Non-Euclidean geometries and algorithms of living bodies

  • Authors:

  • S. V. Petukhov

  • Affiliations:

  • Department of Biomechanics, Mechanical Engineering Research Institute, U.S.S.R. Academy of Sciences, Griboedov Str. 4, Moscow 101830, U.S.S.R.

  • Venue:
  • Computers & Mathematics with Applications
  • Year:
  • 1989

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Abstract

The importance is shown of non-Euclidean geometrical symmetric transformations and iterative algorithms for the structuring of supramolecular biological bodies. The variety of kinematics of biological movements is related with the ''cyclomeric polymorphicity'', or restructuring of the iterative algorithm in the biological structure. The author believes that the morphogenetic significance of iterative algorithms in biology is attributable to the mechanisms of interaction in biological layers of tissues and replication of supramolecular structures. The geometrical fundamentals of classical biomorphology need expansion and a generalized biomorphology has to be developed by replacing the conventional similarity symmetries by broader ranges of higher-order transformations (notably Mo@?bius and projective). The progress of theoretical biology is today contingent on more extensive use of group-theoretic methods incorporating higher-order symmetries.