VISIBILITY OF NON-SELF-SIMILAR SETS

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].