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 |
Acceso al artículo completo |