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

2022/04/07 by Manuj Verma, Verma, Manuj, Amit Priyadarshi +3
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2204.03622

openalex publication_date 2022/04/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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)+i h(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 α_k.

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