W. Banzhaf. Self-replicating sequences of binary numbers. Computers Math. Applic. 26, 1 - 8 (1993).  Home/Search   Document Details and Download   Summary   Related Articles   Check

....Applied Optics, 674, 948] Archiv fur Elektrotechnik, 384] Artificial Intelligence, 228, 782, 1036] Artificial Intelligence in Engineering (UK) 84] Atmospheric Environment Part A General Topics, 162] Aust. Comput. J. Australia) 124] Automotive Engineer, 668] Biological Cybernetics, [74, 92, 93, 249, 529] BioSystems, 303, 304] Bull. Sci. Assoc. Ing. Electr. Inst. Electrotech. Montefiore, 135] Bull. Seismol. Soc. Am. 900] Bulletin of Faculty of Engineering, Tokushima University (Japan) 928] BYTE, 625] Chemical Physics Letters, 1076] Chemometrics and Intelligent Laboratory Systems, ....

....Thomas, 75, 76, 4, 214, 918, 919] Badii, A. 77] Bagchi, Sugato, 78] Baiardi, F. 724] Baker, Ellie, 236] Baker, James Edward, 79, 80] Bala, Jerzy W. 81, 82] Balio, R. Del, 211, 212] Ball, N. R. 83, 84] Baluja, Shumeet, 85, 86] Banks, S. P. 433, 434] Banzhaf, Wolfgang, [87, 88, 89, 90, 91, 92, 93] Barrios, Victor, 94, 95] Barry, A. M. 96] Baskaran, Subbiah, 97] Bassanini, A. 682] Bassett, Steve, 98] Battle, David L. 1036] Baxter, J. 99] Bean, James C. 100] Beard, Nick, 101, 777] Beasley, David, 102, 103, 104, 105, 106] Beaty, Steven J. 107] Beauchamp, James, ....

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Wolfgang Banzhaf. Self-replicating sequences of binary numbers. Foundations II: Strings of length N = 4. Biological Cybernetics, 69(?):275--281, 1993. ga:Banzhaf93e.

....Applied Optics, 674, 948] Archiv fur Elektrotechnik, 384] Artificial Intelligence, 228, 782, 1036] Artificial Intelligence in Engineering (UK) 84] Atmospheric Environment Part A General Topics, 162] Aust. Comput. J. Australia) 124] Automotive Engineer, 668] Biological Cybernetics, [74, 92, 93, 249, 529] BioSystems, 303, 304] Bull. Sci. Assoc. Ing. Electr. Inst. Electrotech. Montefiore, 135] Bull. Seismol. Soc. Am. 900] Bulletin of Faculty of Engineering, Tokushima University (Japan) 928] BYTE, 625] Chemical Physics Letters, 1076] Chemometrics and Intelligent Laboratory Systems, ....

....Thomas, 75, 76, 4, 214, 918, 919] Badii, A. 77] Bagchi, Sugato, 78] Baiardi, F. 724] Baker, Ellie, 236] Baker, James Edward, 79, 80] Bala, Jerzy W. 81, 82] Balio, R. Del, 211, 212] Ball, N. R. 83, 84] Baluja, Shumeet, 85, 86] Banks, S. P. 433, 434] Banzhaf, Wolfgang, [87, 88, 89, 90, 91, 92, 93] Barrios, Victor, 94, 95] Barry, A. M. 96] Baskaran, Subbiah, 97] Bassanini, A. 682] Bassett, Steve, 98] Battle, David L. 1036] Baxter, J. 99] Bean, James C. 100] Beard, Nick, 101, 777] Beasley, David, 102, 103, 104, 105, 106] Beaty, Steven J. 107] Beauchamp, James, ....

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Wolfgang Banzhaf. Self-replicating sequences of binary numbers. Foundations I: General. Biological Cybernetics, 69(4):269--274, 1993. ga:Banzhaf93d.

