alternative design instances are generated using rule probabilities to illustrate the transition sequences of the grammar application. The method both generates design instances and measures their grammatical levels of disparity to support the production of more appropriate design instances in the language. The computational techniques provide both a quantitative and qualitative examination of the schematic “Palladian Grammar.”
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Introduction

This chapter presents a Shape Grammar for analysing and generating Palladian schematic plan layouts. This process involves specifying the set of rules required for this purpose and delineating how these are combined to replicate existing, or create new designs. Conventionally, this process is used to develop insights into a design language and then generate new designs that capture the stylistic characteristics of the original set of works. In the present context, however, the Palladian Grammar is largely used to demonstrate the development of a Shape Grammar for a set of buildings and then provide a new method for improving grammatical applications for design analysis and generation. As such, the grammar’s purpose is largely methodological and developmental. The new method is significant because most grammatical analyses are descriptive or focused on the development of definitions of shapes, rules and sequences of the rule application. However, more recent studies have identified the importance of quantitative approaches for design analysis using Shape Grammars (Merrick, Isaacs, Barlow, & Gu 2013). For example, Tepavčević and Stojaković (2013) use mathematical and fuzzy inference measures developed from the frequencies and probabilities of each shape attribute of design instances. They also calculate correction factors based on the relative frequencies for each building’s properties. In Eilouti and Hamamieh Al Shaar’s research (2012), Shape Grammar rules are associated with numerical parameters developed from a mathematical analysis of a set of domestic designs. More recently, Hyun, Lee, Kim and Cho (2015) present a style analysis method using a similarity index of design elements and weighting elements. Such examples demonstrate the growing importance of quantitative analysis of grammatical data, and the present chapter develops this idea, seeking to enhance the analytical potential of Shape Grammar research as well as providing a more systematic understanding of an entire language.

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