FRACTAL DIMENSION OF PRODUCT OF CONTINUOUS FUNCTIONS WITH BOX DIMENSION

This paper investigates fractal dimension of product of continuous functions with Box dimension on [0, 1]. For two continuous functions with different Box dimensions, the Box dimension of their product has been proved to be the larger one. Furthermore, the Box dimension of product of two continuous functions with the same Box dimension may not exist. Definitions of regular fractal and local fractal functions have been given. Product of a regular fractal function and a local fractal function with the same Box dimension must still be the original Box dimension.

Automated summary

This paper investigates the fractal dimension of the product of continuous functions with Box dimension on [0, 1]. It has been proven that for two continuous functions with different Box dimensions, the Box dimension of their product is the larger one. Furthermore, the Box dimension of the product of two continuous functions with the same Box dimension may not exist. Definitions of regular fractal and local fractal functions are given. It is noted that the product of a regular fractal function and a local fractal function with the same Box dimension will still have the original Box dimension.