.... Chung Kuo Chi Hsueh Kung Ch eng Hsueh Pao, 1018] Clinical Chemistry, 456] Complex Systems, 381, 673, 736, 925] Computer Aided Design, 353] Computer Music Journal, 478] Computers and Geotechnics, 938] Computers Industrial Engineering, 197] Computers Mathematics with Applications, [60, 91, 260, 517] Computers Operations Research, 624, 945] Cryptologia, 689, 954, 956] Current Opinion in Structural Biology, 876] Cybernetics and Systems, 298, 599] Denshi Gijutsu Sogo Kenkyusho Iho, 464] Discrete Applied Mathematics, 41] Doboku Gakkai Rombun Hokokushu, 721, 967] Dr. Dobb s ....

....Thomas, 75, 76, 4, 214, 918, 919] Badii, A. 77] Bagchi, Sugato, 78] Baiardi, F. 724] Baker, Ellie, 236] Baker, James Edward, 79, 80] Bala, Jerzy W. 81, 82] Balio, R. Del, 211, 212] Ball, N. R. 83, 84] Baluja, Shumeet, 85, 86] Banks, S. P. 433, 434] Banzhaf, Wolfgang, [87, 88, 89, 90, 91, 92, 93] Barrios, Victor, 94, 95] Barry, A. M. 96] Baskaran, Subbiah, 97] Bassanini, A. 682] Bassett, Steve, 98] Battle, David L. 1036] Baxter, J. 99] Bean, James C. 100] Beard, Nick, 101, 777] Beasley, David, 102, 103, 104, 105, 106] Beaty, Steven J. 107] Beauchamp, James, ....

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Wolfgang Banzhaf. Self-replicating sequences of binary numbers. Computers & Mathematics with Applications, 26(7):1--8, 1993. ga:Banzhaf93c.

.... references ( 37] 115] Articles in physics journals 80 references ( 116] 195] Biochemistry 17 references ( 196] 212] Chemistry 234 references ( 213] 446] Electromagnetics 103 references ( 447] 549] Geophysics 25 references ( 550] 574] Nucleic acids 67 references ( 575] [641]) Optics 57 references ( 642] 698] Pharmacology 4 references ( 699] 702] Physics 206 references ( 703] 908] Proteins 202 references ( 909] 1110] Spectroscopy 26 references ( 1111] 1136] Structural chemistry 50 references ( 1137] 1186] Observe that each reference is ....

....Molecules and Clusters, 411] Aust. Comput. J. 315] Autom. tech. Prax. Germany) 208] Av. Ing. Quim. 305] Biochemistry, 115, 328, 388] Biochimica et Biophysica Acta Protein Structure and Molecular Enzymology, 333, 1031] Bioinformatics, 700, 240, 702] Biological Cybernetics, [820, 640, 641, 212] Biophysical Chemistry, 632, 1155] Biophysical Journal, 944, 955, 188, 1036] Biophysics Journal, 187, 969] Biopolymers, 1017, 1088] Biospectroscopy, 317] Biosystems, 662] BioSystems, 1064, 1065] Biotechnology and Bioengineering, 352] Bull. Seismol. Soc. Am. 574] Bulletin of the ....

[Article contains additional citation context not shown here]

Wolfgang Banzhaf. Self-replicating sequences of binary numbers. Foundations II: Strings of length N = 4. Biological Cybernetics, 69(?):275-281, 1993. ga:Banzhaf93e.

....Molecules and Clusters, 411] Aust. Comput. J. 315] Autom. tech. Prax. Germany) 208] Av. Ing. Quim. 305] Biochemistry, 115, 328, 388] Biochimica et Biophysica Acta Protein Structure and Molecular Enzymology, 333, 1031] Bioinformatics, 700, 240, 702] Biological Cybernetics, [820, 640, 641, 212] Biophysical Chemistry, 632, 1155] Biophysical Journal, 944, 955, 188, 1036] Biophysics Journal, 187, 969] Biopolymers, 1017, 1088] Biospectroscopy, 317] Biosystems, 662] BioSystems, 1064, 1065] Biotechnology and Bioengineering, 352] Bull. Seismol. Soc. Am. 574] Bulletin of the ....

