Biological Cybernetics

, Volume 69, Issue 4, pp 269–274 | Cite as

Self-replicating sequences of binary numbers. Foundations I: General

  • Wolfgang Banzhaf


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. Analogous to RNA systems, a folding of sequences is introduced to generate alternative two-dimensional forms of the binary sequences. The two-dimensional forms of strings can naturally interact with one-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.


Reaction System Selection Pressure General Framework Binary Sequence Reaction Channel 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. Banzhaf W (1990a) The “molecular” travelling salesman. Biol Cybern 64:7–14Google Scholar
  2. Banzhaf W (1990b) Finding the global minimum of a low-dimensional spin-glass model. In: Voigt HM, Mühlenbein H, Schwefel HP (eds) Selected papers on evolution theory, combinatorial optimization and related topics Academie, BerlinGoogle Scholar
  3. Banzhaf W (1993a) Self-replicating sequences of binary numbers. Foundations II: Strings of length N = 4. Biol Cybern 69:275–281Google Scholar
  4. Banzhaf W (1993b) Self-replicating sequences of binary numbers. Foundations III: Larger systems. Biol Cybern (submitted)Google Scholar
  5. Bryngelson J, Wolynes P (1987) Spin glasses and the statistical mechanics of protein folding. Proc Natl Acad Sci USA 84:7524–7528Google Scholar
  6. Chaitin GJ (1987) Algorithmic information theory. Cambridge University Press, Cambridge, UKGoogle Scholar
  7. Dewdney AK (1985) Computer recreations. Sci Am 257(3): 21–32Google Scholar
  8. Eigen M (1971) Self-organisation of matter and the evolution of biological molecules. Naturwissenschaften 58:465–523Google Scholar
  9. Fontana W (1991) Algorithmic chemistry. In: Langton CG, Taylor C, Farmer JD, Rasmussen S (eds) Artificial life 2. Addison-Wesley, Redwood City, CalifGoogle Scholar
  10. Fontana W, Schuster P (1987) A computer model of evolutionary optimization. Biophys Chem 26:123–147Google Scholar
  11. Fontana W, Schnabl W, Schuster P (1989) Physical aspects of evolutionary optimization and adaptation. Phys Rev A40:3301–3321Google Scholar
  12. Goldberg D (1989) Genetic algorithms in search, optimization and machine learning. Addison-Wesley, Reading, MassGoogle Scholar
  13. 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 35:849–857Google Scholar
  14. Haken H (1983) Synergetics. An Introduction. Springer, BerlinGoogle Scholar
  15. Holland JH (1975) Adaption in natural and artificial systems. University of Michigan Press, Ann ArborGoogle Scholar
  16. Kauffman S (1986) Autocatalytic sets of proteins. J Theor Biol 119:1–24Google Scholar
  17. 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 31:147–157Google Scholar
  18. Lau KF, Dill KA (1989) A lattice statistical mechanics model of the conformational and sequence spaces of proteins. Macromolecules 22:3986–3997Google Scholar
  19. Lewin B (1987) Genes, 3rd edn. Wiley, New YorkGoogle Scholar
  20. Li Z, Scheraga H (1987) Monte Carlo-minimization approach to the multiple-minima problem in protein folding. Proc Natl Acad Sci USA 84:6611–6615Google Scholar
  21. Quian N, Sejnowski T (1988) Predicting the secondary structure of globular proteins using neural network models. J Mol Biol 202:865–884Google Scholar
  22. Rechenberg I (1973) Evolutionsstrategien. Frommann-Holzboog, StuttgartGoogle Scholar
  23. Robson B, Garnier J (1986) Introduction to proteins and protein engineering. Elsevier, AmsterdamGoogle Scholar
  24. Schwefel HP (1981) Numerical optimization of computer models. Wiley, ChichesterGoogle Scholar
  25. Wang Q (1987) Optimization by simulating molecular evolution. Biol Cybern 57:95–101Google Scholar

Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • Wolfgang Banzhaf
    • 1
  1. 1.Central Research Laboratory, Mitsubishi Electric CorporationAmagasakiJapan

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