Table Of ContentSpringer Series in Synergetics
Synergetics, an interdisciplinary field of research, is concerned with the cooper
ation of individual parts of a system that produces macroscopic spatial, temporal
or functional structures. It deals with deterministic as well as stochastic processes.
Volume 1 Synergetics An Introduction 2nd Edition
ByH. Haken
Volume 2 Synergetics A Workshop
Editor: H. Haken
Volume 3 Synergetics Far from Equilibrium
Editors: A. Pacault and C. Vidal
Volume 4 Structural Stability in Physics
Editors: W. Gtittinger and H. Eikemeier
Volume 5 Pattern Formation by Dynamic Systems and
Pattern Recognition
Editor: H. Haken
Pattern Formation
by Dynamic Systems and
Pattern Recognition
Proceedings of the International Symposium
on Synergetics at ScWoB Elmau, Bavaria,
April 30 - May 5, 1979
Editor: H. Haken
With 156 Figures
Springer-Verlag Berlin Heidelberg New York 1979
Professor Dr. Hermann Haken
Institut fUr Theoretische Physik der Universitat Stuttgart
Pfaffenwaldring 57/IV, D-7000 Stuttgart 80, Fed. Rep. of Germany
ISBN-13: 978-3-642-67482-2 e-ISBN-13: 978-3-642-67480-8
001: 10.1007/978-3-642-67480-8
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© by Springer-Verlag Berlin Heidelberg 1979
Softcover reprint of the hardcover 1s t edition 1979
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2153/3130-543210
Preface
This book contains the manuscripts of the papers delivered at the International Sym
posium on Synergetics held at SchloB Elmau, Bavaria, Germany, from April 30 until
May 5, 1979. This conference followed several previous ones (Elmau 1972, Sicily 1974,
Elmau 1977). This time the subject of the symposium was "pattern formation by dynam
ic systems and pattern recognition". The meeting brought together scientists from
such diverse fields as mathematics, physics, chemistry, biology, history as well as
experts in the fields of pattern recognition and associative memory.
When I started this type of conference in 1972 it appeared to be a daring enter
prise. Indeed, we began to explore virgin land of science: the systematic study of
cooperative effects in physical systems far from equi~ibrium and in other disciplines.
Though these meetings were attended by scientists from quite different disciplines,
a basic concept and even a common language were found from the very beginning. The
idea that there exist profound analogies in the behaviour of large classes of complex
systems, though the systems themselves may be quite different, proved to be most
fruitful. I was delighted to see that over the past one or two years quite similar
conferences were now held in various places allover the world. The inclusion of prob
lems of pattern recognition at the present meeting is a novel feature, however. Again
it appears that there are more links between pattern formation and pattern recogni
tion than most scientists had thought of before. At the meeting it became evident
that both groups can profit from each other considerably and that there is good rea
son to believe that again profound common features of these two sciences can be elab
orated by future research.
I hope the readers of this volume will feel the same enthusiasm the participants
of this symposium had when listening to the talks and finding out common features of
phenomena treated in different disciplines.
I wish to express my deep gratitude to my secretary, Mrs. U.Funke, for her tire
less and invaluable help in organizing this symposium.
thank the Volkswagenwerk Foundation for financial support.
Stuttgart. August 1979 H. Haken
v
Contents
Part I. Introduction
Pattern Fonnati on and Pattern Recogniti on-
An Attempt at a Synthesis. By H. Haken (With 10 Figures) .................... 2
Part II. TemporaZ Patterns: Laser OsciZZations and Other
Quantum-OpticaZ Effects
Atomic Cooperation in Quantum Optics: Superfluorescence and
Optlcal Bistability. By R. Bonifacio and L.A. Lugiato
(With 9 Figures) ............................................................ 16
Experimental Aspects of Transition Phenomena in Quantum Optics
By F.T. Arecchi (With 13 Figures) ........................................... 28
Laser with Saturable Absorber. Fluctuations and Stability
By S.T. Dembinski (With 14 Figures) ......................................... 43
Part III. Pattern Formation in FZuids
Patterns of Convection in Plane Layers and in Spherical Shells
By F. H. Busse (With 7 Fi gures) .............................................. 56
Laserlike Approach to the Dynamics of the Rayleigh-Benard and
the Soret-Driven Instabilities. By V. Degiorgio (With 3 Figures) .. , '" ...... 64
Phase Locking in the Oscillations Leading to Turbulence
By J.P. Gollub and S.V. Benson (With 7 Figures) ............................. 74
Part IV. TurbuZence and Chaos
A Simplified Theory of Intermittent Fully-Developed Turbulence
By H. Mori and H. Fujisaka (With 3 Figures) ................................. 82
Chaos and Its Description. By K. Tomita (With 3 Figures) ....................... 90
Part V. Pattern Recognition and Pattern Formation in BioZogy
Figure-Ground Discrimination by the Visual System of the Fly
By W. Reichardt (With 18 Figures) .......................................... 100
VII
A Theory of Drug Induced Visual Hallucination Patterns
By J.D. Cowan and G.B. Ermentrout (With 3 Figures) ........................ 122
Physiological Mechanisms for the Perception of Random Dot
Moire Patterns. By L. Glass (With 4 Figures) ............................... 127
Similarities Between Pattern Formation and Pattern Recognition
(Interpretation) During Biological Development
By H. Meinhardt (With 6 Figures) ............................................ 135
Electrical Effects in Nonlinear Physico-Chemical Systems:
Field Chemical Wave Interaction and Bio-Self Electrophoresis
By R. Larter, S. Schmidt, and P. Ortoleva (With 4 Figures) ............. , ... 144
Patterns in the Immune System. By P.H. Richter (With 12 Figures) ............... 155
The Oscillatory Basis of Cell Enerqy Metabolism
