On the dimensional connection between a class of real number sequences and local fractal functions with a single unbounded variation point

In this paper, we investigate the connection between a class of real number sequences and local fractal functions in terms of fractal dimensions. Under certain conditions, we show that the Box dimension of the graph of a local fractal function with a single unbounded variation point is equal to that of its zero points set plus one. Several concrete examples of such functions whose Box dimension can take any numbers belonging to [1,2] have also been given. This work may provide new approaches to the construction of various local fractal functions with the required Box dimension in the future. •The dimensional connection between local fractal functions and their zero points sets has been studied.•The calculation of the Box dimension of a class of real number sequences has been given.•The Box dimension of graphs of local fractal functions has been investigated.•Several concrete examples of local fractal functions have been constructed.