Title: A Generalized Mandelbrot Set Based On Distance Ratio
Authors: Zhang, Xizhe
Lv, Tianyang
Wang, Zhengxuan
Citation: WSCG '2006: Short Papers Proceedings: The 14-th International Conference in Central Europe on Computer Graphics, Visualization and Computer Vision 2006: University of West Bohemia, Plzen, Czech Republic, January 31 - February 2, 2006, p. 179-184.
Issue Date: 2006
Publisher: Václav Skala - UNION Agency
Document type: konferenční příspěvek
URI: http://wscg.zcu.cz/WSCG2006/Papers_2006/Short/!WSCG2006_Short_Proceedings_Final.pdf
ISBN: 80-86943-05-4
Keywords: fraktály;poměr vzdálenosti;komplexní mapování;Mandelbrotova množina
Keywords in different language: fractals;distance ratio;complex mapping;Mandelbrot set
Abstract: The iteration of complex function can generate beautiful fractal images. This paper presents a novel method based on the iteration of the distance ratio with two points, which generates a generalized Mandelbrot set according to distance ratio convergence times. This paper states the definition of distance ratio and its iteration. Then taking the complex function f(z)=zα+c for example, it discusses the visual structure of generalized Mandelbrot with various exponent and comparing it with Mandelbrot set generated by escape time algorithm. When exponent α>1, the outer border of DRM is same as Mandelbrot set, but has complex inner structure; when α<0, the inner border of DRM is same as Mandelbrot set, DRM is the “outer” region and complement set of Mandelbrot set, the two sets cover the whole complex plane.
Rights: © Václav Skala - UNION Agency
Appears in Collections:WSCG '2006: Short Papers Proceedings

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