FRACTAL DIMENSIONS OF THE LOGARITHM OF CONTINUOUS FUNCTIONS
Affiliation:
1. School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing 210094, P. R. China
Abstract
This paper investigates the variation of fractal dimensions of continuous functions under operations. It is found that the Box dimension of the logarithm of positive continuous functions remains constant, and any nonzero real power of a positive continuous function can keep fractal dimensions variation closed. The study also discusses the fractal dimension of logarithmic function with bases of fractal functions, and the corresponding fractal dimension is determined by the function with the larger fractal dimension.
Funder
National Undergraduate Training Program for Innovation and Entrepreneurship
National Natural Science Foundation of China
Publisher
World Scientific Pub Co Pte Ltd
Subject
Applied Mathematics,Geometry and Topology,Modeling and Simulation