Moiré interferences in the map of orbits of the Mandelbrot Set
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AuthorAlcover Garau, Pedro María
Knowledge AreaLenguajes y Sistemas Informáticos
SponsorsCounting on the publisher’s kindness, I would dedicate this piece of work to our greatly missed professor and researcher Mr. Pedro José García Laencina, who passed away unexpectedly on the evening of August 28th, 2015 at the age of 34. This article is the result of the activity carried out under the “Research Programme for Groups of Scientific Excellence at Region of Murcia” of the Seneca Foundation (Agency for Science and Technology of the Region of Murcia - 19895/GERM/15). The work has been partially supported and funded by the Spanish Ministerio de Economíıa y Competitividad (MINECO) under the Project ViSelTR (TIN2012-39279).
Bibliographic CitationAlcover, P. M. (2017). Moiré interferences in the map of orbits of the Mandelbrot Set. Communications in Nonlinear Science and Numerical Simulation, 42, 545–559. doi:10.1016/j.cnsns.2016.06.016
Real numbers discretization
This article shows the presence of Moiré Interference patterns in the map of periods of the Mandelbrot Set. It describes the requirements for their appearance and shows that such interferences are highly sensitive to the original conditions that define their calculation. The specific case herein studied shows that the Moiré interference patterns appearing in a picture of a section of the map of orbits are unpredictable, even if we obtain different maps from very similar original conditions. It begins with a brief description of the Mandelbrot Set and some of the characteristics of its orbits, the Moiré Patterns, as well as a concise introduction to a description of the Discrete Wavelet Transform. In order to develop the proposed specific case, a Multi-resolution Analysis method based on the Discrete Wavelet Transform has been used. It is significant that Moiré Interference Patterns always appear when the order of magnitudes reaches a certain limit where, what is considered as hypothetically ...
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