Escape Criteria for Generating Fractals of Complex Functions Using DK-Iterative Scheme

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(zm) + c; m >= 2, c 2 C) and complex exponential function (e(zm) + c; m >= 2, c 2 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.

Automated summary

In this article, an escape criteria using DK-iteration, complex sine function, and complex exponential function is established to analyze the dynamical behavior of specific fractals such as Julia set and Mandelbrot set. By generalizing existing algorithms, beautiful fractals for m=2, 3, and 4 are visualized. The image generation time using different input parameter values is also computed.