....Babenko, Vladimir, 700] Bach, Eric, 610] B ack, Thomas, 657, 765] Backofen, R. 595] Backofen, Rolf, 595] Baleja, James D. 115, 328] Balogh, S. 309] Banerjee, S. 682] Bangalore, Arjun S. 1113] Bangalore, Shanthamallikarjuna Shivappa, 1118] Bansal, A. 596] Banzhaf, Wolfgang, [887, 888, 640, 641] B ar, R. 97] Barrett, J. J. 860] Barron, M. 305] Bartal, Y. 755, 759] Bartels, Christian, 288, 1121] Barton, G. W. 221] Barton, Geo rey W. 284] Bartton, G. W. 78] Baskeshki, K. 466] Bass, Michael B. 982] Bastos, R. C. 310] Batenburg, F. H. van, 631, 633, 639, 444] ....

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Wolfgang Banzhaf. Self-replicating sequences of binary numbers. Foundations I: General. Biological Cybernetics, 69(4):269-274, 1993. ga:Banzhaf93d.

....(2) can be integrated numerically. Figure 5 shows an overlay of the same situation for the dynamics of a discrete simulation and a direct numerical integration. It turns out that there is good coincidence between the two methods. This had been observed in other models of similar type in the past [6]. 4 Consequences We have seen that in our model world the degree of cooperation or mutualism influences the speed of the decision dynamics. It might not be far fetched to suspect that similar mechanisms are at work in the natural world. There, we observe an increasing degree of cooperativity ....

W. Banzhaf. Self-replicating sequences of binary numbers. Computers Math. Applic. 26, 1 - 8 (1993).

....the molecuels do not react. 8 Figure 2: Lattice of organizations of the 4 bit matrix multiplication chemistry shown in Tab. 1. 3. 3 Variable Length Matrix Multiplication Chemistry The matrix multiplication chemistry can be generalized to operate on binary strings of arbitrary length as shown by Banzhaf (1994) and Dittrich (2000). Here we take from one of these chemistries a small finite organization that emerged in one run using the MV1 reaction. Molecules: Binary strings of arbitrary length S = f0; 1g . Reaction: The reaction product s 3 is created in a similar way as described for the 4 bit matrixmultiplication ....

Banzhaf, W. (1993a). Self-replicating sequences of binary numbers. Comput. Math. Appl. 26, 1--8.

....cytosceleton or the human made traffic transportation system. 4 The Binary String System This section describes the system where we have applied hashing. The system is inspired by (bio )chemical reaction systems like the RNA world, where molecules collide and interact to produce new molecules [3]. It can be called an artificial chemistry, because the interaction rules are defined by abstract algorithms. Through this abstraction one tries to extract the logic of information processing rather than simulating physical details [5] The system consists of the following three components: 1) A ....

W. Banzhaf. Self-replicating sequences of binary numbers. Computers and Mathematics (26), 1--8. 1993

....that are more adapted than others (provided there are differences at all among entities) an evident idea is to artificially select for those entities that are useful from an outside perspective. We implement this idea in the context of a recently proposed a simple model of selfreplicating strings [6]. These strings form an ensemble called the string soup, in which they can encounter each other and react according to predefined reaction pathways to produce other strings. Details may be found in [7, 8] The system is self organizing in that every string comes in two alternative forms, its ....

W. Banzhaf, Self-replicating sequences of binary numbers, Computers and Mathematics, 26 (1993) 1

....of bits and their interchangeability between data and programs. It is not far fetched to expect that the physical identity between operators (programs) and operands (data) may also play an essential role in self organisation. We have proposed to consider a simple self organising system [1], in which sequences of binary numbers are able to react with each other and sometimes even to replicate themselves. This ability of binary strings was a result of the proposition to consider binary strings similar to sequences of nucleotides in RNA. RNA sequences which presumably stood at the ....

