Topology

   

Mandelbrot Iso-Sets: Iso-Unit Impact Assessment

Authors: Reza Katebi, Nathan O. Schmidt

In this introductory work, we use Santilli's iso-topic lifting as a cutting-edge platform to explore Mandelbrot's set. The objective is to upgrade Mandelbrot's complex quadratic polynomial with iso-multiplication and then computationally probe the effects on this revolutionary fractal. For this, we define the "iso-complex quadratic polynomial" and engage it to generate a locally iso-morphic array of "Mandelbrot iso-sets" by varying the iso-unit, where the connectedness property is topologically preserved in each case. The iso-unit broadens and strengthens the chaotic analysis, and authorizes an enhanced classification and demystification such complex systems because it equips us with an additional degree of freedom: the new Mandelbrot iso-set array is an improvement over the traditional Mandelbrot set because it is significantly more general. In total, the experimental results exemplify dynamic iso-spaces and indicate two modes of topological effects: scale-deformation and boundary-deformation. Ultimately, these new and preliminary developments spark further insight into the emerging realm of iso-fractals.

Comments: 14 pages, 2 figures, accepted in the Hadronic Journal

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Submission history

[v1] 2013-11-04 15:45:13
[v2] 2013-11-20 19:31:09

Unique-IP document downloads: 170 times

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