The Fractal Dimension of Architecture

429 Pages·2016·4.58 MB·English

by  Michael J. Ostwald

Mathematics and the Built Environment 1
Michael J. Ostwald
Josephine Vaughan
The Fractal
Dimension
of Architecture

Mathematics and the Built Environment
Volume 1
Series editor
Kim Williams, Kim Williams Books, Torino, Italy
More information about this series at http://www.springer.com/series/15181
Michael J. Ostwald Josephine Vaughan
(cid:129)
The Fractal Dimension
of Architecture
Michael J.Ostwald Josephine Vaughan
Schoolof Architecture andBuilt Schoolof Architecture andBuilt
Environment Environment
TheUniversity of Newcastle TheUniversity of Newcastle
Newcastle, NSW Newcastle, NSW
Australia Australia
Mathematics andthe BuiltEnvironment
ISBN978-3-319-32424-1 ISBN978-3-319-32426-5 (eBook)
DOI 10.1007/978-3-319-32426-5
LibraryofCongressControlNumber:2016942907
©SpringerInternationalPublishingSwitzerland2016
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Preface
Thisbookdescribesauniquewayofmeasuring,analysingandcomparingbuildings
using fractal dimensions. A fractal dimension is a mathematical determination
of the typical or characteristic level of complexity in an image or object. Thus,
fractaldimensionsprovidearigorousmeasureoftheextenttowhichanobject,say
abuilding,isrelativelysimple,plainorsmoothatoneextreme,orcomplex,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-fivecanonicalhouses designedor constructedbetween 1901and 2007. The
houses include works by Le Corbusier, Eileen Gray, Mies van der Rohe, Frank
LloydWright,RobertVenturi,DeniseScottBrown,FrankGehry,PeterEisenman,
John Hejduk, Richard Meier, Kazuyo Sejima, Ryue Nishizawa, Yoshiharu
Tsukamoto,MomoyoKajima,GlennMurcuttandPeterStutchbury.Theeighty-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 pat-
terns 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.
Inadditiontotheresultsofthisoverarchingstudy,fivespecificargumentsabout
architecture are also tested using mathematical evidence. The first of these is
concernedwiththewaytheformalexpressionofmodernistarchitectureisallegedly
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.
Thefourthofthesestudiesexaminesargumentsaboutfrontalityandrotationinthe
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.
v
vi Preface
As a result of this combined approach—a primary overarching study and five
secondary studies—this book does not possess a neat, singular conclusion about
architecture that can be summarised in a paragraph. Instead, the newly developed
measures are used to illuminate a large number of beliefs about design, including
arguments pertainingtochangingtrendsinplanningandexpression andthe extent
to which different stylistic movements are visually differentiable from each other.
Furthermore,thedataareusedtodistinguishbetweendiverseapproachestospatial
planning, form-making and architectural expression. Thus, the majority of the
resultsofthisresearcharepresentedsequentially,attheendofspecificsectionsand
chapters.
Togivesomecontexttotheresearch,thisbookhasbeenwrittenforpeoplewith
backgroundsinarchitecture,urbandesign,interiordesignanddesigncomputing.It
hasalsobeenwrittenandframedinsuchawaythatitisaccessibletopostgraduate
students, as well as to professionals and academics. For this reason, the level of
mathematics used is relatively general and only basic statistical methods are
employed. This descriptive approach has been taken to the data because, with no
detailed inferences being drawn from it about the relationship between the designs
studied here and the larger body of domestic architecture produced in the same
period,thereisnoneedformorecomplexstatisticalanalysis.Forthesamereason,
the mathematical results are typically analysed using the critical-interpretative
techniques of design theorists and historians. Thus, a common approach in this
book is to use numbers, charts and simple statistical measures (average, median,
standard deviation) in parallel with scholarly arguments, to reach a reasoned con-
clusion about an issue. More mathematically inclined readers are invited to
undertake their own analysis of the data or follow links to our other publications
which contain more detailed results. Similarly, design theorists and historians are
free to interpret the results in their own terms or read our papers, cited in the text,
whichofferamoreintricateinterpretationofthephilosophicalbasisforsomeofthis
material.
Atthisjuncture,itisalsousefultoprovideanoteaboutauthorshipandhowwe
willrefertoourpastresearch.Formuchofthelasttenyears,we—MichaelOstwald
and Josephine Vaughan—have jointly published our research into applications of
computationalfractalanalysisindesign.Acrosstwenty-fiveco-authoredpapersand
chapters,wehavegraduallydevelopedandrefinedthetheoryandpracticeoffractal
analysis for architectural and urban applications. The intellectual content of the
present book is shaped by these publications, a few of which have been substan-
tiallyrevisedandexpandedforinclusionhere.However,priortothistimeMichael
Ostwaldseparatelypublishedalargebodyofresearchonphilosophical,theoretical
andhistoricalconnectionsbetweenarchitecture,non-linearmathematicsandfractal
