The Mathematics of a Daisy

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 Great Clarendon Street, Oxford OX2 6DP Oxford University Press is a department of the University of Oxford. It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide in Oxford New York Auckland Cape Town Dar es Salaam Hong Kong Karachi Kuala Lumpur Madrid Melbourne Mexico City Nairobi New Delhi Shanghai Taipei Toronto With offices in Argentina Austria Brazil Chile Czech Republic France Greece Guatemala Hungary Italy Japan Poland Portugal Singapore South Korea Switzerland Thailand Turkey Ukraine Vietnam Oxford is a registered trade mark of Oxford University Press in the UK and in certain other countries Published in the United States by Oxford University Press Inc., New York # Philip Ball 2009 The moral rights of the author have been asserted Database right Oxford University Press (maker) First published 2009 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, or under terms agreed with the appropriate reprographics rights organization. Enquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above You must not circulate this book in any other binding or cover and you must impose the same condition on any acquirer British Library Cataloguing in Publication Data Data available Library of Congress Cataloging in Publication Data Data available Typeset by SPI Publisher Services, Pondicherry, India Printed in Great Britain on acid-free paper by Clays Ltd., St Ives plc ISBN 978–0–19–923796–8 13579108642 Shapes HERE is beauty to be found in regularity: the same element repeating again and again, typically with geometric order. T There is no better example than the honeycomb, a miracle of hexagonal perfection. This sort of pattern is a lattice. On a leopard’s pelt, the lattice melts but a pattern remains: spots spaced at more or less equal distances but no longer in neat rows. There is a comparable order in stripes and concentric bands: a succession rather strictly enforced on the angelfish, but more loosely applied in the meandering, merging stripes of the zebra or of sand ripples. The means by which these natural patterns are constructed may tell us something about how the far more complicated forms of animals and plants are created by a progressive division and subdivision of space, orchestrated by nothing more than simple physical forces. This page intentionally left blank Contents Preface and acknowledgements ix 1: The Shapes of Things 1 Pattern and Form 2: Lessons of the Beehive 33 Building with Bubbles 3: Making Waves 103 Stripes in a Test Tube 4: Written on the Body 151 Hiding, Warning, and Mimicking 5: Rhythms of the Wild 200 Crystal Communities 6: How Does Your Garden Grow? 226 The Mathematics of a Daisy 7: Unfolding the Embryo 257 The Formation of Body Plans Appendices 287 Bibliography 295 Index 303 This page intentionally left blank Preface and acknowledgements FTER my 1999 book The Self-Made Tapestry: Pattern Formation in Nature went out of print, I’d often be contacted by would-be A readers asking where they could get hold of a copy. That was how I discovered that copies were changing hands in the used-book market for considerably more than the original cover price. While that was gratifying in its way, I would far rather see the material accessible to anyone who wanted it. So I approached Latha Menon at Oxford Uni- versity Press to ask about a reprinting. But Latha had something more substantial in mind, and that is how this new trilogy came into being. Quite rightly, Latha perceived that the original Tapestry was neither conceived nor packaged to the best advantage of the material. I hope this format does it more justice. The suggestion of partitioning the material between three volumes sounded challenging at first, but once I saw how it might be done, I realized that this offered a structure that could bring more thematic organization to the topic. Each volume is self-contained and does not depend on one having read the others, although there is inevitably some cross-referencing. Anyone who has seen The Self-Made Tapestry 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 more work than I’d perhaps anticipated, but I remain deeply indebted to her for her vision of what these books might become, and her encouragement in making that happen. Philip Ball London, October 2007 This page intentionally left blank The Shapes of Things 1 Pattern and Form RRIVING on Earth, the aliens approach the first thing they see and utter the familiar words: ‘take me to your leader’ (Fig. 1.1). A Like many jokes, this one offers a damning critique. It under- mines the venerable and serious scientific quest to find life on other worlds, exploding the question of ‘how would we know if we found it?’ by answering that we tend to imagine it will look like us. Now, let me assure you that astrobiologists (as scientists who study aliens are called nowadays) are not really that foolish. They do not imagine for a moment that when we touch down on another inhabited world, we will be greeted by envoys who look like Leonard Nimoy. Indeed, if there is life in those parts of our own solar system that seem at all habitable (such as the subsurface seas of Jupiter’s icy moon Europa), it is most unlikely to warrant the description ‘intelli- gent’. And we may have to look hard and long to find it, precisely because we don’t know what we’re looking for. Yet even if we know it is not going to be Dr Spock, we have trouble shaking the conviction that it will look something like the forms of life we have seen before. Fig. 1.1: Do we inevitably expect life to ‘look’ like us? 2 j NATURE’S PATTERNS: SHAPES Even if it did, that already makes the challenge of identifying extra- terrestrial life bad enough. Take a look at life on Earth today, and you’ll see such a bewildering variety of shape and form that you could be forgiven for imagining anything is possible (Fig. 1.2). But scientists have a rather more sophisticated view of life (although they still cannot agree Fig. 1.2: Living organisms on Earth come in a bewildering variety of shapes and sizes. (Photos: a, carolsgalaxy; b, Keenan Pepper; c, Sarah Nichols; d, twoblueday; e, Ed Schipul; f, Doug Bowman.) THE SHAPES OF THINGS j 3 on a universal definition of it), which gives them hope of distinguishing it from its inorganic context. They recognize some attributes of living systems that go beyond mere physical appearance, such as the fact that life tends to destroy the chemical equilibrium of its environment. I’ll explain later what I mean by that, but let’s say for now that it’s rather like watching a film in which all you can see are balls being juggled: you know that there is something out of frame that is keeping them in motion. It’s true that some geological and astrophysical processes that don’t involve life at all can also induce this disequilibrium—but nonetheless, searching for disequilibrium as a potential fingerprint of life seems a lot better than looking around for a loitering humanoid alien to whom you can say ‘Take me to your leader’. Nevertheless, old habits die hard. Meteorite ALH84001 is a potato- shaped lump of Mars that was blasted from the Red Planet a few billion years ago in an asteroid or meteorite impact and subsequently found its way through space to Earth. It was discovered in 1984 in the snows of Antarctica. Scientists who made a detailed study of this cosmic intruder claimed in 1996 that it contains a ‘possible relic’ of Martian life. In support of that claim, an image was broadcast around the world that seemed to show worms crawling across the mineral surface (Fig. 1.3). These ‘worms’ Fig. 1.3: These microscopic structures found in Martian meteorite ALH84001 have been interpreted as evidence of ancient bacterial life. Might they be the fossilized remnants of tiny organisms? (Photo: NASA.) 4 j NATURE’S PATTERNS: SHAPES were mineral too, and so tiny that they could only be seen in the electron microscope; but the suggestion was that they could be the fossilized remains of Martian bacteria that once infested this chunk of stone. The researchers who investigated ALH84001 admitted that this con- clusion was tentative, and they didn’t make it lightly. These wormy forms were by no means the sole evidence—and after all, the scientists acknowledged, they were much smaller than earthly bacteria tend to be. All the same, these structures didn’t look like inorganic forms: it was hard to explain them as microscopic rock features formed by physical forces alone. And so the researchers stuck out their necks and used shape, pattern, form—what scientists tend to call morphology—as the partial basis for inferring a possible signature of life.

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