TY - JOUR

T1 - Elliptic curves and Fibonacci numbers arising from Lindenmayer system with symbolic computation

AU - Yoshida, Hiroshi

AU - Miwa, Yoshihiro

AU - Kaneko, Masanobu

PY - 2011/3

Y1 - 2011/3

N2 - 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.

AB - 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.

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U2 - 10.1007/s00200-011-0143-7

DO - 10.1007/s00200-011-0143-7

M3 - Article

AN - SCOPUS:79955864507

VL - 22

SP - 147

EP - 164

JO - Applicable Algebra in Engineering, Communications and Computing

JF - Applicable Algebra in Engineering, Communications and Computing

SN - 0938-1279

IS - 2

ER -