geometry. Furthermore, he also worked closely with several other co-authors on
thisearlyresearch.Forthisreason,throughoutthepresentbookwewillrefertopast
researchpublishedbyMichaelalone,orinpartnershipwithothercolleagues,inthe
third person. In contrast, we will tend to refer to our joint research in the first
person, and in this way hope to remain clear about authorship.
Preface vii
The software used for the majority of the calculations in this book is called
ArchImage.Wedevelopedandrefinedthissoftwarewiththesupportofcolleagues
from computer science and software engineering at the University of Newcastle
(see the Acknowledgments section for full details). ArchImage’s basic properties
are described in Chap. 6 and it is available for download through the authors’
websites.
In this book, we present the results of our mathematical analysis of more than
625 reconstructed architectural plans and elevations and over 200 specially pre-
pared views offamous buildings. Using software that has been specially authored
for this project,over five million separate pieces of data were extracted from these
images and subjected to over 9000 mathematical operations to measure the
dimensionalpropertiesofeighty-fivedesigns.Tothebestofourknowledge,thisis
the largest mathematical study ever undertaken into architectural design and the
largestsingleapplicationoffractal analysisinanyfield.We hopethat through this
research the reader will be inspired to think about architecture—its history, theory
and analysis—in a new way.
Newcastle, Australia Michael J. Ostwald
2016 Josephine Vaughan
Acknowledgements
Several past and present colleagues have contributed to the development of ideas
contained in this book. In particular, we wish to thank Stephan Chalup, Steven
NicklinandChrisTuckerwhoworkedwithusonstagesofthisresearchandmade
valuable contributions to it. We are also indebted to the ideas of Carl Bovill who
published important early research in this field. Special thanks also to Anna
Mätzener and Sarah Goob (Birkhäuser, Basel), Thomas Hempfling (Springer,
Basel) and to series editor for Mathematics for the Built Environment, Kim
Williams.
ArchImage software was used for the majority of the calculations in this book.
Naomi Henderson authored the prototype version of this software with Michael
OstwaldandStephanChalup.StevenNicklinwrotethefinalversionofArchImage
with Stephan Chalup and ourselves. In addition, our research has also been ably
assistedbytheeffortsofMichaelDawes,MariaRobertsandIanOwen,alongwith
Romi McPherson, Lachlan Seegers, Jasmine Richardson, Raeana Henderson and
Kelly Campbell. The Australian Research Council (ARC) supported this project
through the award of a Discovery Grant (DP1094154) and a Future Fellowship
(FT0991309).
Some sections of this book are derived from material that was previously pub-
lished in journals and chapters and has been substantially revised, expanded or
updated for the present work. Specifically, in Chap. 3, the worked examples were
initiallydevelopedbyMichaelJ.OstwaldandMichaelDawes,andthefirstofthese
waspreviouslypresentedaspartof:ÖzgürEdizandMichaelJ.Ostwald,2012.‘The
SüleymaniyeMosque’,ARQ,16(2).Chapter4isarevisedandexpandedversionof:
Michael J. Ostwald and Josephine Vaughan, 2013. ‘Representing Architecture for
Fractal Analysis’, Architectural Science Review, 56(3). Chapter 5 includes revised
sections and results from two previously published papers: Michael J. Ostwald,
2013.‘TheFractalAnalysisofArchitecture’,EnvironmentandPlanningB,40;and
Michael J. Ostwald and Josephine Vaughan, 2013. ‘Limits and Errors’, ArS:
ArchitecturalScienceResearch,7.InChap.7,thebackgroundsectionandpartofthe
additional application were adapted from, respectively: Michael J. Ostwald and
ix
x Acknowledgements
Josephine Vaughan, 2011. ‘The Mathematics of Domestic Modernism
(1922–1934)’, Design Principles and Practices, 4(6); and Josephine Vaughan and
Michael J. Ostwald, 2009. ‘A Quantitative Comparison between the Formal
Complexity of Le Corbusier’s Pre-Modern (1905–1912) and Early Modern
(1922–1928) Architecture’, Design Principles and Practices, 3(4). Chapter 8
includes cases presented in preliminary form in the following: Josephine Vaughan
andMichaelJ.Ostwald,2011.‘TheRelationshipBetweentheFractalDimensionof
PlansandElevationsintheArchitectureofFrankLloydWright’,ArS:Architectural
Science Research, 4; and Michael J. Ostwald and Josephine Vaughan, 2010.
‘The Mathematics of Style in the Architecture of Frank Lloyd Wright’, in Paul
S. Geller (ed). Built Environment: Design, Management and Applications, Nova:
New York. In Chap. 10, some of the project descriptions were adapted from the
following: Michael J. Ostwald and Josephine Vaughan, 2013. ‘Differentiating the
Whites’,EmpiricalStudiesintheArts,31(1).Finally,theadditionalmethodological
applicationinChap.11wasdevelopedfromthefollowing:JosephineVaughanand
Michael J. Ostwald, 2015. ‘Measuring the Significance of Façade Transparency in
Australian Regionalist Architecture’, Architectural Science Review. Full details
ofthesepublicationsarecontainedinthereferences.Wegratefullyacknowledgethe
adviceandsupportofrefereesandeditorsinvolvedintheproductionoftheseworks.