A Computational Investigation into the Fractal Dimensions of the Architecture of Kazuyo Sejima

By Michael J. Ostwald, Josephine Vaughan and Stephan K. Chalup.

Published by The Design Collection

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Article: Print $US10.00
Article: Electronic $US5.00

In the late 1980’s and early 1990’s a range of approaches to using fractal geometry for the design and analysis of the built environment were developed. Mandelbrot’s “box counting” approach was later refined and developed by Carl Bovill (1996) who demonstrated a method for determining an approximate fractal dimension of architectural elevations and plans.

This paper is the first investigation of the fractal dimensions of five house designs by Kazuyo Sejima, a famous, late 20th century minimalist designer (Aoki 2003; Hasegawa 2006). The fractal dimensions are calculated using a combination of Archimage and Benoit software, the former of which uses an extrapolation of Bovill’s box-counting method for the fractal analysis of house designs. Significantly, past research using the box-counting approach has only been applied to the works of Frank Lloyd Wright, Le Corbusier and a limited selection of ancient buildings. This paper will not only expand the set of cases tested by adding a selection of late Twentieth Century examples, but these will also be the first examples of minimalist architecture tested by this method.

This paper will conclude by first providing a discussion of the five houses of Kazuyo Sejima, with a comparison between their design features and their box-counting results. Second, a brief description will be presented of how the fractal geometry of Sejima’s architecture differs from that of other architects’ works recorded in past research.

Keywords: Fractal Architecture, Computational Tools, Design Assessment, Kazuyo Sejima

Design Principles and Practices: An International Journal, Volume 3, Issue 1, pp.231-244. Article: Print (Spiral Bound). Article: Electronic (PDF File; 1.381MB).

Prof. Michael J. Ostwald

Dean of Architecture, School of Architecture and Built Environment, The University of Newcastle, Newcastle, NSW, Australia

Dr. Michael J. Ostwald is Professor and Dean of Architecture at the University of Newcastle, Australia. He is a Visiting Fellow at SIAL and a Professorial Research Fellow at Victoria University Wellington. He has a PhD in architectural philosophy and a higher doctorate (DSc) 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. 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).

Josephine Vaughan

Research Assistant, School of Architecture and Built Environment, The University of Newcastle, Newcastle, NSW, Australia

Josephine Vaughan 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’s architectural designs have been exhibited and installed regionally and nationally.

Dr. Stephan K. Chalup

Senior Lecturer, School of Electrical Engineering & Computer Science, The University of Newcastle, Newcastle, NSW, Australia

Dr. Stephan Chalup received his PhD from Queensland University of Technology in 2001. He is the director of the Newcastle Robotics Laboratory and a senior lecturer in computer science and software engineering at the University of Newcastle in Australia. In his research publications he investigated machine-learning techniques such as neural networks, evolutionary algorithms, and kernel methods and their application in image processing and autonomous system design.

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