A Four Step Feedback Iteration and Its Applications in Fractals

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(z)=z(n)+c, h(z)=sin(z(n))+c and h(z)=e(zn)+c, n >= 2,c is an element of 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.

Automated summary

This paper investigates the escape criterion for generating specific fractals such as Julia sets, Mandelbrot sets, and Multi-corns using F-iteration with complex functions. The authors observed and visualized beautiful Julia sets, Mandelbrot sets, and Multi-corns for different values of n. Additionally, they calculated the image generation time at various input parameter values.