Burning Ship and Its Quasi Julia Images Using Mann Iteration

An invented form of Mandelbrot set came into existence in 1992 when Michelitsch and Rossler have applied seemingly small changes in complex analytic Mandelbrot set function and got an image resembled to a ship going into flame. He named it burning ship. Our goal in this paper is to apply Mann Iteration method to burning ship function and produce a collection of stunning images. We have also calculated the fixed points of such images to measure the convergence rate and those fixed points can be further useful in various fractal applications such as fractal cryptography. Hence we are in position to examining numerically the stability of the fractals.