Self-Similar Planar Fractals Based on Branching Trees and Bushes
نویسندگان
چکیده
منابع مشابه
Self-similar fractals and arithmetic dynamics
The concept of self-similarity on subsets of algebraic varieties is defined by considering algebraic endomorphisms of the variety as `similarity' maps. Self-similar fractals are subsets of algebraic varieties which can be written as a finite and disjoint union of `similar' copies. Fractals provide a framework in which, one can unite some results and conjectures in Diophantine g...
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Dube proved some undecidability on self-affine fractals. In this paper, we obtain the decidability for self-similar fractal of Dube’s type. In fact, we prove that the following problems are decidable to test if the Hausdorff dimension of a given Dube’s self-similar set is equal to its similarity dimension, and to test if a given Dube’s self-similar set satisfies the strong separation condition.
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Tube formulas (by which we mean an explicit formula for the volume of an (inner) ε-neighbourhood of a subset of a suitable metric space) have been used in many situations to study properties of the subset. For smooth submanifolds of Euclidean space, this includes Weyl’s celebrated results on spectral asymptotics, and the subsequent relation between curvature and spectrum. Additionally, a tube f...
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Self-similar fractals arise as the unique attractors of iterated function systems (IFSs) consisting of finitely many contracting similarities satisfying an open set condition. Each point x in such a fractal F arising from an IFS S is naturally regarded as the “outcome” of an infinite coding sequence T (which need not be unique) over the alphabet Σk = {0, . . . , k − 1}, where k is the number of...
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ژورنال
عنوان ژورنال: Progress of Theoretical Physics Supplement
سال: 2003
ISSN: 0375-9687
DOI: 10.1143/ptps.150.176