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IJSTR >> Volume 2- Issue 7, July 2013 Edition



International Journal of Scientific & Technology Research  
International Journal of Scientific & Technology Research

Website: http://www.ijstr.org

ISSN 2277-8616



An Exploration Of The Generalized Cantor Set

[Full Text]

 

AUTHOR(S)

Md. Shariful Islam Khan, Md. Shahidul Islam

 

KEYWORDS

Keywords: Cantor set, Dimension, Fractal, Generalization, Self-similar.

 

ABSTRACT

Abstract: In this paper, we study the prototype of fractal of the classical Cantor middle-third set which consists of points along a line segment, and possesses a number of fascinating properties. We discuss the construction and the self-similarity of the Cantor set. We also generalized the construction of this set and find its fractal dimension.

 

REFERENCES

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R. B. Sher, Concerning wild Cantor sets in R^3, Proc. Amer. Math. Soc. 19, 11951200, 1968.

D. G. Wright, Cantor sets in 3-manifolds, Rocky Mountain J. Math. 9, 377383, 1979.

K. Falconer, The Geometry of Fractal Sets, Cambridge University Press, Cambridge, 1985.

S. H. Strogatz, Nonlinear Dynamics and Chaos, West view, Cambridge, MA, 1994.

Robert L. Devaney, A First Course in Chaotic Dynamical Systems, Boston University.