Geodesic
Fractal properties of binary matrices constructed using the generalized Pascal's triangle and applications
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Algebra, Geometry, and Combinatorics, Tome 214 (2022), pp. 69-75

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In this paper, we describe a method for composing binary matrices based on the generalization of Pascal's triangle. The method of parameterization of these binary matrices by choosing certain generatrices is discussed and the properties of this construction are examined. We also present a well-known method for constructing a binary matrix by reducing the Pascal triangle by a simple or composite modulus and compare it with the method proposed in this paper. The fractal properties of these binary matrices are considered, and possible applications of fractal properties are presented.
Keywords: combinatorial analysis, generalized Pascal's pyramid, recurrent property
Mots-clés : Pascal's triangle, fractal, fractal dimension. 
@article{INTO_2022_214_a7,
     author = {B. A. Starkov},
     title = {Fractal properties of binary matrices constructed using the generalized {Pascal's} triangle and applications},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {69--75},
     publisher = {mathdoc},
     volume = {214},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2022_214_a7/}
}
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B. A. Starkov. Fractal properties of binary matrices constructed using the generalized Pascal's triangle and applications. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Algebra, Geometry, and Combinatorics, Tome 214 (2022), pp. 69-75. http://geodesic.mathdoc.fr/item/INTO_2022_214_a7/