Generation of Cantor sets from fractal squares : A mathematical prospective

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Abstract
Fractal square is a concept evolved from mathematics, which subsequently achieved its importance in the area of computer graphics, pattern recognition, and machine vision to analyze or generate complex objects. The self-similarity and self-affine nature of fractals was introduced by Mandelbrot to create different patterns. Furthermore, the multiple reduction copy machine (MRCM) concept has been utilized for a long time in the design of fractals. Apart from this, some new programs have recently been employed in this area. However, all the existing models were limited in terms of their topological properties and not even concerned with the connected and disconnected set of fractals. Even the fractal square that is used to distinguish different distinct patterns is not being studied deeply. In this paper, we have focused on fractal square to generate cantor set by using its different topological properties in terms of disconnected fractal sets, designing the process of various patterns with the help of fractal square and to make a topological classification among them.

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