Genetic System, Fibonacci Numbers, and Phyllotaxis Laws

This chapter describes data suggesting a connection between matrix genetics and one of the most famous branches of mathematical biology: phyllotaxis laws of morphogenesis. Thousands of scientific works are devoted to this morphogenetic phenomenon, which relates with Fibonacci numbers, the golden section, and beautiful symmetrical patterns. These typical patterns are realized by nature in a huge number of biological bodies on various branches and levels of biological evolution. Some matrix methods are known for a long time to simulate in mathematical forms these phyllotaxis phenomena. This chapter describes connections of the famous Fibonacci (2x2)-matrices with genetic matrices. Some generalizations of the Fibonacci matrices for cases of (2nx2n)-matrices are proposed. Special geometrical invariants, which are connected with the golden section and Fibonacci numbers and which characterize some proportions of human and animal bodies, are described. All these data are related to matrices of the genetic code in some aspects.