### Abstract

Original language | English |
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Pages (from-to) | 31-39 |

Number of pages | 9 |

Journal | Chaos, Solitons & Fractals |

Volume | 60 |

Early online date | 4 Feb 2014 |

DOIs | |

Publication status | Published - Mar 2014 |

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### Cite this

*Chaos, Solitons & Fractals*,

*60*, 31-39. https://doi.org/10.1016/j.chaos.2013.12.010

**Dyadic Cantor set and its kinetic and stochastic counterpart.** / Hassan, M K ; Pavel, N I ; Pandit, R K; Kurths, J.

Research output: Contribution to journal › Article

*Chaos, Solitons & Fractals*, vol. 60, pp. 31-39. https://doi.org/10.1016/j.chaos.2013.12.010

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TY - JOUR

T1 - Dyadic Cantor set and its kinetic and stochastic counterpart

AU - Hassan, M K

AU - Pavel, N I

AU - Pandit, R K

AU - Kurths, J

PY - 2014/3

Y1 - 2014/3

N2 - Firstly, we propose and investigate a dyadic Cantor set (DCS) and its kinetic counterpart where a generator divides an interval into two equal parts and removes one with probability (1-p)(1-p). The generator is then applied at each step to all the existing intervals in the case of DCS and to only one interval, picked with probability according to interval size, in the case of kinetic DCS. Secondly, we propose a stochastic DCS in which, unlike the kinetic DCS, the generator divides an interval randomly instead of equally into two parts. Finally, the models are solved analytically; an exact expression for fractal dimension in each case is presented and the relationship between fractal dimension and the corresponding conserved quantity is pointed out. Besides, we show that the interval size distribution function in both variants of DCS exhibits dynamic scaling and we verify it numerically using the idea of data-collapse.

AB - Firstly, we propose and investigate a dyadic Cantor set (DCS) and its kinetic counterpart where a generator divides an interval into two equal parts and removes one with probability (1-p)(1-p). The generator is then applied at each step to all the existing intervals in the case of DCS and to only one interval, picked with probability according to interval size, in the case of kinetic DCS. Secondly, we propose a stochastic DCS in which, unlike the kinetic DCS, the generator divides an interval randomly instead of equally into two parts. Finally, the models are solved analytically; an exact expression for fractal dimension in each case is presented and the relationship between fractal dimension and the corresponding conserved quantity is pointed out. Besides, we show that the interval size distribution function in both variants of DCS exhibits dynamic scaling and we verify it numerically using the idea of data-collapse.

U2 - 10.1016/j.chaos.2013.12.010

DO - 10.1016/j.chaos.2013.12.010

M3 - Article

VL - 60

SP - 31

EP - 39

JO - Chaos, Solitons & Fractals

JF - Chaos, Solitons & Fractals

SN - 0960-0779

ER -