RELATIVE SUPERIOR MANDELBROT AND JULIA SETS FOR INTEGER AND NON-INTEGER VALUES

Rajeshri Rana, Yashwant Singh Chauhan

Abstract: The fractals generated from the self-squared function, 2 z z c ? ? where z and c are complex quantities have been studied extensively in the literature. This paper studies the transformation of the function , 2 n z z c n ? ? ? and analyzed the z plane and c plane fractal images generated from the iteration of these functions using Ishikawa iteration for integer and non-integer values. Also, we explored the drastic changes that occurred in the visual characteristics of the images from n = integer value to n = non integer value.

Keywords: Complex dynamics, Relative Superior Julia set, Relative Superior Mandelbrot set.

DOI: https://doi.org/10.15623/ijret.2012.0102011