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Symmetry: Culture and Science
Volume 37, Number 3, pages 259-277 (2026)
https://doi.org/10.26830/symmetry_2026_3_259

GENETIC CODE, SCREW CALCULUS, AND INHERITANCE OF PHYLLOTAXIS LAWS

S. V. Petoukhov^1*, V. I. Svirin²

¹ Department of Biomechanical Systems, Mechanical Engineering Research Institute, Russian Academy of Sciences, Moscow, M. Kharitonievsky pereulok, 4, 101990, Russia
Email: spetoukhov@gmail.com
Web: http://petoukhov.com
ORCID: 0000-0001-7355-1813

² Department of Biomechanical Systems, Mechanical Engineering Research Institute, Russian Academy of Sciences, Moscow, M. Kharitonievsky pereulok, 4, 101990, Russia
Email: vitaly.i.svirin@gmail.com
ORCID: 0000-0001-9878-5640

^* Corresponding author

Abstract: The study of the biological laws of phyllotaxis (leaf arrangement) constitutes one of the most well-known branches of mathematical biology and has been pursued in science for over 200 years. It concerns ensembles of spiral (helical) structures associated with the Fibonacci number series, representing an important class of biological symmetries at different levels and branches of biological evolution. These phyllotaxis ensembles are inherited through generations, meaning they are somehow connected to the system of molecular genetic coding. This article is dedicated to clarifying this connection and exploring the possibilities of matrix-algebraic modeling of the inheritance phenomena of phyllotaxis ensembles. These possibilities have been identified through an analysis of the alphabetical structure of molecular genetic coding, which has revealed its coupling with the matrix apparatus of screw calculus and Fibonacci matrices. The presented data suggest possible applications of algebraic-alphabetical bioinformatics and algebraic-genetic grammar to the study of evolutionary biology, inherited biosymmetries, genetic information, and gene-like models of artificial intelligence.

Keywords: genetic code, algebraic alphabets of bioinformatics, biosymmetries, matrices, dyadic numbers, screw calculus, Fibonacci matrix, grammar

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