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
Unique-IP document downloads: 175 times
Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.
Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.