Work

Visibility of Non-self-similar Sets

Year: 2025

Type: article

Abstract: The visible problem is related to the arithmetic on the fractals. The visibility of self-similar set has been studied in the past. In this work, we investigate the visibility of non-self-similar sets. We begin by analyzing the structure of [Formula: see text], where [Formula: see text]:= [Formula: see text] and [Formula: see text] is the middle [Formula: see text] Cantor set, we show that it lacks self-similarity. Due to the nonlinear phenomena exhibited by [Formula: see text], we develop a different approach to characterize the visible set. Our results also reveal that the complement of visible set may contain a closed interval within a large range of [Formula: see text].

Source: Fractals

DOI: 10.1142/s0218348x25501002

Authors: YI CAI, YANG YANG

Institution: Shanghai Institute of Technology

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Natural Science Foundation of China

Award: G5499034214