Mandelbrot and Julia Sets of Complex Polynomials Involving Sine and Cosine Functions via Picard-Mann Orbit

The purpose of this paper is to generate fractals of sine and cosine functions for a complex polynomial z(k) + c via Picard-Mann iterations. To generate Mandelbrot and Julia sets, escape criteria are established and proven for sin z(k) + c and cos z(k) + c for Picard-Mann iterations. Various input parameters for different k are used to compare images between sine and cosine. generation time and average number of iterations of the generated Mandelbrot and Julia sets are presented.

Automated summary

The purpose of this paper is to generate fractals of sine and cosine functions for a complex polynomial z(k) + c via Picard-Mann iterations. Escape criteria are established and proven for sin z(k) + c and cos z(k) + c for generating Mandelbrot and Julia sets using Picard-Mann iterations. Images, generation time, and average number of iterations of the generated Mandelbrot and Julia sets are compared using various input parameters for different k.