Web of Science: 1 cites, Scopus: 1 cites, Google Scholar: cites
Arithmetic based fractals associated with Pascal's triangle
Gamelin, T. W.
Mnatsakanian, M. A.

Data: 2005
Resum: Our goal is to study Pascal-Sierpinski gaskets, which are certain fractal sets defined in terms of divisibility of entries in Pascal's triangle. The principal tool is a "carry rule" for the addition of the base-q representation of coordinates of points in the unit square. In the case that q = p is prime, we connect the carry rule to the power of p appearing in the prime factorization of binomialcoefficients. We use the carry rule to define a family of fractal subsets Bqr of the unit square, and we show that when q = p is prime, Bqr coincides with the Pascal-Sierpinski gasket corresponding to N = pr . We go on to describe Bqr as the limit of an iterated function system of "partial similarities", and we determine its Hausdorff dimension. We consider also the corresponding fractal sets in higher-dimensional Euclidean space.
Drets: Tots els drets reservats.
Llengua: Anglès
Document: Article ; recerca ; Versió publicada
Publicat a: Publicacions matemàtiques, V. 49 n. 2 (2005) p. 329-349, ISSN 2014-4350

Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/128380
DOI: 10.5565/PUBLMAT_49205_04

21 p, 200.2 KB

El registre apareix a les col·leccions:
Articles > Articles publicats > Publicacions matemàtiques
Articles > Articles de recerca

 Registre creat el 2006-05-09, darrera modificació el 2022-02-20

   Favorit i Compartir