A new class of exceptional self-affine fractals
نویسندگان
چکیده
منابع مشابه
Exceptional sets for self-affine fractals
Under certain conditions the ‘singular value function’ formula gives the Hausdorff dimension of self-affine fractals for almost all parameters in a family. We show that the size of the set of exceptional parameters is small both in the sense of Hausdorff dimension and Fourier dimension.
متن کاملRandom subsets of self-affine fractals
We find the almost sure Hausdorff and box-counting dimensions of random subsets of self-affine fractals obtained by selecting subsets at each stage of the hierarchical construction in a statistically self-similar manner.
متن کاملGenerating Self-Affine Fractals by Collage Grammars
Self-affinity and self-similarity are fundamental concepts in fractal geometry. In this paper, they are related to collage grammars syntactic devices based on hyperedge replacement that generate sets of collages. Essentially, a collage is a picture consisting of geometric parts like line segments, circles, polygons, polyhedra, etc. The overlay of all collages in a collage language yields a frac...
متن کاملA Class of Self-affine and Self-affine Measures
Let I = {φj}j=1 be an iterated function system (IFS) consisting of a family of contractive affine maps on Rd. Hutchinson [8] proved that there exists a unique compact set K = K(I), called the attractor of the IFS I, such that K = ⋃m j=1 φj(K). Moreover, for any given probability vector p = (p1, . . . , pm), i.e. pj > 0 for all j and ∑m j=1 pj = 1, there exists a unique compactly supported proba...
متن کاملA class of multiresolution stochastic models generating self-affine images
Fractal image compression is based on the rather poorly motivated assumption that “natural” images exhibit significant affine self-similarity. The accuracy of this assumption is evaluated by a comparison between the statistics of natural images and those of a multiresolution stochastic model designed to generate images exhibiting affine self-similarity as assumed by fractal coding techniques. T...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2013
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2012.10.065