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 two-dimensional forms of the binary sequences. The interaction of two-dimensional and one-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. Nonlinear rate equations are proposed which provide a model for this simplest system.
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Banzhaf W (1993a) Self-replicating sequences of binary numbers. Foundations I: General. Biol Cybern 69:269–274
Banzhaf W (1993b) Self-replicating sequences of binary numbers. III. Larger systems
Banzhaf W (1993c) Self-replicating sequences of binary numbers. Comp Math (in press)
Banzhaf W (1993d) Self-replicating binary strings: the buildup of complexity. Complex Syst (submitted)
Cech TR, Bass BL (1986) Biological catalysis by RNA. Annu Rev Biochem 55:599–629
Eigen M, Schuster P (1977) The hypercycle: a principle of natural self-organization, part A. Naturwissenschaften 64:541–565
Eigen M, Schuster P (1978a) The hypercycle: a principle of natural self-organization, part B. Naturwissenschaften 65:7–41
Eigen M, Schuster P (1978b) The hypercycle: a principle of natural self-organization, part C. Naturwissenschaften 65:341–369
Fraunfelder H (1988) Biomolecules. In: Pines D (ed) Emerging synthesis in science. (SFI studies in the sciences of complexity, vol 1). Addison-Wesley, Reading, Mass
Gillespie DT, Mangel M (1981) Conditioned averages in chemical kinetics. J Chem Phys 75:704–709
Guerrier-Takada C, Gardiner K, Marsh T, Pace N, Altman S (1983) The RNA moiety of ribonuclease P is the catalytic subunit of the enzyme. Cell 35:849–857
Haken H (1983) Synergetics. An Introduction. Springer, Berlin
Kauffman S (1986) Autocatalytic sets of proteins. J Theor Biol 119:1–24
Kruger K, Grabowski PJ, Zaug AJ, Sands J, Gottschling DE, Cech TR (1982) Self-splicing RNA: autoexcision and autocyclization of the ribosomal RNA intervening sequence of Tetrahymena. Cell 31:147–157
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Dedicated to Professor Hermann Haken on the occasion of his 65th Birthday
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Banzhaf, W. Self-replicating sequences of binary numbers. Foundations II: Strings of length N=4. Biol. Cybern. 69, 275–281 (1993). https://doi.org/10.1007/BF00203124
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DOI: https://doi.org/10.1007/BF00203124