List of Publications in Artificial Life and Self-organization
Wolfgang Banzhaf
Older papers (from 1993 back) are represented by abstracts only
and are available upon email request
We give titles and links. If you click the underlined words in a title
you will see an abstract and source information of the paper. If you click
the corresponding filename you will retrieve a copy.
2021
2016
2015
2013
2012
2011
2010
2009
2008
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
-
Emergent Computation by Catalytic Reactions
1995
1994
1993
List of Abstracts and Sources
TITLE: Artificial Life
AUTHORS: W. Banzhaf and B. McMullin
SOURCE: Handbook of Natural Computing, G. Rozenberg, T. Baeck, J.N. Kok (Eds.), 2012,
Springer, Heidelberg, 1805 - 1834
ABSTRACT:
Artificial life has now become a mature inter-discipline. In this contribution, its roots are
traced, its key questions are raised, its main methodological tools are discussed, and finally its
applications are reviewed. As part of the growing body of knowledge at the intersection
between the life sciences and computing, artificial life will continue to thrive and benefit
from further scientific and technical progress on both sides, the biological and the computational.
It is expected to take center stage in natural computing.
TITLE: Self-Organizing Systems
AUTHORS: Wolfgang Banzhaf
SOURCE: Encyclopedia of Complexity and Systems Science, 2009,
Springer, Heidelberg, 8040 - 8050
ABSTRACT:
An updated overview of self-organzing systems in Science, Humanities and Engineering.
FILENAME:
sos.pdf
(184 kB)
TITLE: Artificial chemistries - Toward Constructive Dynamical Systems
AUTHORS:
W. Banzhaf
SOURCE:
Solid State Phenomena, 97/98 (2004) pp. 43 - 50
ABSTRACT:
In this contribution we consider constructive dynamical systems,
taking one particular Artificial Chemistry as an example.
We argue that constructive dynamical systems are in fact
widespread in combinatorial spaces of Artificial Chemistries.
TITLE: Evolving Dynamics in an Artificial Regulatory Network Model
AUTHORS: Paul Dwight Kuo, Andre Leier and Wolfgang Banzhaf
SOURCE: Proc. of the Parallel Problem Solving from Nature Conference
(PPSN-04), Birmingham, UK, September 2004,
Yao X., Burke E., Lozano J.A., Smith J., Merelo-Guervós J.J., Bullinaria J.A.,
Rowe J., Tino P., Kabán A., Schwefel H.-P. (Eds.), Springer, LNCS 3242, Berlin, pp. 571 --- 580
ABSTRACT: In this paper artificial regulatory networks (ARN) are evolved to match the
dynamics of test functions. The ARNs are based on a genome representation generated
by a duplication / divergence process. By creating a mapping between the protein
concentrations created by gene excitation and inhibition to an output function,
the network can be evolved to match output functions such as sinusoids, exponentials
and sigmoids. This shows that the dynamics of an ARN may be evolved and thus may be
suitable as a method for generating arbitrary time series.
TITLE: Small World and Scale-Free Network Topologies in an Artificial
Regulatory Network Model
AUTHORS: Paul Dwight Kuo and Wolfgang Banzhaf
SOURCE: Proc. Artificial Life IX, (ALIFE-9),
Boston, USA, 2004, J. Pollack, M. Bedau, P. Husbands, T. Ikegami, R. Watson
(Eds.), MIT Press, Cambridge, pp. 404 --- 409
ABSTRACT: Small world and scale free network topologies commonly exist in natural and artificial systems.
Many mechanisms for producing these topologies have been presented in the literature.
We present an artificial regulatory network model generated by a duplication / divergence
process on a randomly generated genetic string and show that networks with small world and
scale free topologies can be produced with some regularity.
TITLE: How to Program Artificial Chemistries
AUTHORS: Jens Busch and Wolfgang Banzhaf
SOURCE: Advances in Artificial Life, Proceedings of the 7th
European Conference (ECAL-2003), Dortmund, September 15-17, 2003
W. Banzhaf, T. Christaller, P. Dittrich, J. Kim, J. Ziegler (Eds.)
Springer, Berlin, Lecture Notes in Artificial Intelligence, LNAI 2801, 2003, pp. 20 ---
30
ABSTRACT:
Using the framework of artificial chemistries (ACs) an automated
theorem prover (ATP) is constructed. Though it is an application
of its own, in the context of ACs automated theorem proving can
serve a second purpose. In this paper, we present a resolution-based AC
named RESAC. Once converted to the first-order predicate calculus a
problem straightly fits to this non-deterministic AC model. The calculus
therefore provides a general and intuitive language for ÓprogrammingÓ
RESAC. The fixed implicit interaction scheme and predefined structure
of the objects is advantageous and helps to predict the systemÕs dynamics.
