On the convergence of multicomplex M-J sets to the Steinmetz hypersolids

• Autorzy: Katunin A.

Identyfikatory

DOI

10.17512/jamcm.2016.3.07

• Języki publikacji: EN

Abstrakty

EN

In this paper, the analysis of generalized multicomplex Mandelbrot-Julia (henceforth abbrev. M-J) sets is performed in terms of their shape when a degree of an iterated polynomial tends to infinity. Since the multicomplex algebras result from a tensor product of complex algebras, the dynamics of multicomplex systems described by iterated polynomials is different with respect to their complex and hypercomplex analogues. When the degree of an iterated polynomial tends to infinity the M-J sets tend to the higher dimensional generalization of the Steinmetz solid, depending on the dimension of a vector space, where a given generalization of M-J sets is constructed. The paper describes a case of bicomplex M-J sets with appropriate visualizations as well as a tricomplex one, and the most general case - the muticomplex M-J sets, and their corresponding geometrical convergents.

Słowa kluczowe

EN

generalized M-J sets; multicomplex M-J sets; convergence; Steinmetz hypersolid

PL

uogólniony zbiór Mandelbrot-Julia; analiza fraktalna; konwergencja

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2016
• Tom: Vol. 15, nr 3
• Strony: 67--74
• Opis fizyczny: Bibliogr. 21 poz., rys.

Twórcy

autor

Katunin A.

• Institute of Fundamentals of Machinery Design, Silesian University of Technology Gliwice, Poland

Bibliografia

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Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.