Fractals are essential in representing the natural environment due to their important characteristic of self similarity. The dynamical behavior of fractals mostly depends on escape criteria using different iterative techniques. In this article, we establish an escape criteria using DK-iteration as well as complex sine function $(sin\left(z^m\right)+c;m\ge 2,c\in \mathbb{C})$ and complex exponential function $(e^{z^m}+c;m\ge 2,c\in \mathbb{C})$. We use this to analyze the dynamical behavior of specific fractals namely Julia set and Mandelbrot set. This is achieved by generalizing the existing algorithms, which led to the visualization of beautiful fractals for $m=2,3$ and 4. Moreover, the image generation time in seconds using different values of input parameters is also computed.

Fractals play a vital role in modeling the natural environment. The present aim is to investigate the escape criterion to generate specific fractals such as Julia sets, Mandelbrot sets and Multi-corns via F-iteration using complex functions $h\left(z\right)=z^n+c$, $h\left(z\right)=sin\left(z^n\right)+c$ and $h\left(z\right)=e^{z^n}+c$, $n\ge 2,c\in \mathbb{C}$. We observed some beautiful Julia sets, Mandelbrot sets and Multi-corns for n = 2, 3 and 4. We generalize the algorithms of the Julia set and Mandelbrot set to visualize some Julia sets, Mandelbrot sets and Multi-corns. Moreover, we calculate image generation time in seconds at different values of input parameters.