Fibonacci Sequences, Symmetry and Ordering in Biological Patterns, Their Sources, Information Origin and the Landauer Principle

Abstract

Physical roots, exemplifications and consequences of periodic and aperiodic ordering (represented by Fibonacci series) in biological systems are discussed. The role and physical and biological roots of symmetry and asymmetry appearing in biological patterns is addressed. Generalization of the Curie-Neumann Principle as applied to biological objects is presented, briefly summarized as: “asymmetry is what creates a biological phenomenon”. The “up-bottom approach” and “bottom up” approaches to the explanation of symmetry in organisms are presented in detail. The “up-bottom approach”, implies that the symmetry of the biological structure follows the symmetry of media in which this structure is functioning; the “bottom-up” approach, in turn, adopt that the symmetry of biological structures emerges from the symmetry of molecules constituting the structure. A diversity of mathematical measures applicable for quantification of ordering in biological patterns is introduced. The continuous, Shannon and Voronoi measures of symmetry/ordering and their application to biology objects are addressed. The fine structure of the notion of “ordering” is discussed. Informational/algorithmic roots of ordering inherent for the biological systems are considered. Ordered/symmetrical patterns provide economy of biological information, necessary for algorithmic description of a biological entity. Application of the Landauer principle bridging physics and theory of information to the biological systems is discussed.

Optima and Simplicity in Nature

“…We argued that these types of optimisations are common in nature, due to the fact that many objective functions derive from generic physics and engineering-based constraints, and these constraints can be described by simple O(1) equations and laws. Our result is perhaps a generalisation of the finding of Cohn and Kumar [31] that symmetrical configurations can often be built using very simple potential functions, and perhaps also the statement of Bormashenko [32] that the symmetry of biological structures follow the symmetry of media in which the structure is functioning. In ref.…”

Fitness, Optima, and Simplicity

“…See refs. [51][52][53][54] for more discussions on when morphological (a)symmetry affords selective advantages.…”