Fractal dimension for a class of complex-valued fractal interpolation functions

Abstract

There are many research papers dealing with fractal dimension of real-valued fractal functions in the recent literature. The main focus of the present paper is to study fractal dimension of complex-valued functions. This paper also highlights the difference between dimensional results of the complex-valued and real-valued fractal functions. In this paper, we study the fractal dimension of the graph of complex-valued function $g(x)+ih(x)$, compare its fractal dimension with the graphs of functions $g(x)+h(x)$ and $(g(x),h(x))$ and also obtain some bounds. Moreover, we study the fractal dimension of the graph of complex-valued fractal interpolation function associated with a germ function $f$, base function $b$ and scaling functions ${\alpha }_k$.