Abstract
The aim of this paper is to present an application of a fixed point iterative process in generation of fractals namely Julia and Mandelbrot sets for the complex polynomials of the form T ( x ) = x n + m x + r where m , r ∈ C and n ≥ 2 . Fractals represent the phenomena of expanding or unfolding symmetries which exhibit similar patterns displayed at every scale. We prove some escape time results for the generation of Julia and Mandelbrot sets using a Picard Ishikawa type iterative process. A visualization of the Julia and Mandelbrot sets for certain complex polynomials is presented and their graphical behaviour is examined. We also discuss the effects of parameters on the color variation and shape of fractals.
Subject
Physics and Astronomy (miscellaneous),General Mathematics,Chemistry (miscellaneous),Computer Science (miscellaneous)
Reference34 articles.
1. Fractals Everywhere;Barnsley,1993
2. On the convergence of fixed point iterations for the moving geometry in a fluid-structure interaction problem
3. Travel time estimation from sparse floating car data with consistent path inference: A fixed point approach
4. Nonlinear Dynamics and Chaos With Applications to Physics, Biology, Chemistry, and Engineering;Strogatz,2018
5. Memoire sur l’iteration des functions rationnelles;Julia;J. Math. Pures Appl.,1918
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