Elliptic curves and Fibonacci numbers arising from Lindenmayer system with symbolic computation

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Abstract

Starting from an egg, the multicell becomes a set of cells comprising a variety of types to serve functions. This phenomenon brings us a bio-motivated Lindenmayer system. To investigate conditions for a variety of cell types, we have constructed a stochastic model over Lindenmayer systems. This model considers interactive behaviors among cells, yielding complicated polynomials. Using symbolic computation, we have derived explicit relations between cell-type diversity and cell-type ratio constraint. These relations exhibit elliptic curve- and Fibonacci number-related patterns. This is the first example of elliptic curves to appear in the Lindenmayer context. A survey of the rational points and the quadratic irrational numbers on the derived curves has revealed Fibonacci-related periodic and quasiperiodic patterns. Further we have found that in some region, there are only two elliptic curve-related periodic patterns.

Original languageEnglish
Pages (from-to)147-164
Number of pages18
JournalApplicable Algebra in Engineering, Communications and Computing
Volume22
Issue number2
DOIs
Publication statusPublished - Mar 2011

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Applied Mathematics

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