Article
Version 1
Preserved in Portico This version is not peer-reviewed
An Investigation on Fractal Characteristics of the Superposition of Fractal Surfaces
Version 1
: Received: 4 October 2023 / Approved: 5 October 2023 / Online: 12 October 2023 (09:57:26 CEST)
A peer-reviewed article of this Preprint also exists.
Wang, X. An Investigation on Fractal Characteristics of the Superposition of Fractal Surfaces. Fractal Fract. 2023, 7, 802. Wang, X. An Investigation on Fractal Characteristics of the Superposition of Fractal Surfaces. Fractal Fract. 2023, 7, 802.
Abstract
In this paper, we make research on fractal characteristics of the superposition of fractal surfaces in the view of fractal dimension. We give the upper bound of the lower and upper Box dimension 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 proved that the superposition of two continuous surfaces cannot keep the fractal dimensions invariable unless both of them are two-dimensional. A concrete example of 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.
Keywords
bivariate continuous functions; fractal dimension; the Box dimension; superposition of 9 fractal surfaces
Subject
Computer Science and Mathematics, Geometry and Topology
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Comments (0)
We encourage comments and feedback from a broad range of readers. See criteria for comments and our Diversity statement.
Leave a public commentSend a private comment to the author(s)
* All users must log in before leaving a comment
