Mathematics and Statistics Vol. 6(3), pp. 25 - 33
DOI: 10.13189/ms.2018.060301
Reprint (PDF) (397Kb)


Hausdorff Measures and Hausdorff Dimensions of the Invariant Sets for Iterated Function Systems of Geometric Fractals


Md. Jahurul Islam 1,*, Md. Shahidul Islam 1, Md. Shafiqul Islam 2
1 Department of Mathematics, University of Dhaka, Bangladesh
2 School of Mathematics and Computational Science, University of Prince Edward Island, Canada

ABSTRACT

In this paper, we discuss Hausdorff measure and Hausdorff dimension. We also discuss iterated function systems (IFS) of the generalized Cantor sets and higher dimensional fractals such as the square fractal, the Menger sponge and the Sierpinski tetrahedron and show the Hausdorff measures and Hausdorff dimensions of the invariant sets for IFS of these fractals.

KEYWORDS
Hausdorff Measure, Hausdorff Dimension, Invariant Set, Iterated Function System

Cite this paper
Md. Jahurul Islam , Md. Shahidul Islam , Md. Shafiqul Islam (2018). Hausdorff Measures and Hausdorff Dimensions of the Invariant Sets for Iterated Function Systems of Geometric Fractals. Mathematics and Statistics, 6 , 25 - 33. doi: 10.13189/ms.2018.060301.