NDLI: The self-similar numbers as a special case of cyclic numbers and their relation to the cyclic (genetic) codes

Content Provider	IEEE Xplore Digital Library
Author	Mišić, N.Z.
Copyright Year	2010
Description	Author affiliation: Lola Institute, Belgrade, Serbia (Mišić, N.Z.)
Abstract	The genetic code is analyzed as one of the major natural codes, which as such can reveal the deeper principles of optimal coding. The analysis is based on a discovery that the symmetrical architecture of genetic code and the nucleon number of its constituents — the free canonical amino acids and bases, are strictly determined by the prime number with a cycling digit property −037. A detailed derivation for all types of analogues of 037 is given and shown that they represent a special case of cyclic numbers whose digits and multipliers are equidistant. The derived generic formula for analogues of 037 is correlated with cyclotomic and generalized Golden Mean polynomials, by which is shown their relation with discrete self-similarity, why author named them the Self-similar Numbers. Also it is given their relationship with the cyclic codes, which is with fact that the genetic code is arranged in multiple ways at different levels as a cyclic code, generally indicate that the hierarchically nested cyclicality is one of the principles of fractal organization of the genetic code, as well as the other organic codes in the living organisms.
Starting Page	97
Ending Page	102
File Size	762447
Page Count	6
File Format	PDF
ISBN	9781424488216
e-ISBN	9781424488209
DOI	10.1109/NEUREL.2010.5644099
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2010-09-23
Publisher Place	Serbia
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Genetics Amino acids Polynomials Artificial neural networks Encoding Proteins Error correction codes Cyclic and Nested Codes Self-Similarity Genetic Code Cyclic Numbers Golden Mean
Content Type	Text
Resource Type	Article

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