Furthermore, the versatility of the methodology is demonstrated by
implementing the Adleman problem. An analysis of the dynamic behavior
is performed delivering insight into the synthesis of non-deterministic
emerging processes. This analysis include a discussion of some general
AC parameters.
TITLE: On the Dynamics of an Artificial Regulatory Network
AUTHORS: Wolfgang Banzhaf
SOURCE: Advances in Artificial Life, Proceedings of the 7th
European Conference (ECAL-2003), Dortmund, September 15-17, 2003
W. Banzhaf, T. Christaller, P. Dittrich, J. Kim, J. Ziegler (Eds.)
Springer, Berlin, Lecture Notes in Artificial Intelligence, LNAI 2801, 2003, pp. 217 ---
227
ABSTRACT:
We investigate a simple artificial regulatory networks (ARNs) able
to reproduce phenomena found in natural genetic regulatory networks. Notably
heterochrony, a variation in timing of expression, is easily achievable
by simple mutations of bits in the genome. It is argued that ARNs are
useful and important new genetic representations for artificial evolution.
TITLE: Advances in Artificial Life, Proceedings of the 7th
European Conference (ECAL-2003), Dortmund, September 15-17, 2003
AUTHORS: W. Banzhaf, T. Christaller, P. Dittrich, J. Kim, J. Ziegler (Eds.)
SOURCE: Springer, Berlin, Lecture Notes in Artificial Intelligence, LNAI 2801, 2003
ABSTRACT:
Conference Proceedings, 905 pages
TITLE: On the Dynamics of Competition in a simple Artificial Chemistry
AUTHORS: Wolfgang Banzhaf
SOURCE: Nonlinear Phenomena in Complex Systems, 5 (2002) 318 - 324
ABSTRACT:
We examine a simple system of competing and cooperating
entities in terms of the speed of settling their competition.
It turns out that the larger the degree of cooperativity among
entities the quicker the competition is decided. This result,
derived in a simple artificial chemistry system, demonstrates
that cooperativity is a decisive element
of a world of entities competing for resources.
It also hints at the fact that
growth of complexity (in terms of increasing cooperativity) is a native tendency
of such a world.
TITLE: Self-Organizing Systems
AUTHORS: Wolfgang Banzhaf
SOURCE: Encyclopedia of Physical Science and Technology, 2002,
Academic Press, New York, Vol. 14, 589 - 598
ABSTRACT:
Overview of self-organzing systems in Science, Humanities and Engineering.
TITLE: Artificial Chemistries - A Review
AUTHORS: Peter Dittrich, Jens Ziegler and Wolfgang Banzhaf
SOURCE: Artificial Life, 7 (2001) 225 - 275
ABSTRACT:
This article reviews the growing body of scientific work
in Artificial Chemistry. First, common motivations and fundamental
concepts are introduced. Second, current research activities
are discussed along three application dimensions: modeling,
information processing and optimization. Finally, common phenomena
among the different systems are summarized.
It is argued here that Artificial Chemistries are ``the right stuff''
for the study of pre-biotic and bio-chemical evolution, and
they provide a productive framework for questions regarding
the origin and evolution of organizations in general.
Furthermore, Artificial Chemistries have a broad application range
to practical problems as shown in this review.
TITLE: Survival of the Unfittest? - The Seceder Model and its
Fitness Landscape
AUTHORS: Peter Dittrich and Wolfgang Banzhaf
SOURCE: Advances in Artificial Life, Proc. of the 6th European
Conference ECAL 2001, Prague, September 2001, J. Kemelen and P. Sosik (Eds.)
pp. 100 - 109
ABSTRACT:
The seceder model is an extremely simple individual based model which shows how the local tendency to be
dierent gives rise to the formation of hierarchically structured groups, called the seceder eect. The
model consists of a population of simple entities which reproduce and die. In a single reproduction event
three individuals are chosen ran- domly and the individual which possesses the largest distance to their
mean is reproduced by creating a mutated copy (ospring). The o- spring replaces a randomly chosen
individual of the population. In this contribution we investigate the eective tness landscape of the
seceder model. Fitness is measured as reproductive success. The investigation of the tness landscape
revealed an on the rst view counterintuitive phe- nomena: The individuals of the basic seceder model are
always located in the worst regions of the tness landscape where the replication rate is relatively low.
