Generation of Fractals using Polar Coordinates

The article describes an algorithm for generating fractals using polar coordinates. The classic Julia and Mandelbrot polynomial iteration applied to a complex number is replaced by an iteration with separate functions for distance and angle. A polynomial function is used for an angle and a power function for a distance. Varying the functions parameters allows to create a wide range of attractive pictures. Distance values are used for coloring fractal images.

Content

Author and article information

Journal

Title: ScienceOpen Preprints

Publisher: ScienceOpen

Publication date (Electronic preprint): 13 September 2021

Affiliations

[1 ] Horiba France SAS, 455 Avenue Eugène Avinée, 59120 Loos, France

Author notes

[* ]Email: serguei.charonov@ 123456horiba.com .

Author information

Serguei Charonov https://orcid.org/0000-0002-6281-0514

Article

DOI: 10.14293/S2199-1006.1.SOR-.PPBKDMO.v1

SO-VID: 6b409839-0986-4ba5-9172-139aa6c0c528

License:

This work has been published open access under Creative Commons Attribution License CC BY 4.0 , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Conditions, terms of use and publishing policy can be found at www.scienceopen.com .

History

Date received : 13 September 2021

Data availability: The datasets generated during and/or analysed during the current study are available in the repository: https://doi.org/10.6084/m9.figshare.16608541

ScienceOpen disciplines: Computer science

Keywords: Fractals, Julia set, Mandelbrot set