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Box dimension of Neimark–Sacker bifurcation
Journal of Difference Equations and Applications, 2014In this paper we show how a change of a box dimension of orbits of two-dimensional discrete dynamical systems is connected to their bifurcations in a nonhyperbolic fixed point. This connection is already shown in the case of one-dimensional discrete dynamical systems and Hopf bifurcation for continuous systems.
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Network Box Counting Dimension
2020In this chapter we begin our detailed study of fractal dimensions of a network \(\mathbb {G}\). There are two approaches to calculating a fractal dimension of \(\mathbb {G}\). One approach, applicable if \(\mathbb {G}\) is a spatially embedded network, is to treat \(\mathbb {G}\) as a geometric object and apply techniques, such as box counting or ...
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On the Box Dimension of Typical Measures
Monatshefte f�r Mathematik, 2002zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Myjak, Józef, Rudnicki, Ryszard
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BOX DIMENSION OF BILINEAR FRACTAL INTERPOLATION SURFACES
Bulletin of the Australian Mathematical Society, 2018Bilinear fractal interpolation surfaces were introduced by Ruan and Xu in 2015. In this paper, we present the formula for their box dimension under certain constraint conditions.
QING-GE KONG, HUO-JUN RUAN, SHENG ZHANG
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BOX-COUNTING DIMENSION COMPUTED BY α-DENSE CURVES
Fractals, 2017We introduce a method to reduce to the real case the calculus of the box-counting dimension of subsets of the unit cube [Formula: see text], [Formula: see text]. The procedure is based on the existence of special types of [Formula: see text]-dense curves (a generalization of the space-filling curves) in [Formula: see text] called [Formula: see text ...
García Macías, Gonzalo +2 more
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Computing the Box Counting Dimension
2020From roughly the late 1980s to the mid-1990s, a very large number of papers studied computational issues in determining fractal dimensions of geometric objects, or provided variants of algorithms for calculating the fractal dimensions, or applied these techniques to real-world problems.
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Topological and Box Counting Dimensions
2020A mind once stretched by a new idea never regains its original dimension. Oliver Wendell Holmes, Jr. (1841–1935), American, U.S. Supreme Court justice from 1902 to 1932.
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Box fractal dimension in speckle images
Optical Methods for Inspection, Characterization, and Imaging of Biomaterials III, 2017In this paper, we propose a generalization of the box fractal dimension in images by considering the curve obtained from its value as a function of the binarization threshold. This curve can be used to describe speckle patterns. We show some examples of both objective simulated and experimental and subjective speckle in some cases of interest.
Marcelo Trivi +4 more
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Box and packing dimensions of projections and dimension profiles
Mathematical Proceedings of the Cambridge Philosophical Society, 2001For E a subset of ℝn and s ∈ [0, n] we define upper and lower box dimension profiles, B-dimsE and B-dimsE respectively, that are closely related to the box dimensions of the orthogonal projections of E onto subspaces of ℝn. In particular, the projection of E onto almost all m-dimensional subspaces has upper box dimension B-dimmE and lower box ...
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