Michael Ostwald, Josephine Vaughan, Chris Tucker
University of Newcastle, School of Architecture and Built Environment, Faculty of Engineering and Built Environment
New South Wales, 2308 AUSTRALIA

Third stage grid placed over the east elevation of the Tomek house showing box-counting

In the late 1970s Mandelbrot argued that natural systems frequently possess characteristic geometric or visual complexity over multiple scales of observation, suggesting that systems which have evolved over time may exhibit certain local visual qualities that also possess deep structural resonance. In mathematics this realization, founded on seemingly irrational or "monstrous" numbers, lead to the formulation of fractal geometry and was central to the rise of the sciences of non-linearity and complexity. During the last decade this concept was developed in relation to architectural design and urban planning, and more recently architectural scholars have suggested that such approaches might be used in the analysis of historic buildings. At the heart of this approach, in both its theoretical and computational forms, is a set of rules for analyzing buildings. However, the assumptions implicit in this method have never been adequately questioned. The present paper returns to the origins of the conventional "box counting" method of fractal analysis for historic buildings to reconsider the initial interpretations of the architecture of Le Corbusier and Frank Lloyd Wright. This new analysis uses "Archimage" software, developed by the authors, to undertake a multi-dimensional review of the fractal dimension of the houses of Wright and Le Corbusier and, in doing so, to develop a more consistent method for the application of such mathematical tools to the analysis of historic buildings.

About the authors
Dr This email address is being protected from spambots. You need JavaScript enabled to view it. is Professor and Dean of Architecture at the University of Newcastle, Australia. He is a Visiting Professor at RMIT University in Melbourne and a Professorial Research Fellow at Victoria University Wellington. He has a Ph.D. in architectural philosophy and a D.Sc. in the mathematics of design. He is co-editor of the journal Architectural Design Research and on the editorial boards of Architectural Theory Review and the Nexus Network Journal. He has authored more than 200 scholarly publications and his recent books include The Architecture of the New Baroque (2006), Homo Faber: Modelling Design (2007) and Residue: Architecture as a Condition of Loss (2007).

This email address is being protected from spambots. You need JavaScript enabled to view it. is a research higher degree candidate at the University of Newcastle, where she is also a member of the architectural computing research group. Her postgraduate studies are focused on the fractal dimensions of buildings. Josephine directs the design firm, One Thousand Years, which specialises in sustainable houses and community facilities and she also tutors in design at the University. Her designs have been exhibited and installed regionally and nationally.

This email address is being protected from spambots. You need JavaScript enabled to view it. is a lecturer in the School of Architecture at the University of Newcastle and is a director of the architectural practice Herd. Chris has been awarded regional, state and international prizes for architecture and his buildings and designs have been widely exhibited and published. His research interests revolve around the development of software tools to analyse the geometric and mathematical qualities of buildings. He is currently completing a research higher degree on the algorithmic analysis of streetscapes.

The correct citation for this paper is:
Michael Ostwald, Josephine Vaughan, Chris Tucker, "Characteristic Visual Complexity: Fractal dimensions in the architecture of Frank Lloyd Wright and Le Corbusier", pp. 217-231 in Nexus VII: Architecture and Mathematics, ed. Kim Williams, Turin: Kim Williams Books, 2008.