Fractal Complex Analysis

Abstract

In this paper, we begin by providing a concise overview of fractal calculus. We then explore the concepts of fractal complex numbers and functions, define the fractal complex derivative, and derive the fractal Cauchy-Riemann equations. Additionally, we introduce fractal contour integrals, offer illustrative examples, and present their visualizations. Finally, we examine and visualize the transformations of circles under fractal complex functions.