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THE ORDER OF A 2-SEQUENCE AND THE COMPLEXITY OF DIGITAL IMAGES

Research Group for Mathematical and Numerical Analysis of Dynamical Systems, Kaunas University of Technology, Studentu 50-147, Kaunas LT-51368, Lithuania

E-mail Address: [email protected]

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ZENONAS NAVICKAS

Research Group for Mathematical and Numerical Analysis of Dynamical Systems, Kaunas University of Technology, Studentu 50-147, Kaunas LT-51368, Lithuania

E-mail Address: [email protected]

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MARTYNAS VAIDELYS

Research Group for Mathematical and Numerical Analysis of Dynamical Systems, Kaunas University of Technology, Studentu 50-147, Kaunas LT-51368, Lithuania

E-mail Address: [email protected]

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MINVYDAS RAGULSKIS

Research Group for Mathematical and Numerical Analysis of Dynamical Systems, Kaunas University of Technology, Studentu 50-147, Kaunas LT-51368, Lithuania

E-mail Address: [email protected]

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https://doi.org/10.1142/S0219525916500107Cited by:1 (Source: Crossref)

Abstract

The concept of the order of a 2-sequence is introduced in this paper. The order of a 2-sequence is a natural but not trivial extension of the order of one-dimensional (1D) linear recurrent sequences. Necessary and sufficient conditions for the generation of 2-sequences with finite order from the minimal information subset are derived. It is demonstrated that the order of 2-sequences can be used to estimate the complexity of self-organizing patterns with respect to each spatial coordinate.

Keywords:

PACS: 02.10.Hh, 89.75.Kd

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