Investigation on the invariance of fractal characteristics preserved under horizontal linear stretching

Abstract

In this paper, we mainly make research on whether fractal characteristics of an object with a fractal curve shape will keep invariable under being subjected to horizontal linear stretching. For two continuous functions [Formula: see text] and [Formula: see text], it has been proven that the graph of [Formula: see text] has the same fractal dimensions with the graph of [Formula: see text] when [Formula: see text] is a linear function. Some examples have also been provided to corroborate our theoretical results. This work may contribute to the dimensional theory of fractal curves and have practical application significance in physics.