منابع مشابه
Computability of Self-Similar Sets
We investigate computability of a self-similar set on a Euclidean space. A nonempty compact subset of a Euclidean space is called a self-similar set if it equals to the union of the images of itself by some set of contractions. The main result in this paper is that if all of the contractions are computable, then the self-similar is a recursive compact set. A further result on the case that the ...
متن کاملComputability of the Hausdorff and packing measures on self-similar sets and the self-similar tiling principle
We state a self-similar tiling principle which shows that any open subset of a self-similar set with open set condition may be tiled without loss of measure by copies under similitudes of any closed subset with positive measure. We use this method to get the optimal coverings and packings which give the exact value of the Hausdorff-type and packing measures. In particular, we show that the exac...
متن کاملStatistically Self - Similar Fractal Sets
In the present paper we define statistically self-similar sets, and, using a modification of method described in [2], [3], find a Hausdorff dimension of a statistically self-similar set.
متن کاملOn the classification of self-similar sets
We classify binary self-similar sets, which are compact sets determined by two contractions on the plane, into four classes from the viewpoint of functional equations. In this classification, we can not only show close relationships among functions with self-similarity but also give solutions to a few open problems in other field.
متن کاملBilipschitz Embedding of Self-similar Sets
This paper proves that the self-similar set satisfying the strong separation condition can be bilipschitz embedded into self-similar set with larger Hausdorff dimension, and it can be embedded into a self-similar set with the same Hausdorff dimension if and only if these two self-similar sets are bilipschitz equivalent.
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ژورنال
عنوان ژورنال: Mathematical Logic Quarterly
سال: 1999
ISSN: 0942-5616
DOI: 10.1002/malq.19990450103