The Fractal Dimension of Architecture PDF
Preview The Fractal Dimension of Architecture
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 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpart of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission orinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar methodologynowknownorhereafterdeveloped. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfrom therelevantprotectivelawsandregulationsandthereforefreeforgeneraluse. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authorsortheeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinor foranyerrorsoromissionsthatmayhavebeenmade. Printedonacid-freepaper ThisbookispublishedunderthetradenameBirkhäuser. TheregisteredcompanyisSpringerInternationalPublishingAGSwitzerland (www.birkhauser-science.com) 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.
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