Arithmetic based fractals associated with Pascal's triangle.

Título inglés Arithmetic based fractals associated with Pascal's triangle.
Título español Fractales con base aritmética asociados al triángulo de Pascal.
Autor/es Gamelin, T.W. ; Mnatsakanian, Mamiron A.
Organización Dep. Math. UCLA, Los Angeles, Estados Unidos;Project MATHEMATICS Caltech, Pasadena, Estados Unidos
Revista 0214-1493
Publicación 2005, 49(2): 329-349, 8 Ref.
Tipo de documento articulo
Idioma Inglés
Resumen inglés 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 binomial coefficients. 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.
Clasificación UNESCO 120208
Palabras clave español Ecuaciones funcionales ; Sistemas de funciones iteradas ; Fractales ; Dimensión de Hausdorff
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