Dilatation Structures Ii. Linearity, Self-similarity and the Cantor Set
نویسندگان
چکیده
منابع مشابه
Self-similarity analysis of the fields diffracted from zone plates with complex geometry
We extend the results obtained for different cases of the product superposition of periodic functions, and the determination of the scattered fields, for the case of circular symmetry. The characteristics of focalization for such cases are studied. We name Cantor-Fresnel zone plate the structures obtained with this method. Also, in this study can be included the focalization by periodic, Cantor...
متن کاملTransmission properties of one dimensional fractal structures
In this paper, the optical properties of one dimensional fractal structures are investigated. We consider six typical fractal photonic structures: the symmetric dual cantor-like fractal structure, the asymmetric dual cantor-like fractal structure, the single cantor-like fractal structure, the symmetric dual golden-section fractal structure, the asymmetric dual golden-section fractal structure a...
متن کاملLinear dilatation structures and inverse semigroups
A dilatation structure encodes the approximate self-similarity of a metric space. A metric space (X, d) which admits a strong dilatation structure (definition 2.2) has a metric tangent space at any point x ∈ X (theorem 4.1), and any such metric tangent space has an algebraic structure of a conical group (theorem 4.2). Particular examples of conical groups are Carnot groups: these are simply con...
متن کاملAn Exploration Of The Generalized Cantor Set
In this paper, we study the prototype of fractal of the classical Cantor middle-third set which consists of points along a line segment, and possesses a number of fascinating properties. We discuss the construction and the self-similarity of the Cantor set. We also generalized the construction of this set and find its fractal dimension.
متن کاملContraction groups and linear dilatation structures
A dilatation structure on a metric space, introduced in [3], is a notion in between a group and a differential structure, accounting for the approximate self-similarity of the metric space. The basic objects of a dilatation structure are dilatations (or contractions). The axioms of a dilatation structure set the rules of interaction between different dilatations. A metric space (X, d) which adm...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006