An non-centered asymmetric Cantor-like Set

TL;DR

This paper explores various generalizations of the classic ternary Cantor set, introducing a non-centered asymmetric Cantor-like set to highlight the diversity and unique properties of such fractal constructions.

Contribution

It presents a novel example of a non-centered asymmetric Cantor-like set, expanding the understanding of Cantor set variants beyond the traditional symmetric construction.

Findings

Introduces a new non-centered asymmetric Cantor-like set

Highlights differences from the classical symmetric Cantor set

Provides insights into the structure and properties of generalized Cantor sets

Abstract

The ternary Cantor set $C$, constructed by George Cantor in 1883, is probably the best-known example of a perfect nowhere-dense set in the real line, but as we will see later, it is not the only one. The present article will delve into the richness and the peculiarities of $C$ through the exploration of several variants and generalizations and will provide an example of a non-centered asymmetric Cantor-like set.