The Language of Frank Lloyd Wright's Prairie Houses

This chapter uses a combined syntactical and grammatic method to analyse 19 of Frank Lloyd Wright's Prairie houses. The purpose of this analysis is to illuminate the formal and social properties of Wright's early architecture. The data developed through this process is used to provide mathematical insights into the topological and geometric patterns that provide the foundation for Wright's Prairie style language. The data is then used to generate a new socially and formally derived and compliant instance of this style. Whereas past research has shown how Wright's architecture might be computationally generated solely on the basis of its formal composition, this chapter shows how its social and functional properties can also be replicated as part of such a process.

Mathematical Analysis and Generation of Palladian Designs

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.”

The Language of Architecture

This chapter provides a background to the common “linguistic” analogies in architectural thinking, which are concerned with the “grammar” of form and the “syntax” of space. The chapter then links these linguistic properties to the classical Vitruvian architectural values of firmness, commodity, and delight. Thereafter, the chapter introduces the two most well-known computational design approaches, Shape Grammar and Space Syntax, and briefly outlines the general applications of each. In addition, throughout this book, new grammatical and syntactical approaches are typically demonstrated using the domestic architecture of Andrea Palladio, Frank Lloyd Wright, and Glenn Murcutt. Thus, this chapter also introduces these three architects and their architectural languages.

A Combined Grammatical and Syntactical Method

This chapter presents a method that combines Shape Grammar and Space Syntax approaches to offer a rigorous way of understanding an architectural style and then producing variations of that style. The two approaches have only rarely been connected in the past, and the relationship between them has never been fully developed. The method commences with a justified plan graph (JPG) grammar and illustrates the grammatical interpretation of the structure of this syntax. The JPG technique is then followed by a massing grammar, which adds a consideration of architectural form. A significant strength of this method is that it encapsulates both the formal and functional properties of architecture. As part of the introduction to this method, the chapter employs two generic grammars, drawn from the combined method, along with their abstraction, measures, and configurations.

Syntactical and Mathematical Measures of Spatial Configuration

This chapter presents a detailed explanation of the construction and analysis of a justified plan graph (JPG) of a building plan. It introduces the classic syntactical and mathematical measures derived from a JPG and discusses their interpretation in terms of the original architectural plan the results are derived from. Thereafter, an alternative weighted and directed JPG is introduced which uses four measures: centrality, degree centrality, centrality closeness, and betweenness. The mathematical measures introduced in this chapter are applied in Section 3 of this book to examine two syntactical and grammatical applications. Throughout the present chapter, three “Palladian” villas—Villa Saraceno, Villa Sepulveda, and Villa Poiana—are used as examples to explain and demonstrate the concepts.

Space Syntax Approaches in Architecture

This chapter introduces three Space Syntax techniques – axial line analysis, convex space analysis, and visibility graph analysis (VGA). Conventional applications of the axial line technique typically range from domestic buildings to urban environments, providing a quantitative understanding of spatial configurations. Convex space analysis is typically used to capture relationships between human behaviour and the built environment, and VGA is used to reveal human spatial perceptions and responses in a specific built environment. This chapter provides a brief explanation of each technique before reviewing recent trends and developments in Space Syntax research. Two case studies are presented in the chapter to demonstrate axial line analysis and VGA for four urban neighbourhoods in Seoul (South Korea) and architectural plans for four aged care developments, two in Australia and two in South Korea.

Shape Grammar Approaches in Architecture

This chapter reviews emerging Shape Grammar research, categorising it into three themes: design analysis and generation, automated design and generative algorithms, and algebraic Shape Grammars. The first theme consists of theoretical Shape Grammar approaches, two-dimensional architectural design, three-dimensional architectural design, urban design, and design in art and engineering. The second theme addresses four alternative perspectives to grammatical approaches based on design automation, procedural modelling, genetic algorithms, and other algorithmic generation and evaluation methods. The last theme examines research using algebraic shape descriptions and operations. The purpose of this chapter is to provide a critical summary of recent trends in Shape Grammar research and an overview of the relationship between grammatical and generative systems in architecture.

Conclusion

The final chapter of the book revisits the emerging Shape Grammar research presented in Chapter 2 and the quantitative analysis and guided generation using a Palladian Grammar in Chapter 3. It then revisits the limitations of Space Syntax approaches and of the justified planning graph (JPG) method and its measures, described in Chapters 4 and 5. Finally, this chapter discusses the new combined grammatical and syntactical method presented in Chapters 6, 7, and 8. This concluding chapter emphasises the book's contribution to advances in Shape Grammar and Space Syntax research for architectural design analysis and generation. In addition to these theoretical contributions, the primary computational approaches in the book, which have been demonstrated using the domestic designs of Palladio, Wright, and Murcutt, are also valuable for architectural education and practice.

The Language of Glenn Murcutt's Domestic Architecture

This chapter presents a JPG grammar and massing grammar for Glenn Murcutt's domestic architecture, demonstrating the analytical and generative capability of the combined grammatical and syntactical method. The chapter commences with a JPG-grammar-based analysis of 10 of Murcutt's rural domestic designs. Using this as a starting point, the chapter then describes the massing grammar that configures the form of each design, defining block properties, composition, and roof types. Throughout this process, the new method is used to develop the mathematical indicators of the properties of each house that are most similar or disparate. This information supports the generation of a “dominant design” as well as potential new variations that are consistent with the language of Murcutt's domestic architecture. Thus, the combined grammatical and syntactical method contributes to a deeper and more rigorous understanding of an architectural style and its design instances.