....and operative form of strings. Technically, we considered as this alternative a two dimensional matrix form that is able to perform operations on other one dimensional binary strings. Reactions between binary strings The fundamental ideas of this model have been outlined elsewhere (see ref. [1], 4] 7] for details) Here we only give a brief overview of what has been learned so far. Let us consider sequences s = s 1 ; s 2 ; s i ; s N ) 1) of binary symbols s i 2 f0; 1g; i = 1; N organised in 1 dimensional strings. Then we ask the question: Does there exist an ....

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W. Banzhaf, Self-replicating sequences of binary numbers, Computers and Mathematics, 26 (1993) 1

....the build up of complexity in a simplified system which was derived using metaphors of the RNA paradigm. It is based on the fact that the major information processing machines of today, digital computers, use sequences of binary numbers to represent and manipulate information. In previous work [5, 6] we have proposed to introduce a mapping of these one dimensional sequences of binary numbers into two dimensional forms naturally able to interact with one dimensional forms. A restricted class of sequences, namely those whose length was a square number, could be assigned corresponding 2D ....

....a somewhat special situation occurs in approach (a) since the 1 dimensional form of a string and the 2 dimensional form look alike, except for a possible transposition. In Table 2 we list all strings of length N = 2 and N = 3. Note that the system N = 1 is trivial and N = 4 was treated elsewhere [5, 6]. 3 Interaction of strings of different length The basis for the interaction of strings was a new interpretation of mathematical operations. We consider the outcome of an interaction in the form of a new string generated by a cooperation of two strings as being added to the existing population of ....

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W. Banzhaf. Self-replicating sequences of binary numbers. Computers and Mathematics, 26:1 -- 8, 1993.

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W. Banzhaf. Self-replicating sequences of binary numbers. foundations ii: Strings of length n=4. Biological Cybernetics, 69:275--281, 1993.

....as we observe it in this system. Section 6, finally contrasts present results with results in other Alife systems and draws some conclusions. 2 The binary string system without topology (the well stirred case) The original system was introduced in [9] and subsequently discussed in more detail in [15 18]. We shall discuss it here in a variant suitable for the following sections. Binary strings of length N as used here are defined as follows: s = s 1 ; s 2 ; s N ) s i 2 IB = f0; 1g; 1 i N; N 2 fn 2 j n 2 IINIg: The number of different sorts of binary strings in a population is jIB ....

....helps to avoid artifacts due to string types going extinct simply by accident. Indeed, the average number of strings of any given sort is 667, greatly reducing the probability of spurious effects. Two folding algorithms F are considered: topological folding and non topological folding. Following [15], a folding is called topological if neighboring string elements in the string sequence remain neighbors after the folding. If this condition is not met, we call the folding non topological. Here we use: F t : s 1 ; s 2 ; s 3 ; s 4 ) 7 0 B s 1 s 2 s 4 s 3 1 C A F nt : s 1 ; s 2 ; s 3 ; ....

W. Banzhaf. Self-replicating sequences of binary numbers. foundations i: General. Biological Cybernetics, 69:269--274, 1993.

....GERMANY Preprint submitted to Elsevier Preprint 3 November are necessarily leading to complex phenomena like Life without, however, being forced to copy nature to a large extent or in great detail. A simpler variant of the binary string system we consider here has been proposed earlier [9] to serve as a study ground for phenomena of selforganization. It was inspired by pre biotic evolution and the so called RNA world [10,11] RNA is a macromolecule that does not only serve as a storage device for biological information (like DNA, if only less stable) but that also shows some ....

....intended to discuss the phenomenon of metabolism, as we observe it in this system. Section 6, finally contrasts present results with results in other Alife systems and draws some conclusions. 2 The binary string system without topology (the well stirred case) The original system was introduced in [9] and subsequently discussed in more detail in [15 18] We shall discuss it here in a variant suitable for the following sections. Binary strings of length N as used here are defined as follows: s = s 1 ; s 2 ; s N ) s i 2 IB = f0; 1g; 1 i N; N 2 fn 2 j n 2 IINIg: The number of ....

W. Banzhaf. Self-replicating sequences of binary numbers. Computers and Mathematics with Applications, 26(7):1--8, 1993.

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