Fractal Geometry and Computer Graphics

270 Pages·1992·11.983 MB·English

by  F. v. Haeseler, H.-O. Peitgen, G. Skordev (auth.), José L. Encarnação, Georgios Sakas, Heinz-Otto Peitgen, Gabriele Englert (eds.)

Beitdige zur Graphischen Datenverarbeitung
Editor:
Zentrum filr Graphische Datenverarbeitung e.V. Darmstadt (ZGDV)
J. L. H.-O. Peitgen
Encarna~ao
G. Sakas G. Englert (Eds.)
Fractal Geometry
and Computer Graphics
With 172 Figures
Springer-Verlag
Berlin Heidelberg New York
London Paris Tokyo
Hong Kong Barcelona
Budapest
Series Editor
ZGDV, Zentrum fur Graphische Datenverarbeitung e. V.
WilhelminenstraBe 7, W-6100 Darmstadt, FRG
Editors
Jose L. Encama~ao
Georgios Sakas
Technische Hochschule Darmstadt
Institut fur Informationsverwaltung und Interaktive Systeme
WilhelminenstraBe 7, W-6100 Darmstadt, FRG
Heinz-Otto Peitgen
Institut fur Dynamische Systeme
UniversWit Bremen, W-2800 Bremen 33, FRG
Gabriele Englert
Fraunhofer Gesellschaft
Institut fUr Graphische Datenverarbeitung
WilhelminenstraBe 7, W-6100 Darmstadt, FRG
ISBN-13: 978-3-540-55317-5 e-ISBN-13: 978-3-642-95678-2
DOl: 10.1007/978-3-642-95678-2
Library of Congress Cataloging-in-Publication Data
Fractal geometry and computer graphics / J. L. Encarna~ao ... let al.], (eds.).
p. em. - (Beitriige zur graphischen Datenverarbeitung) Includes bibliographical references and index.
I. Fractals. 2. Computer graphics. I. Encarna~ao, Jose Luis. II. Series.
QA614.86.F68 1992 514'.74-dc20 92-10008
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned,
specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction
on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof
is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current
version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for
prosecution under the German Copyright Law.
© Springer-Verlag Berlin Heidelberg 1992
Softcover reprint of the hardcover lst edition 1992
Cover picture shows turbulent motion of 2-D clouds simulating condensation see page 192, Fig. 67 by G. Sakas
Typesetting: Camera ready by author
33/3140-5 43 2 I 0 -Printed on acid-free paper
Foreword
Fractal Geometry and Computer Graphics have been in the past two areas of research
developing independent from each other. They have developed their mathematics,
algorithms, techniques, and applications with their own priorities and addressing the
issues relevant to their own, specific development. Now, based on the hardware
developments (microelectronics, workstations, etc.) and driven by application needs,
these two disciplines are getting more and more a common interface, where both inte
grate the know-how, the technologies and the methodologies coming from both sides.
This book is a collection of papers addressing this issue. The nineteen papers
published are structured around four main topics:
Fundamentals,
Computer Graphics,
Simulation,
Picture Analysis,
and are a first attempt to collect statements, views and first experiences with basics,
interrelationships and applications of Fractal Geometry and Computer Graphics.
We hope that this book is a first, very promising start in developing synergies and
interrelationships between these two disciplines.
Included in part V are two reports on the results of discussions which took place
in working groups during the workshop. These reports give surveys and perspectives
on
modeling and simulation, and
random fractals.
Here we tried to collect opinions, open issues, and trends, which we hope will be
the basis for intensive research in the near future.
I would like to thank H.-G. Peitgen for co-chairing the workshop, all partici
pants for their contributions, and specially G. Englert and G. Sakas for all the effort
they had in the very successful organization and implementation of the workshOp, as
well as in co-editing the book reporting on it.
Darmstadt, November 1991 J.L. Encamac;ao
Contents
List of Authors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. IX
I. Part: Fundamentals
Linear Cellular Automata, Substitutions, Hierarchical Iterated
Function Systems and Attractors
F. v. Haeseler, H.-D. Peitgen, G. Skordev . . . . . . 3
Escape-time Visualization Method for Language-restricted
Iterated Function Systems
P. Prusinkiewicz, M.S. Hammel. . . . . . . . . . . . . . . . . . . . .. 24
1/fNoise and Fractals in Economic Time Series
