DOI: 10.1142/s0218348x24500038 ISSN: 0218-348X
FRACTAL DIMENSIONS OF THE LOGARITHM OF CONTINUOUS FUNCTIONS
PEIZHI LIU- Applied Mathematics
- Geometry and Topology
- Modeling and Simulation
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.