By E.E. Sel'kov (With 4 Figures) ................................•........... 166
Part VI. Pattern Recognition and Associations
Recent Advances in Syntactic Pattern Recognition
By K.S. Fu (With 1 Figure) ................................................. 176
Abduction of Semantic Patterns. By U. Grenander (With 3 Figures) .............. 186
Representation and Processing of Associations Using
Vector Space Operations. By T. Kohonen (With 5 Figures) .................... 199
Part VII. Pattern Formation in Ecology, Sociology and History
Non-Uniform Stable Solutions to Reaction-Diffusion Equations:
Applications to Ecological Pattern Formation
By S.A. Levin (With 1 Figure) .............................................. 210
Socioeconomic Inequalities: Adaptation and Application of a Theory
of Biological Pattern Formation. By A. Gierer (With 6 Figures) ............. 223
Systems and Changes of Systems in History
By A. Nitschke (With 6 Figures) ............................................ 234
Part VIII. General Approaches
Bifurcation and Nonlinear Focusing. By A.C. Newell (With 2 Figures) ............ 244
Thermodynamics of Nonequilibrium Processes
By J. Keizer (With 1 Figure) ............................................... 266
Growth of Fluctuations in Thermodynamically Unstable Systems
By K. Kawasaki (With 3 Fi gures) ............................................ 278
Evolution of Systems. Time Scaling and Scaling Factors
By A. Pacault and A. Marchand (With 8 Figures) ............................. 289
Index of Contributors ........................................................ 305
VIII
Part I
Introduction
Pattern Fonnation and Pattern Recognition - An Attempt at a Synthesis
H. Haken
Institut fUr Theoretische Physik der Universitat Stuttgart
D-7000 Stuttgart 8, Fed. Rep. of Germany
One of the most interesting aspects of the world is that it can be
considered to be made up of patterns. A pattern is essentially an
arrangement. It is characterized by the order of the elements of
which it is made rather than by the intrinsic nature of these elements.
Norbert Wiener
1. Introduction
The above sentences by Norbert Wiener form by themselves a pattern.
When we look at such a pattern our first impression might be that a
pattern is something static. However, when thinking somewhat more
about patterns we realize that patterns are intimately connected with
processes. First of all, a pattern has been formed. For instance the
above pattern .was first conceived, then printed etc. On the other
hand, when we look at a pattern, it induces processes in our brain
leading to the perception of the pattern. Similarly, patterns induce
processes in other biological systems or in machines. In this way
both pattern formation and pattern recognition are connected with
dynamic processes.
The scientists and the topics presented by them at this symposium
belong to two groups, namely those dealing with pattern formation
and those dealing with pattern recognition. So far meetings on
synergetics [1] - [4J have brought together only the members of the
group dealing with pattern formation. It is therefore one of the
main purposes of my lntroductory notes to show why I think that
bringing together these two groups seems to be a promising step in the
synergeti cs enterpri.se.
2. Pattern formation
In the first part of my introductory remarks I should like to deal
with pattern formation. It seems useful to distinguish between man
made patterns and those created by nature. Man-made patterns often serve
a purpose. Such a pattern might be connected with spoken or written
language, with music or painting. Of course, there are many other
man-made patterns, just think of machines, buildings etc. Now let us
turn to patterns formed by nature. Here we may distinguish between
patterns formed by the inanimate world and those formed by biological
systems. To deal with pattern formation it is most natural to start
with processes which seem to be more easily describable. This leads
us to start with patterns formed by the inanimate world, though we
shall see that some of the general ideas still extend to biological
and other processes.
Let me first present, more or less at random, some patterns we
find in the inanimate world.
2
Fig~ Snow crystal Fig~ A typical pattern of cloud
streets (After R.Scorer: Clouds of
the world, Lothian Publ. Co., Mel
bourne 1972)
Fig. 1 shows a snow crystal with its striking symmetries, exhibiting
a very pronounced structure. When we look at the microscopic origin
of this pattern we discover that the water molecules are arranged in
a well defined static order.
Fig. 2 shows a pattern which at a first sight seems to be static, too.
However, glider pilots know that the air shows an up and downward
motion depending on the position. We may call such patterns dynamic
patterns.
Fluids can show still more complicated patterns, for instance Fig.3
shows a picture taken by Busse and Whitehead.
When looking at the corresponding movie one realizes that this pattern
is generated by motions of the volume elements of the fluid. The
previous meetings on synergetics have dealt with many further patterns
formed by inanimate matter. Numerous examples will be found in the
proceedings of this symposium, too.
From the very beginning one of the interesting features of
synergetics has been its capability to reveal striking analogies between
quite different systems. For instance it could be demonstrated mathe
matically that continuously extended media may develop patterns of
the same kind in spite of the fact that these media are composed of
Fig~ Pattern of fluid motion at
elevated Rayleigh number [after F.H.
Busse, J.A.Whitehead: J.Fluid Mech. 47,
305 (1971) 1
3
Description:This book contains the manuscripts of the papers delivered at the International Sym posium on Synergetics held at SchloB Elmau, Bavaria, Germany, from April 30 until May 5, 1979. This conference followed several previous ones (Elmau 1972, Sicily 1974, Elmau 1977). This time the subject of the symp