TITLE: Stability of Metabolic and Balanced Organizations
AUTHORS: Pietro Speroni di Fenizio and Wolfgang Banzhaf
SOURCE: Advances in Artificial Life, Proc. of the 6th European
Conference ECAL 2001, Prague, September 2001, J. Kemelen and P. Sosik (Eds.)
pp. 196 - 205
ABSTRACT: We investigate the possible organisations emerging from an artificial chemistry (AC) of
colliding molecules in a well stirred reactor. The molecules are generated from 7 basic components
(atoms), each with a different behavior. After discovering two main types of organisations (metabolic o.
and balanced o.), we deepen our analysis by studying their behavior over time. The phases they pass
through and their stability with respect to an external influx of random information are examined. We
notice that no organisation seems to be totally stable over time, yet metabolic organisations pass through
a growth phase with a much higher stability. Lastly we observe how the different phases are triggered by
the presence or absence of particular atoms.
TITLE: Spontaneous Formation of Proto-Cells in a Universal
Artificial Chemistry on a Planar Graph
AUTHORS: Pietro Speroni di Fenizio, Peter Dittrich and Wolfgang Banzhaf
SOURCE: Advances in Artificial Life, Proc. of the 6th European
Conference ECAL 2001, Prague, September 2001, J. Kemelen and P. Sosik (Eds.)
pp. 206 - 215
ABSTRACT:
An artificial chemistry is embedded in a triangular planar graph, that allows the molecules to act only
locally along the edges. We observe the formation of e ectively separated components in the graph
structure. Those components are kept separated by elastic reactions from molecules generated inside the
component itself. We interpret those components as self-maintaining proto-cells and the elastic nodes as
their proto-membrane. The possibility for these cells to be autopoietic is discussed.
TITLE: Evolving Control Metabolisms for a Robot
AUTHORS: Jens Ziegler and Wolfgang Banzhaf
SOURCE: Artificial Life, 7 (2001) 171 - 190
ABSTRACT:
This paper demonstrates a new method of programming artificial chemistries.
It uses the emerging capabilities of the system's dynamics for information
processing purposes. By evolution of metabolisms that act as control programs
for a small robot one achieves the adaptation of the internal metabolic pathways
as well as the selection of the most relevant available exteroreceptors.
The underlying artificial chemistry evolves efficient information processing
pathways with most benefit for the desired task, robot navigation.
The results show certain relations to biological systems like motile bacteria.
TITLE: Spontaneous Group Formation in the Seceder Model
AUTHORS: Peter Dittrich, Fredrik Liljeros, Arne Soulier and Wolfgang Banzhaf
SOURCE: Physical Review Letters, 84 (2000) 3205 - 3208
ABSTRACT: The seceder model shows how
the local tendency to be different gives rise to the formation of groups. The model
consists of a population of simple entities which reproduce and die. In a single
reproduction event three individuals are chosen randomly and the individual which
possesses the largest distance to their center is reproduced by creating a mutated
offspring. The offspring replaces a randomly chosen individual of the population. The
paper demonstrates the complex group formation behavior and its dependency on the
population size.
FILENAME:
PRL84.pdf
(122 kB)
TITLE: Towards a Theory of Organizations
AUTHORS: Pietro Speroni di Fenizio, Peter Dittrich, Wolfgang Banzhaf and Jens Ziegler
SOURCE: Proc. German Workshop on Artificial Life, Bayreuth, Germany, 2000
ABSTRACT: In this paper we develop an algebra to describe organizations.
Its application is demonstrated with five examples.
We start from definitions given by Fontana (1992) of an organization
as a closed and self-maintaining set of interacting objects.
We develop a formal framework to describe
the inner structure of an organization and a relationship
between different organizations. The definitions of intersection and union
of organizations are developed.
Those definitions naturally give rise to a lattice
(an algebraic structure over a partially ordered set)
which provides a precise basis to study the hierarchical nature
of organizations. Some fundamental properties are described and the usefulness
of the mathematical concepts demonstrated by application.
