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Advances in Complex Systems, Vol. 10, Suppl. No. 1 (2007) 1–3
!World Scientiﬁc Publishing Company
Department of Mechanics, Faculty of Applied Sciences,
University of West Bohemia, Univerzitn´ı 22,
306 14 Pilsen, Czech Republic,
Received 31 January 2007
This special journal issue of Advances in Complex Systems presents a collection of papers
describing current research delivered by recognized researchers actively working in vari-
ous corners of the ﬁeld of modeling of complex systems by cellular automata and related
methods. All included papers are self-contained and present the latest developments in
the areas where the authors work. Hence, all papers can be read independently, but it
is strongly recommended to study the issue as a whole to get a general overview of the
various methods and techniques from the ﬁeld. The main aim of this special issue is to
provide researchers from neighboring ﬁelds with suﬃcient information and vital exam-
ples of how to design models in complex systems. The whole issue is organized in such a
way that common features occurring repeatedly in most models of complex systems are
Keywords: Complex systems; cellular automata; modeling.
During the development of various models of natural phenomena observed within
diverse ﬁelds expressing complex behavior — where those models were developed
by researchers having completely diﬀerent backgrounds — a set of unifying features
repeatedly occurring within those models of complex systems has emerged. From a
certain perspective, one could say that those common features represent an alphabet
for the design of new models of complex phenomena in other ﬁelds as well — and not
necessarily using cellular automata as the computational method. This observation
automatically leads us to the main purpose of this special issue: to show the “Lego
blocks” of the game so that everybody can apply them in their own ﬁeld and build
Eight researchers each present ongoing research work in their ﬁelds of interest.
Each paper provides self-contained information and can be studied independently
of the others, but it is recommended to spend some extra time studying the various
∗Corresponding address: J. Kroc, Havl´ıˇckova 482, 332 03 ˇ
t´ahlavy, Czech Republic.
approaches to handling complexity within all of the papers. This will provide one
with a deeper understanding of complexity in general and help to build a sense of
complex systems and their modeling overall.
We would like to direct the reader’s attention to those common features occur-
ring repeatedly in most of the models of complex systems presented here. In order
to recognize those common features easily, an explicit list of them is provided in
this editorial. It is worth emphasizing one important fact: those who study all the
papers in this issue — and not only those close to their own ﬁeld — will bene-
ﬁt much more. A well-known principle observed within complex systems work says
that the whole is more than a mere sum of the parts. The very same principle works
for this special issue. Those who spend their time reading the whole issue will get
not only an overview of possible applications of complexity, but also a better sense
Special attention should be given to the following “Lego blocks”: self-
organization (1), emergence (1, 2, 7), topology of CAs (1, 4), swarm intelligence
(1, 8), predictability and genetic programming (2, 3). It is worth thinking about
the topology — mesh, meshless, or networked — of CAs playing the key role in
problem solutions. The way of viewing the problem is diﬀerent for each application.
There are computational problem solving methods (1–4, 8), theoretical predictions
(5, 6), and typical computational models (6, 7). Usually, there are combinations of
several of the above mentioned “blocks” in each paper. This means that one has
the freedom to use the best available tools in order to achieve the goal; there are
no limits to the reader’s creativity. But what is necessary to stress is the fact that
nature — especially when working with biological processes — shows unbeatable
creativity. Hence, careful studies of nature and its ways of problem solving might
serve as our best teacher.
(1) The paper by A. Rodrigues, A. Grushin and J. A. Reggia presents research
in the ﬁeld of swarm intelligence with a special focus on self-organization and
emergence. Solutions are achieved through local component interactions with-
out any central control. It is extremely diﬃcult to design swarms having the
desired control functions and this work proposes new layered, hierarchical con-
trolling of swarm components that facilitates a greater ﬂexibility in design.
(2) A. Hauptman and M. Sipper demonstrate how the emergence of chess endgame
complex strategies using the genetic programming (GP) technique works. GP is
often used in complex simulations — and, hence, in CAs as well — to ﬁnd
the best rule or strategy. This paper teaches us how to work with genetic
programming and what people might expect from it.
(3) Z. Pan, J. A. Reggia and D. Gao present an extremely eﬃcient technique for
ﬁnding CA rules performing self-replication of structures based on a unique
modiﬁcation of genetic programming using diﬀerent trees for data structures
and for rule encoding. This leads to an extreme speed-up of search for new
rules performing self-replication of structures, and makes it possible to generate
families of replicators and systematically study their properties for the ﬁrst
(4) C. Darabos, M. Giacombini and M. Tomassini study performance and robust-
ness of collective tasks of networked CAs tested on both density classiﬁ-
cation and synchronization tasks. They demonstrate the crucial inﬂuence
of topology — such as random graphs, Small Worlds, and/or scale-free
graphs — on the solution of problems.
(5) L. Gonzales presents a theoretical, uniﬁed approach allowing extremely eﬃcient
comparison of occurrence probabilities within complex stochastic Boolean sys-
tems. The theoretical results enable rapid determination of all the binary strings
with probabilities less than or equal to (or greater than or equal to) the prob-
ability of any ﬁxed binary string. The approach is based on use of the intrinsic
ordering graph, which enables ordering those probabilities without the neces-
sity of evaluating them on what is, in general, a computationally intractable
(6) D. Hiebeler uses statistical methods to make predictions of CA behavior for
stochastic rules updated asynchronously. He studies voter models computa-
tionally and stochastically using a pair approximation moment-closure method
leading to a system of diﬀerential equations predicting the behavior of the
(7) J. L. Guisado, F. Jim´enez–Morales and F. Fern´andez de Vega present a CA sim-
ulation of laser behavior, and its parallel implementation for computer clusters.
The global physical laser response emerges from local interactions of photons
operating at the lowest model level where photons are emitted by stimulated
emission of excited electrons. Electrons are excited by pumping energy from
outside. Modeled collective behavior of photon populations creates diﬀerent
laser modes: steady-state, oscillatory, or possibly chaotic, which are observed
(8) J. Kennedy presents the particle swarm algorithm, which is a problem-solving
method based on social-psychological principles. The particle swarm is used for
optimization of problems through the interactions of topologically connected
particles with one another and mutual sharing of knowledge about a problem
space. The population tends to converge towards robust problem solutions as
individuals discover and share better problem solutions.
We conclude with the following about the preparation of this issue. This issue
is the result of intensive discussions between the editor and the contributors. The
authors present their work in a way which is tractable for non-specialists.
The work done by J. Kroc on preparation of this special journal issue was in
large part sponsored by the Czech Ministry of Education, Youth and Sports under
Grant No. MSM 4977751303, and by the University of West Bohemia.