R.F. Voss. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 45
Fractal Sounds
J. Schwietering . . . . . . . . . . . . . . . . . . . . . .. 53
Fractal Geometry in Vaporisation
J.H. Spurk ........ . . ................. 64
MRTImaging of Time Dependent Processes
J. Syha, A. Haase. . . . . . . . . . . . . . . . . . . . . . . . . . . .. 74
II. Part: Computer Graphics
Fractals and Formal Texture Specification
G. Englert, M. Schendel ..... . . . . . . . .. 83
Boundary Tracking of Complicated Surfaces with Applications
to 3-D Julia Sets
C. Zahlten ......... . 103
3D-Rendering of Fractal Landscapes
H. Jiirgens ......... . 111
Fractal Interpolation of Random Fields of Fractional Brownian Motion
W.Riimelin 122
VIII
m.
Part: Simulation
Simulation of Malignant Cell Growth
W. Diichting . . . . . . . . . 135
Simulation of Individual Behaviour
E.J. Swart, P.J. Plath ..... 144
Improbable Events in Detenninistically Growing Patterns
P.J. Plath, J. Schwietering ............. . 162
Modeling Turbulent Gaseous Motion Using Time-Varying Fmctals
G. Sakas .......................... . 173
Devil's GealWorks
G. Mantica . 195
IV. Part: Picture Analysis
Dentronic Analysis of Pictures, Fractals and other Complex Structures
P. Hanusse, P. Guillataud ................... . 203
Texture Analysis Using Fractal Dimensions
U. Miissigmann ........... . 217
limited Selfs imilarity
H.R. Bittner 231
Fmctal3D Analysis of Blood Vessels and Bones
P. Wlczek, A. Odgaard, M. Semetz .... 240
v.
Part: Working Group Results
Random Fmctals
Working Group Results . 251
Modeling and Simulation
Working Group Results . 254
List of Authors
Dr. H.R. Bittner F. v. Haeseler
Pfarrer-Bleymann-Gasse 7 Universitiit Bremen
W-8730 Bad Kissingen -Poppenroth Institut fur Dynamische Systeme
Bibliothekstr. 1
W-2800 Bremen 33
Prof. Dr. W. Duchting
Universitiit Siegen
FB 12 M.S. Hammel
HOlderlinstr. 3 University of Calgary
W-59OO Siegen MS247
2500 University CA NW
Calgary AB T2N IN4
Prof. Dr. J.L. Encarna~o
Canada
GRIS (Graphisch-Interaktive System e)
FB 20 der 1H Darmstadt
Wilhelminenstr. 7 Dr. P. Hanusse
W-61OO Darmstadt Centre de Recherche Paul Pascal
CNRS
Domaine Universitaire
Gabriele Englert
F-33405 Talence Cedex
FhG-AGD
Fraunhofer-Arbeitsgruppe fUr
Graphische Datenverarbeitung Dr. H. Jurgens
Wilhelminenstr. 7 UniversiUit Bremen
W-61OO Darmstadt Institut fUr Dynamische Systeme
Bibliothekstr. 1
W-2800 Bremen 33
P. Guillattaud
Centre de Recherche Paul Pascal
CNRS Prof. G. Mantica
Domaine Universitaire Service de Physique Theorique
F-33405 Talence Cedex Laboratoire de l' Institut de
Recherche Fondamentale du
commisariat a l' Energie Atomique
A. Haase
CEN-SACLAY
Universitiit Wurzburg
F-91191 Gif-sur-Yvette Cedex
Physikalisches Institut
Am Hubland
W-87OO Wurzburg
x
U. Miissigmann M.Schendel
Fraunhofer-Institut IPA FbG-AGD
Postfach 800 469 Fraunhofer-Arbeitsgruppe fUr
W-7000 Stuttgart 80 Graphische Datenverarbeitung
Wilhelminenstr. 7
W-6100 Darmstadt
A. Odgaard
Orthopaedic Hospital Arhus
8000Arhus J. Schwietering
Danemark Leher Heerstr. 17
W-2800 Bremen 33
Prof. Dr. H.-O. Peitgen
Prof. Dr. M. Semetz
Universitat Bremen
Justus-Liebig-Universitat
Institut fUr Dynamische Systeme
Inst. f. Biochemie u. Endokrinologie
Bibliothekstr.1
Frankfurter Str. 100
W-2800 Bremen 33
W-6300 GieBen
Prof. Dr. P.J. Plath
G. Skordev
Universitat Bremen
Universitat Bremen
FBChemie
Institut fUr Dynamische Systeme
Postfach 33 04 40
Bibliothekstr.1
W-2800 Bremen 33
W-2800 Bremen 33
Prof. P. Prusinkiewicz
Prof. Dr. J.H. Spurk
University of Calgary
1H Darmstadt
MS247
FB 16, FG Techn. Stromungslehre
2500 University CA NW
Petersenstr. 30
Calgary AB TIN 1N4
W-6100 Darmstadt
Canada
Dr. Elisabeth Swart
Dr. W. Riimelin
Universitat Bremen
MSG Marine-und
FB2
Sondertechnik GmbH
Postfach 33 04 40
MT731
W-2800 Bremen 33
Hiinefeldstr.1-5
W-2800 Bremen 1
Dr. Jutta Syha
Universitat Wi.irzburg
G.Sakas
Physikalisches Institut
GRIS (Graphisch-Interaktive Systeme)
Am Hubland
FB 20 der TIl Darmstadt
W-8700 Wiirzburg
Wilhelminenstr.7
W-6100 Darmstadt
XI
Prof. Dr. R.F. Voss
IBM Research
P.O. Box 218
Yorktown Heights, NY 10598
USA
P. Wlczek
Justus-Liebig-Universitat
I08t. f. Biochemie u. Endokrinologie
Frankfurter Str. 100
W-6300 GieBen
Cornelia Zahlten
Universitat Bremen
Institut fUr Dynamische Systeme
Bibliothekstr. 1
W-2800 Bremen 33
I. Part: Fundamentals