TITLE: Artificial Chemistry (in German)
AUTHORS: Andre Skusa, Wolfgang Banzhaf, Jens Busch, Peter Dittrich and Jens Ziegler
SOURCE: Kuenstliche Intelligenz, 1 / 2000, 12 - 19
ABSTRACT:
Unter einer Kuenstlichen Chemie (Artificial Chemistry) versteht man ein
System, das mit seinen Komponenten und Interaktionsregeln das Paradigma der
natuerlichen Chemie zum Vorbild hat, jedoch von den tatsa3chlichen physikalischen
Randbedingungen abstrahiert. Die Dynamik einer Kuenstlichen Chemie,
die durch die Interaktionen der Molekuele und den
Reaktionsalgorithmus bestimmt wird, ist dabei der anderer komplexer Systeme
aehnlich. Somit koennen unterschiedliche komplexe Systeme als
Realisierungen der gleichen Organisation verstanden werden. Diese
Organisation gilt es, abstrakt und realisierungsunabhaengig zu
beschreiben. Von besonderem Interesse sind deshalb solche fuer natuerliche und
komplexe Systeme kennzeichnenden Phaenomene wie Selbstorganisation,
Strukturbildung, Evolution und Informationsverarbeitung.
Die Zielsetzungen bei der Untersuchung Kuenstlicher Chemien lassen sich
vereinfachend in Modellbildung, Informationsverarbeitung und Optimierung
unterteilen. Dies umfasst sowohl grundlagentheoretische
Untersuchungen zur Evolution des Lebens, als auch anwendungsorientierte
Ansaetze, die eine Kuenstliche Chemie z.B. zur metabolischen Steuerung von
Robotern oder zum automatischen Beweisen einsetzen.
TITLE: Self-organizing Algorithms derived from RNA interactions
AUTHORS: W. Banzhaf
EDITORS: W. Banzhaf and F. Eeckman
ABSTRACT:
We discuss algorithms based on the RNA interaction found in
Nature. Molecular biology has reveiled that strands of RNA, besides
being autocatalytic, can interact with each other.
They play a double role of being information
carriers and enzymes. The first role is realized by the 1-dimensional
sequence of nucleotides on a strand of RNA, the second by the 3-dimensional
form strands can assume under appropriate temperature and solvent
conditions. We use this basic idea of having two alternative forms
of the same sequence to propose a new Artificial Life algorithm. After a
general introduction to the area we report our findings in a specific
application studied recently: an algorithm which allows
sequences of binary numbers to interact. We introduce folding methods
to achieve 2-dimensional alternative forms of the sequences. Interactions
between 1- and 2-dimensional forms of binary sequences generate new
sequences, which compete with the original ones due to selection
pressure. Starting from random sequences, replicating and self-replicating
sequences are generated in considerable numbers. We follow the evolution
of a number of sample simulations and analyse the resulting
self-organising system.
FILENAME:
TITLE: Mesoscopic Analysis of Self-Evolution in an Artificial Chemistry
AUTHORS: Peter Dittrich, Jens Ziegler and Wolfgang Banzhaf
EDITORS: C. Adami, R.K. Belew, H. Kitano and C.E. Taylor (Eds.)
ABSTRACT: In an algorithmic artificial chemistry the objects (molecules)
are data structures and the interactions (reactions) among them are defined
by an algorithm. The same object can appear in two forms: (1) as an active
machine (operator), (2) as passive data (operand). Thus, the same object
can act on other objects or it can be processed by others. This dualism
allows the implicit definition of constructive artificial chemical systems,
which exhibit quite complex behaviors. In our case even evolutionary behavior
has been observed which is notable, because no explicit mutation, recombination
or fitness function is involved. Every variation is exclusively performed
by the objects (molecules) in their machine form. In addition to microscopic
methods (e.g. monitoring the actions of single molecules) and macroscopic
measurements (e.g. diversity, complexity) we developed a stepwise mesoscopic
analysis method based on classification and dynamic clustering. Knowledge
about the system is accumulated in a cyclic process, where measuring tools
(classifiers) extract information, which is again used to create new classifiers.
TITLE: Self-Evolution in a Constructive Binary String System
AUTHORS: Peter Dittrich and Wolfgang Banzhaf
SOURCE: Artificial Life, 4 (1998) 203 - 220
ABSTRACT: We examine the qualitative dynamics of a catalytic self-organizing
reaction system of binary strings that is inspired by the chemical information
processing metaphor. A string is interpreted in two different ways: either
(i) as raw data or (ii) as a machine which is able to process another string
as data in order to produce a third one. This paper focuses on the phenomena
of evolution whose appearance is notable because no explicit mutation,
recombination or artificial selection operators are introduced. We call
the system self-evolving because every variation is performed by the objects
themselves in their machine form.
