Preface

This book describes a unique way of measuring, analysing and comparing buildings using fractal dimensions. A fractal dimension is a mathematical determination of the typical or characteristic level of complexity in an image or object. Thus, fractal dimensions provide a rigorous measure of the extent to which an object, say a building, is relatively simple, plain or smooth at one extreme, or complex, jagged and rough at the other. After introducing the method for calculating fractal dimensions in Part I of the book, Part II presents the results of a major study of the plans and elevations of eighty-five canonical houses designed or constructed between 1901 and 2007. The houses include works by Le Corbusier, Eileen Gray, Mies van der Rohe, Frank Lloyd Wright, Robert Venturi, Denise Scott Brown, Frank Gehry, Peter Eisenman, John Hejduk, Richard Meier, Kazuyo Sejima, Ryue Nishizawa, Yoshiharu Tsukamoto, Momoyo Kajima, Glenn Murcutt and Peter Stutchbury. The eighty-five houses are measured to examine trends in individual designer’s works, across different stylistic movements and over more than a century of shifting social patterns and aesthetic tastes. These trends are encapsulated in a series of three hypotheses which are proposed in the introduction and examined in the book’s conclusion. In addition to the results of this overarching study, five specific arguments about architecture are also tested using mathematical evidence. The first of these is concerned with the way the formal expression of modernist architecture is allegedly shaped in response to its orientation and address. The second examines claims about the changing visual experience of walking through one of Frank Lloyd Wright’s houses and the third is about the extent to which façade permeability (the presence of windows and doors) shapes the formal expression of a building. The fourth of these studies examines arguments about frontality and rotation in the early domestic architecture of Eisenman, Hejduk and Meier. The fifth and final study investigates the degree to which Murcutt’s architecture is shaped by either literal or phenomenal transparency. These secondary studies all use variants of the fractal analysis method that are attuned to testing specific architectural properties.