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.



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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.

FILENAME: BanzhafMcMullin_Alife.pdf (312 kB)




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.

FILENAME: selfformation.pdf (251 kB)




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.

FILENAME: ARNOptimizeNew.pdf (256 kB)




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.

FILENAME: Genome_final.pdf (256 kB)




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.

FILENAME: BuschBanzhaf2003pdf (792 kB)




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.

FILENAME: ecal2003_final.pdf (811 kB)




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

FILENAME: Springer Link to LNAI 2801




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.

FILENAME: acceleration.pdf (180 kB)




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.

FILENAME: article3.ps.gz (4,396 kB) or article3.pdf (214 kB)




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.

FILENAME: alchemistry_review_MIT.pdf (589 kB)




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.

FILENAME: ecal01_survival.pdf (1.209 kB)




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.

FILENAME: ecal01_stab.ps.gz (144 kB)




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.

FILENAME: ecal01_spont.ps.gz (353 kB)




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.

FILENAME: metabolism.pdf (383 kB)




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.

FILENAME: gwal.ps.gz (158 kB) or gwal.pdf (395 kB)




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.

FILENAME: finalversion_journal.pdf (233 kB)





TITLE: Self-organizing Algorithms derived from RNA interactions

AUTHORS: W. Banzhaf

SOURCE: Evolution and Biocomputation, Lecture Notes in Computer Science, LNCS, Vol. 899, Springer, Berlin, 1995, pp. 69 -- 102

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.

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TITLE: Mesoscopic Analysis of Self-Evolution in an Artificial Chemistry

AUTHORS: Peter Dittrich, Jens Ziegler and Wolfgang Banzhaf

SOURCE: Proc. on the 6th Int. Conf. on Artificial Life, Los Angeles, 1998, MIT Press, Cambridge, MA, 95 - 103

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. 

FILENAME: alife6.ps.gz (77 kB) or alife6.pdf (292 kB)




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. 

FILENAME: dittrichBanzhaf.ps.gz (126 kB) or dittrichBanzhaf.pdf (369 kB)




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. 

FILENAME: gwal97.ps.gz (73 kB)




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. 

FILENAME: physica_d2.ps.gz (609 kB) or physica_d2.pdf (597 kB)




TITLE: Towards a metabolic robot control system

AUTHORS: Jens Ziegler, Peter Dittrich and Wolfgang Banzhaf

SOURCE: Proceedings International Workshop on Information Processing in Cells and Tissues (IPCAT'97) Sheffield, UK, September 1-4, 1997, Plenum Press, New York, 1998, 305 - 317 

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. 

FILENAME: ipcat_final.ps.gz (105 kB) or ipcat_final.pdf (210 kB)




TITLE: A Topological Structure Based on Hashing - Emergence of a ''Spatial'' Organisation

AUTHORS: Peter Dittrich and Wolfgang Banzhaf

SOURCE: Online papers at 4th European Conference on Artificial Life (ECAL97), Brighton, UK

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. 

FILENAME: ECAL97_final.ps.gz (91 kB)




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. 

FILENAME: nano.ps.gz (68 kB)




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. 

FILENAME: alife94.ps.gz (91 kB)




TITLE: Evolution and Biocomputation --- Computational Models of Evolution

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. 

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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. 

FILENAME: CompSys94.ps.gz (48 kB)




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. 

FILENAME: ci94.ps.gz (137 kB)




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. 

FILENAME: comp_appl93.ps.gz (85 kB)




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. 

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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. 

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Wolfgang Banzhaf
Last updated: Jan 25, 2017