TITLE: Macroscopic and Microscopic Computation in an Artificial Chemistry
AUTHORS: Peter Dittrich, Wolfgang Banzhaf, Hilmar Rauhe, and Jens Ziegler
SOURCE: 2nd German Workshop on Artificial Life, University of Dortmund,
April 1997
ABSTRACT: Chemical and biochemical systems as part of living organisms
have been shown to possess interesting computational properties. Example:
the information flow in the chemotaxis system of Escherichia Coli. In a
parallel development, the chemical computation metaphor is becoming more
and more frequently used as part of the emergent computation paradigm in
Computer Science. In this contribution we will discuss two ways of how
information can be processed by a collection of molecules floating around
in well-stirred tank reactor. In the first case the information is stored
as a concentration of a substances and computation is carried out by increase
and decrease of concentration levels. We will refer to this as macroscopic
computation. In the second case -- microscopic computation -- the result
of a computation is represented by single molecules. The dynamics is stochastic,
in contrast to macroscopic computation where the dynamics can be described
with ordinary differential equations. In both cases the result emerges
from many simple and parallel interactions. In order to show the abilities
of such systems we will use artificial chemistries which are simulated
reaction systems of mathematical or algorithmic objects.
TITLE: Selforganization in a system of binary strings with topological
interactions
AUTHORS: Wolfgang Banzhaf, Peter Dittrich and Burkart Eller
SOURCE: Physica D, 125 (1999) 85 - 104
ABSTRACT: We consider an artificial reaction system whose components are
binary strings. Upon encounter, two binary strings produce a third string
which competes for storage space with the originators. String types or
species can only survive when produced in sufficient numbers. Spatial interactions
through introduction of a topology and rules for distance-dependent reactions
are discussed. We observe three different kinds of survival strategies
of binary strings: cooperation of strings, exploitation of niches and parasitic
behavior.
TITLE: Towards a metabolic robot control system
AUTHORS: Jens Ziegler, Peter Dittrich and Wolfgang Banzhaf
EDITORS: W.M.L. Holcombe, R. Paton (Eds.)
ABSTRACT: The signal processing system of a cell is very robust in its
dependence upon the observation of central metabolites and, on the other
hand, on the hierarchical division into functional blocks. Therefore it
can act as a model for the construction of robust, highly parallel and
distributed control systems. We have used the metabolic paradigm as a guideline
to develop a robot architecture for simple navigation tasks. Results on
obstacle avoidance and light searching behavior are reported here.
TITLE: A Topological Structure Based on Hashing - Emergence of a ''Spatial''
Organisation
AUTHORS: Peter Dittrich and Wolfgang Banzhaf
ABSTRACT: A topological structure based on hashing for an algorithmic reaction
system is introduced. Hashing, as a very efficient storage method for certain
problems, uses an important property of the computer: Its ability to accurately
access a specific address in memory space. It is shown, how a self-organising
system can be built with this method. We discuss experiments with a reaction
system based on the resulting hash topology.
TITLE: Emergent Computation by Catalytic Reactions
AUTHORS:Wolfgang Banzhaf, Peter Dittrich, Hilmar Rauhe
SOURCE: Nanotechnology, 7 (1996) 307 --- 314
ABSTRACT: Recently, biochemical systems have been shown to possess interesting
computational properties. In a parallel development, the chemical computation
metaphor is becoming more and more frequently used as part of the emergent
computation paradigm in Computer Science. We review in this contribution
the idea behind the chemical computational metaphor and outline its relevance
for nanotechnology. We set up a simulated reaction system of mathematical
objects and examine its dynamics by computer experiments. Typical problems
of computer science, like sorting, parity checking or prime number computation
are placed within this context. The implications of this approach for nanotechnology,
parallel computers based on molecular devices and DNA-RNA-protein information
processing are discussed.
TITLE: Self-organization in a system of binary strings
AUTHORS: Wolfgang Banzhaf
SOURCE: Proceedings ARTIFICIAL LIFE IV, R. Brooks and P. Maes (Eds.), MIT
Press, Cambridge, MA, 1994, pp. 109 --- 118
ABSTRACT: We discuss a system of autocatalytic sequences of binary numbers.
Sequences come in two forms, a 1-dimensional form (operands) and a 2-dimensional
form (operators) that are able to react with each other. The resulting
reaction network shows signs of emerging metabolisms. We discuss the general
framework and examine specific interactions for a system with strings of
length 4 bits. A self-maintaining network of string types and parasitic
interactions are shown to exist.
