# Dyadic Cantor set and its kinetic and stochastic counterpart

@article{Hassan2014DyadicCS,
title={Dyadic Cantor set and its kinetic and stochastic counterpart},
author={M. Kamrul Hassan and Neeaj I. Pavel and R. K. Pandit and J{\"u}rgen Kurths},
journal={Chaos Solitons \& Fractals},
year={2014},
volume={60},
pages={31-39}
}
• Published 1 January 2014
• Computer Science
• Chaos Solitons & Fractals

## Figures from this paper

Multi-multifractality and dynamic scaling in stochastic porous lattice
• Mathematics
The European Physical Journal Special Topics
• 2021
In this article, we extend the idea of stochastic dyadic Cantor set to weighted planar stochastic lattice that leads to a stochastic porous lattice. The process starts with an initiator which we
Is there always a conservation law behind the emergence of fractal and multifractal?
• M. K. Hassan
• Mathematics, Physics
The European Physical Journal Special Topics
• 2019
Abstract One of the most basic ingredients of fractal or multifractal is its scale-invariance or self-similar property albeit they appear seemingly disordered or apparently bewildering. In this
Evolution through the stochastic dyadic Cantor Set: the uniqueness of mankind in the Universe
• D. Mahecha
• Physics
International Journal of Astrobiology
• 2015
Abstract The search for intelligent life or any type of life involves processes with nonlinear chaotic behaviours throughout the Universe. Through the sensitive dependence condition, chaotic dynamics
On the Broader Sense of Life and Evolution: Its Mechanisms, Origin and Probability across the Universe
• Physics
• 2017
We consider connection between the mechanisms of evolution of life and the existence of conditions suitable for life in the universe. In particular we review the problem of calculating the number of

## References

SHOWING 1-10 OF 27 REFERENCES
Emergence of fractal behavior in condensation-driven aggregation.
• Physics
Physical review. E, Statistical, nonlinear, and soft matter physics
• 2009
It is shown that the particle size spectra exhibit transition to scaling c(x,t) approximately t;{-beta}varphi(xt{z}) accompanied by the emergence of a fractal of dimension d {f}=1/(1+2alpha) accompaniedBy using scaling theory for the case when a particle grows by an amount alphax over the time it takes to collide with another particle of any size.
Multifractality and the shattering transition in fragmentation processes.
• Hassan
• Mathematics
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
• 1996
A hierarchy of independent exponents suggest the existence of multiple phase boundary for the shattering transition when two orthogonal cracks are placed randomly on a fragments (Model A) and a unique exponent suggesting a single phase boundary when four equal sized fragments are produced at each fragmentation event is found.
Random walk with shrinking steps
• Mathematics
• 2004
We outline the properties of a symmetric random walk in one dimension in which the length of the nth step equalsl, with l,1. As the number of steps N→`, the probability that the end point is at x
FRACTAL DIMENSION AND DEGREE OF ORDER IN SEQUENTIAL DEPOSITION OF MIXTURE
It is shown that the fractal dimension of the resulting pattern increases as beta increases and reaches a constant non-zero value in the limit $\beta \to \infty$ when the pattern becomes perfectly ordered or non-random fractals.
Wave propagation through Cantor-set media: chaos, scaling, and fractal structures.
• Physics
Physical review. E, Statistical, nonlinear, and soft matter physics
• 2009
It is shown that transmission coefficients exhibit a local scaling behavior near complete transmission if the complete transmission is achieved at a wave number kappa=kappa* with a rational kappa*/pi.
Kinetics of random sequential parking on a line
We study the kinetics of irreversible random sequential parking of intervals of different sizes on an infinite line. For the simplest fixed-length parking distribution the model reduces to the known
Stationary Kolmogorov solutions of the Smoluchowski aggregation equation with a source term.
• Computer Science
Physical review. E, Statistical, nonlinear, and soft matter physics
• 2004
The method of Zakharov transformations may be used to analyze the stationary solutions of the Smoluchowski aggregation equation with a source term for arbitrary homogeneous coagulation kernel to derive a "locality criterion," expressed in terms of the asymptotic properties of the kernel, that must be satisfied in order for the Kolmogorov spectrum to be an admissible solution.
Cantor set fractals from solitons
• Sears
• Physics
Physical review letters
• 2000
This work uses numerical simulations to demonstrate the formation of Cantor set fractals by temporal optical solitons through the dynamical evolution from a single input soliton.
Power laws, Pareto distributions and Zipf's law
When the probability of measuring a particular value of some quantity varies inversely as a power of that value, the quantity is said to follow a power law, also known variously as Zipf's law or the