Study of Variants of Cantor Sets Using Iterated Function System

The classical Cantor set discovered and introduced by the famous mathematicians Henery Smith and George Cantor has many interesting properties in the field of set theory, Topology and fractal geometry. One of the way in which the behavior of Cantor sets can be specified is through the use of Iterated Function System. In (2008), Gerald Edgar in his book gave a systematic study of classical Cantor ternary set in iterated function system and introduced some beautiful properties. Our goal in this paper is to present two new examples of Cantor variants using iterated function system.