EDITORS: Wolfgang Banzhaf and Frank H. Eeckman
SOURCE: Lecture Notes in Computer Science. Eds.: G. Goos, J. Hartmanis,
J. van Leeuwen. Vol. 899 1995. VII, 277 pp. Softcover $49.00 ISBN 3-540-59046-3
ABSTRACT: This volume comprises ten papers from an interdisciplinary workshop
on biocomputation entitled "Evolution as a Computational Process". Key
words: Population genetics, emergence, artificial life, self-organization,
evolutionary algorithms, selection.
You can buy this book immediately by clicking on the title.
TITLE: Self-replicating Sequences of Binary Numbers --- The Build-up of
Complexity
AUTHORS: Wolfgang Banzhaf
SOURCE: Complex Systems, Volume 8 (1994), pp. 205 --- 215
ABSTRACT: A recently introduced system of self-replicating sequences of
binary numbers (strings) is generalized. It is extended to include strings
of arbitrary length. For this purpose, first, the folding methods of strings
into two-dimensional operators are expanded to include strings of arbitrary
size. Second, rules of interaction between strings of different lengths
are established. As natural consequence of these interactions, changes
in string length are observed. Using an effective model of length changes,
the build-up of complexity as measured by the average sequence length in
a string population is studied.
TITLE: Artificial Selection in a System of Self-Replicating Strings
AUTHORS: Wolfgang Banzhaf
SOURCE: Proceedings of 1st IEEE Conference on Evolutionary Computation
(World Congress on Computational Intelligence (WCCI-94)), Orlando, FL,
USA, 1994, IEEE Press, Piscataway, Vol. II, pp. 651 --- 655
ABSTRACT: We investigate the use of external selection pressure in a system
of self-replicating binary strings. As it turns out, these systems are
remarkably flexible in responding to external selection pressure evolving
in arbitrarily chosen directions. We introduce different kinds of selection
pressure and illustrate their use.
TITLE: Self-replicating Sequences of Binary Numbers
AUTHORS: Wolfgang Banzhaf
SOURCE: Computers and Mathematics with Applications, Vol. 26 (1993), pp.
109 --- 118
ABSTRACT: An algorithm is proposed which allows sequences of binary numbers
to interact. We introduce a 2-dimensional matrix form of the sequences
achieved by a general folding method. Interactions between 1- and 2-dimensional
forms of binary sequences generate new sequences, which compete with the
original ones due to selection pressure. Starting from random initial populations,
replicating and self-replicating sequences are generated in large numbers.
We report on results for 4-digit sequences and propose non-linear differential
equations modelling the system.
TITLE: Self-replicating sequences of binary numbers --- I. Foundations
AUTHORS: Wolfgang Banzhaf
SOURCE: Biological Cybernetics, Volume 69 (1993), pp. 269 --- 274
ABSTRACT: We propose the general framework of a new algorithm derived from
the interactions of chains of RNA which is capable of self-organization.
It considers sequences of binary numbers (strings) and their interaction
with each other. In analogy to RNA systems, a folding of sequences is introduced
to generate alternative 2-dimensional forms of the binary sequences. The
2-dimensional forms of strings can naturally interact with 1-dimensional
forms and generate new sequences. These new sequences compete with the
original strings due to selection pressure. Populations of initially random
strings develop in a stochastic reaction system following the reaction
channels between string types. In particular, replicating and self-replicating
string types can be observed in such systems.
FILENAME: To obtain it, please send me an email!
TITLE: Self-replicating sequences of binary numbers --- II. Strings of
length N=4
AUTHORS: Wolfgang Banzhaf
SOURCE: Biological Cybernetics, Volume 69 (1993), pp. 275 --- 281
ABSTRACT: We study an algorithm which allows sequences of binary numbers
(strings) to interact with each other. The simplest system of this kind
with a population of 4-bit-sequences is considered here. Previously proposed
folding methods are used to generate alternative 2-dimensional forms of
the binary sequences. The interaction of 2-dimensional and 1-dimensional
forms of strings is simulated in a serial computer. The reaction network
for the N=4 system is established. Development of string populations initially
generated randomly is observed. Non-linear rate equations are proposed
which provide a model for this simplest system.
FILENAME: To obtain it, please send me an email!
Wolfgang Banzhaf
Last updated: Aug 21, 2021