Abstract
In this paper we construct three primitive mappings based on three kinds of genetic attribute equivalences. We then apply the mappings and basic addition operation to the universal genetic code to generate three square matrices. We show that these square matrices are stochastic in nature. They demonstrate some fractal similarity properties and resemble the similar properties to the original stochastic matrices.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bapat, R. B. and T. E. S. Raghavan (1997). Nonnegative Matrices and Applications, Cambridge University Press.
He, M. (2003). Symmetry in structure of genetic code, in Proceedings of the Third All-Russian Interdisciplinary Scientific Conference, “Ethics and the Science of Future. Unity in Diversity”, February 12–14, Moscow.
Petoukhov, S. V. (2001). The Bi-periodic Table of Genetic Code and Number of Protons, Foreword of K. V. Frolov, Moscow, p. 258 (in Russian).
Petoukhov, S. V. (2002). Binary sub-alphabets of genetic language and problem of unification bases of biological languages, in IX International Conference “Mathematics, Computer, Education”, Russia, Dubna, January 28–31, p. 191 (in Russian).
Romanovsky, V. (1931). Sur les zeros des matrices stocastiques. C. R. Acad. Sci. Paris 192, 266–269.
Wittmann, H. G. (1961). Ansatze zur Entschlusselung des Genetishen Codes. Die Naturwissenschaften B.48 24, S. 55.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
He, M. Genetic code, attributive mappings and stochastic matrices. Bull. Math. Biol. 66, 965–973 (2004). https://doi.org/10.1016/j.bulm.2003.10.002
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1016/j.bulm.2003.10.002