Abstract
The new façade of Storey Hall in Melbourne, by the architects ARM, is covered in a particular set of giant aperiodic tessellations which were discovered by the mathematician Roger Penrose in the 1970s and have since become known as Penrose tiles. While architecture has, historically, always been closely associated with the crafts of tiling and patterning, Storey Hall represents a resurrection and expansion of that tradition. However, what is Penrose tiling and what does it have to do with architecture? This paper provides an overview of the special properties and characteristics of Penrose tiling before describing the way in which they are used in Storey Hall. The purpose of this binary analysis is not to critique Storey Hall but to use the design as a catalyst for considering applications of tiling in the context of architectural form generation.
First published as: Michael J. Ostwald , “Aperiodic Tiling, Penrose Tiling and the Generation of Architectural Forms”, pp. 99–111 in Nexus II: Architecture and Mathematics, ed. Kim Williams, Fucecchio (Florence): Edizioni dell’Erba, 1998.
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Notes
- 1.
In theory it does not matter how large the set of tiles is. An infinite set of different shapes that fills a plane is still a form of tiling although an unconventional kind.
- 2.
Whereas minor or subtle references to the art of tiling may be discerned in various translations of the works of Vitruvious as well as in those of Alberti , Vignola and Serlio , even such minor references are increasingly rare in the treatises that followed; see Kruft (1994).
- 3.
It must be noted that there is some confusion surrounding the terminology “aperiodic” and “non-periodic” as both terms are used interchangeably in popular mathematics and science. This chapter generally conforms to the wording used in Grünbaum and Shephard’s encyclopedic work Tilings and Patterns (1987) and uses “aperiodic” as an accurate description of the properties of a tile set and “non-periodic” only when quoting from another work or when using the term as a broad, non-definitive, descriptor.
- 4.
Although Robbin’s arguments to the contrary are very intriguing, this author remains sceptical; see Robbin (1990: 140–142).
References
Ashton Raggatt McDougall. 1996. New Patronage. In Ashton Raggatt McDougall, eds. RMIT Storey Hall, Melbourne: Faculty of Environmental Design and Construction, RMIT.
Cracknell, Arthur. 1969. Crystals and their Structure. London: Pergamon.
Day, Norman. 1995. Storey Hall. Architecture Australia 85, 1 (1995): 36.
Eisenman, Peter. 1982. House X. New York: Rizzoli.
———. 1995. Eisenman Architects: Selected And Current Works. Mulgrave: Images Publishing.
Gardner, Martin. 1989. Penrose Tiles To Trapdoor Ciphers. New York: W. H. Freeman.
Grünbaum, Branko and Geoffrey Colin Shephard. 1987. Tilings and Patterns. New York: W. H. Freeman.
Kohane, Peter. 1996. Ashton Raggatt and McDougall’s Imitative Architecture: Real and Imaginary Paths through Storey Hall. Transition 52/53 (1996): 8–15.
Kruft, Hanno Walter. 1994. A History of Architectural Theory from Vitruvius to the Present. In R. Taylor, E. Callander, and A. Wood, trans. New York: Princeton Architectural Press.
Miyazaki, Koji. 1977. On Some Periodical and Non-Periodical Honeycombs. Kobe: University Monograph.
Ostwald, Michael J., and R. John Moore. 1995. Mathematical Misreadings in Nonlinearity: Architecture as Accessory/Theory. In Mike Linzey, ed. Accessory/Architecture. Vol. 1. Auckland: University of Auckland. 1995.
———. 1997. Unravelling the Weave: an Analysis of Architectural Metaphors in Nonlinear Dynamics. Interstices. Vol. 4 (1997) CD-ROM.
Ostwald, Michael J., Peter Zellner and Charles Jencks. 1996. An Architecture Of Complexity. Transition 52/53 (1996): 30.
Penrose, Roger. 1990. The Emperor’s New Mind: Concerning Computers, Minds, and the Laws of Physics. London: Vintage.
———. 1996. Fax to Howard Raggatt. In Ashton Raggatt McDougall, eds. RMIT Storey Hall. Melbourne: Faculty of Environmental Design and Construction, RMIT.
Rubinsteim, Heim. 1996. Penrose Tiling. Transition 52/53 (1996): 20–21.
Robbin, Tony. 1990. Quasicrystals for Architecture: The Visual Properties of Three-Dimensional Penrose Tessellations. Leonardo 23, 1: 140–141.
Stewart, Ian and Martin Golubitsky. 1993. Fearful Symmetry: Is God A Geometer? London: Penguin.
Van Schaik, Leon. 1996. Preface. In Ashton Raggatt McDougall, eds. RMIT Storey Hall. Melbourne: Faculty of Environmental Design and Construction, RMIT.
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Ostwald, M.J. (2015). Aperiodic Tiling, Penrose Tiling and the Generation of Architectural Forms. In: Williams, K., Ostwald, M. (eds) Architecture and Mathematics from Antiquity to the Future. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-00143-2_31
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