Article
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Generation of Fractals using Polynomial Iterations in Polar Coordinates
Version 1
: Received: 24 September 2021 / Approved: 24 September 2021 / Online: 24 September 2021 (12:39:34 CEST)
How to cite: Charonov, S. Generation of Fractals using Polynomial Iterations in Polar Coordinates. Preprints 2021, 2021090430 Charonov, S. Generation of Fractals using Polynomial Iterations in Polar Coordinates. Preprints 2021, 2021090430
Abstract
This article describes an algorithm for generating fractals using polar coordinates. The classic Julie and Mandelbrot polynomial iteration applied to a complex number is replaced by a separate iteration for distance and angle. By varying the polynomial parameters of the iteration functions, a wide range of attractive images can be created. Distance and angle values are used to colorize fractal images.
Supplementary and Associated Material
https://doi.org/10.6084/m9.figshare.16673947: Data sets
https://spectralmultiplatform.blogspot.com/p/polar-polynomial-fractals.html: The online fractal generator
Keywords
Fractals, Julia set, Mandelbrot set.
Subject
Computer Science and Mathematics, Applied Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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