Fractals as julia sets of complex sine function via fixed point iterations

Abstract

We explore some new variants of the Julia set by developing the escape criteria for a function sin(zn) + az + c, where a, c ∈ C, n ≥ 2, and z is a complex variable, utilizing four distinct fixed point iterative methods. Furthermore, we examine the impact of parameters on the deviation of dynamics, color, and appearance of fractals. Some of these fractals represent the stunning art on glass, and Rangoli (made in different parts of India, especially during the festive season) which are useful in interior decoration. Some fractals are similar to beautiful objects found in our surroundings like flowers (to be specific Hibiscus and Catharanthus Roseus), and ants.