An Investigation on Fractal Characteristics of the Superposition of Fractal Surfaces
Xuefei Wang
Abstract: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… Show more
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