MANDELBROT FRACTALS USING FIXED-POINT TECHNIQUE OF SINE FUNCTION.

Here, we develop escape criteria for p_c(z) = sin(z ⁿ)−az +c, a, c ∈ C, n ≥ 2, exploiting four different iterations of fixed point theory to explore various Mandelbrot sets which are different than the classical Mandelbrot set . Our concern is to utilize the lesser number of iterations that are necessary to attain the fixed point of the transcendental complex-valued sine function. Further, we investigate the effect of variables on the shape, size, color, and dynamics of fractals. Noticeably, some of the obtained fractals symbolize the Swastika (a symbol of spirituality and divinity in Indian religions), Shivling (an abstract representation of the Hindu God Shiva), flowers, spiders, butterflies, Rangoli (made mainly in the festive season in India), art on glass, and so on. Interestingly, the higher-order Mandelbrot set in Picard-orbit has a resemblance to Corona-virus. [ABSTRACT FROM AUTHOR]