FRACTAL SETS AND THEIR RELATION WITH WAVELET SETS

A. Askari Hemmat (Iran) and M. J. Kheirdeh (Iran)

Received February 11, 2008

Abstract

Sets with non-integral Hausdorff dimension are called fractals by Mandelbrot, when they have the additional property of being in some sense either strictly or statistically self similar, have been used to model various physical phenomena. In this article, we briefly review the theory of wavelet sets and fractals. In case of dimension 2, we prove that under certain conditions the product of two sets is a wavelet set. This presents certain new examples. We further explain fractal sets and give one example to show how some fractal sets are related to wavelet sets.

Keywords and phrases: fractals, multiresolution analysis, wavelets, wavelet sets, digits.