Graphs of continuous functions and fractal dimensions

Verma, Manuj; Priyadarshi, Amit

doi:10.1016/j.chaos.2023.113513

Cited by 19 publications

(1 citation statement)

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“…This problem can be traced back to the research made first by Falconer [33], who showed that the box dimension of the sum of two continuous functions equals the greater of the box dimensions of them. On this basis, a group of academic workers has pushed this study forward and obtained a series of preliminary conclusions, whose related progress can be found in [34][35][36][37][38][39][40]. So in this paper, we shall focus on the fractal dimension of the superposition of two fractal surfaces and investigate whether it has the same result as that of fractal curves.…”

Section: Introductionmentioning

confidence: 99%

An Investigation on Fractal Characteristics of the Superposition of Fractal Surfaces

Wang

2023

Fractal Fract

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In this paper, we conduct research on the fractal characteristics of the superposition of fractal surfaces from the view of fractal dimension. We give the upper bound of the lower and upper box dimensions of the graph of the sum of two bivariate continuous functions and calculate the exact values of them under some particular conditions. Further, it has been proven that the superposition of two continuous surfaces cannot keep the fractal dimensions invariable unless both of them are two-dimensional. A concrete example of a numerical experiment has been provided to verify our theoretical results. This study can be applied to the fractal analysis of metal fracture surfaces or computer image surfaces.

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