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Nature’s Patterns This page intentionally left blank Nature’s Patterns A Tapestry in Three Parts Philip Ball Nature’s Patterns is a trilogy composed of Shapes, Flow, and Branches 1 3 GreatClarendonStreet,OxfordOX26DP OxfordUniversityPressisadepartmentoftheUniversityofOxford. ItfurtherstheUniversity’sobjectiveofexcellenceinresearch,scholarship, andeducationbypublishingworldwidein Oxford NewYork Auckland CapeTown DaresSalaam HongKong Karachi KualaLumpur Madrid Melbourne MexicoCity Nairobi NewDelhi Shanghai Taipei Toronto Withofficesin Argentina Austria Brazil Chile CzechRepublic France Greece Guatemala Hungary Italy Japan Poland Portugal Singapore SouthKorea Switzerland Thailand Turkey Ukraine Vietnam OxfordisaregisteredtrademarkofOxfordUniversityPress intheUKandincertainothercountries PublishedintheUnitedStates byOxfordUniversityPressInc.,NewYork #PhilipBall2009 Themoralrightsoftheauthorhavebeenasserted DatabaserightOxfordUniversityPress(maker) Firstpublished2009 Allrightsreserved.Nopartofthispublicationmaybereproduced, storedinaretrievalsystem,ortransmitted,inanyformorbyanymeans, withoutthepriorpermissioninwritingofOxfordUniversityPress, orasexpresslypermittedbylaw,orundertermsagreedwiththeappropriate reprographicsrightsorganization.Enquiriesconcerningreproduction outsidethescopeoftheaboveshouldbesenttotheRightsDepartment, OxfordUniversityPress,attheaddressabove Youmustnotcirculatethisbookinanyotherbindingorcover andyoumustimposethesameconditiononanyacquirer BritishLibraryCataloguinginPublicationData Dataavailable LibraryofCongressCataloginginPublicationData Dataavailable TypesetbySPIPublisherServices,Pondicherry,India PrintedinGreatBritain onacid-freepaperby ClaysLtd.,StIvesplc ISBN 978–0–19–923798–2 1 3 5 7 9 10 8 6 4 2 Branching S EEINGthesplayed,forkingchannelsofrivers,naturalphilosophers were reminded of veins and arteries. These in turn speak of trees—andwhynot,forallarenetworksthatdistributevitalfluids. Whataretherulesthatmakebranches?Whydoesalightningboltseek many routes from heaven to earth, or a crack begin to wander and divide? Branching forms find a compromise between disorder and determinism:theyhintatanewandpeculiargeometry.Yetsometimes order reasserts itself, as when the arms of snowflakes insist on their hexagonality.Andifbranchesreunite,theloopsformawebthatoffers manyroutestothesamedestination.Navigationanddisseminationon suchnetworksthendependsonthepatternofconnections. This page intentionally left blank Contents Prefaceandacknowledgements ix 1: AWinter’sTale 1 TheSix-PointedSnowflake 2: TenuousMonsters 27 ShapesbetweenDimensions 3: JustFortheCrack 71 CleanBreaksandRaggedRuptures 4: WaterWays 101 LabyrinthsintheLandscape 5: TreeandLeaf 131 BranchesinBiology 6: WebWorlds 150 WhyWe’reAllinThisTogether Epilogue: TheThreadsoftheTapestry 180 PrinciplesofPattern Appendix 210 Bibliography 212 Index 217 This page intentionally left blank Preface and acknowledgements A FTER my1999bookTheSelf-MadeTapestry:PatternFormation inNaturewentoutofprint,I’doftenbecontactedbywould-be readers asking where they could get hold of a copy. That was how I discovered that copies were changing hands in the used-book marketforconsiderablymorethantheoriginalcoverprice.Whilethat wasgratifyinginitsway,Iwouldfarratherseethematerialaccessibleto anyone whowanted it. So Iapproached Latha Menon at Oxford Uni- versityPresstoaskaboutareprinting.ButLathahadsomethingmore substantialinmind,andthatishowthisnewtrilogycameintobeing. Quite rightly, Latha perceived that the original Tapestry was neither conceivednorpackagedtothebestadvantage ofthematerial.Ihope thisformatdoesitmorejustice. The suggestion of partitioning the material between three volumes sounded challenging at first, but once I saw how it might be done, Irealizedthatthisofferedastructurethatcouldbringmorethematic organizationtothetopic.Eachvolumeisself-containedanddoesnot depend on one having read the others, although there is inevitably somecross-referencing.AnyonewhohasseenTheSelf-MadeTapestry will find some familiar things here, but also plenty that is new. In adding that material, I have benefited from the great generosity of many scientists who have given images, reprints and suggestions. I am particularly grateful to Sean Carroll, Iain Couzin, and Andrea Rinaldo for critical readings of some of the new text. Latha set me moreworkthanI’dperhapsanticipated,butIremaindeeplyindebted to her for her vision of what these books might become, and her encouragementinmakingthathappen. PhilipBall London,October2007
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