A note on fractal dimensions of graphs of certain continuous functions

This article investigates fractal dimensions variation of fractal functions under certain operations, which corroborates the conjecture raised in our previous work Yu and Liang (2024) [1]. It has been shown that when polynomial operations are applied to the independent variable of a function, the fractal dimension of the function’s graph remains unchanged. This finding holds significance for the construction of fractal functions. •The note studies how fractal dimensions change with specific operations on fractal functions.•It proves that applying polynomial operations to the independent variable does not alter the fractal dimension of the function’s graph.•This finding is significant in constructing fractal functions.