Aperiodic Tiling, Penrose Tiling and the Generation of Architectural Forms

In September 1995 the Australian architectural practice Ashton Raggatt McDougall (ARM) invited the eminent mathematician Roger Penrose to open their soon-to-be-completed refurbishment of the historic Storey Hall complex of buildings at the Royal Melbourne Institute of Technology. Penrose, who admitted that the design seemed "extremely exciting", regretfully declined on the grounds that he was already overcommitted to many projects to visit Australia at the required time. He concluded his response to the invitation with an enigmatic postscript which records that he is currently working on "the single tile problem" and recently "found a tile set consisting of one tile together with complicated matching rule that can be enforced with two small extra pieces". This postscript contains the first clue to understanding the mysterious connection between Penrose and Storey Hall, between a scientist and a controversial, award-winning, building.

Storey Hall is significant for many reasons but only one prompted ARM to invite Penrose to open it. The newly completed Storey Hall is literally covered in a particular set of giant, aperiodic tiles that were discovered by Roger Penrose in the 1970's 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 of that tradition.

But what is Penrose tiling and what does it have to do with architecture in general and Storey Hall in particular? This paper provides an overview of the special properties and characteristics of Penrose's tilings before describing the way in which they are used in ARM's Storey Hall. The purpose of this binary analysis is not to critique Storey Hall or its use of aperiodic tiling but to use ARM's design as a catalyst for taking the first few steps in a greater analysis of Penrose tiling in the context of architectural form generation.

ABOUT THE AUTHOR
Michael J. Ostwald is Dean of Architecture at the University of Newcastle, Australia. He has lectured in Asia, Europe and North America and has written and published extensively on the relationship between architecture, philosophy and geometry. He has a particular interest in fractal, topographic and computational geometry and has been awarded many international research grants in this field. Michael is also Co-Editor of the journal Architectural Design Research and was previously Book Review Editor of the Nexus Network Journal.

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