V O L U M E 63 $: T Martin Alexander Ronald Phillips Cornell University University of Minnesota Kenneth J. Frey Larry P. Wilding Iowa State University Texas A&M University Prepared in cooperation with the American Society of Agronomy Monographs Committee P. S. Baenziger Jon Bartels Jerry M. Bigham M. B. Kirkham William T Frankenberger, Jr., Chaimnan David H. Kral Dennis E. Rolston Diane E. Storr Sarah E. Lingle Kenneth J. Moore Joseph W. Stucki Gary A. Peterson L D V A N C E SI N T T VOLUME 63 . I Edited by Donald L. Sparks Department of Plant and Soil Sciences University of Delaware Newark, Delaware ACADEMIC PRESS San Diego London Boston New York Sydney Tokyo Toronto This book is printed on acid-free paper. @ Copyright 0 1998 by ACADEMIC PRESS All Rights Reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the Publisher. The appearance of the code at the bottom of the first page of a chapter in this book indicates the Publisher’s consent that copies of the chapter may be made for personal or internal use of specific clients. This consent is given on the condition, however, that the copier pay the stated per copy fee through the Copyright Clearance Center, Inc. (222 Rosewood Drive, Danvers. Massachusetts 01923), for copying beyond that permitted by Sections 107 or 108 of the U.S. Copyright Law. This consent does not extend to other kinds of copying, such as copying for general distribution, for advertising or promotional purposes. for creating new collective works, or for resale. Copy fees for pre-1998 chapters are as shown on the title pages. If no fee code appears on the title page, the copy fee is the same as for current chapters. 0065-21 13/98 $25.00 Academic Press a division of Harcourt Brace & Company 525 B Street, Suite 1900, San Diego, California 92101-4495, USA http://www.apnet.com Academic Press Limited 24-28 Oval Road, London NWI 7DX, UK http://www.hbuk.co.uk/ap/ International Standard Book Number: 0-12-000763-0 PRINTED IN THE UNITED STATES OF AMERICA 97 98 9 9 0 0 01 0 2 B B 9 8 7 6 5 4 3 2 1 Contents CONTRIBUTORS ........................................... PREFACE ................................................. vii ix APPLICATIONSOF FRACTALS TO SOILSTUDIES Alison N. Anderson, Alex. B. McBratney, and John W. Crawford I. TI. 111. N. V VI. VII. VIII. lX. Fractals.. . . . . . . . . . . . . . . ...................... Fractal Dimensions and Their Measurement. . . Approximating Soil Smicture Using Fractals. . . . . . . . . . . . . . . . . . . . Soil Fragmentation . . . . . . . . . . . . . . . . . . . . . . . ............ Applications of Fractal Models in the Prediction of Soil Physical Processes . . . . . . . . . . . . - ........................ Other Applications of Fractal G