Results 1 to 10 of about 964,966 (303)
Box-counting by Hölder’s traveling salesman [PDF]
Archiv der Mathematik, 2019 11 ...
Zoltán M. Balogh, Roger Züst
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On distance sets, box-counting and Ahlfors-regular sets [PDF]
Discrete Analysis, 2017 On distance sets, box-counting and Ahlfors-regular sets, Discrete Analysis 2017:9, 22 pp. A well-known problem of Falconer, a sort of continuous analogue of the Erdős distinct-distance problem, asks how large the Hausdorff dimension of a Borel subset of
Pablo Shmerkin
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A spatial randomness test based on the box-counting dimension. [PDF]
Adv Stat Anal, 2022 Statistical modelling of a spatial point pattern often begins by testing the hypothesis of spatial randomness. Classical tests are based on quadrat counts and distance-based methods. Alternatively, we propose a new statistical test of spatial randomness based on the fractal dimension, calculated through the box-counting method providing an inferential ...
Caballero Y, Giraldo R, Mateu J.
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Results in Engineering, 2020 Fractal dimension is an appropriate indicator to describe the complexity of a certain geometry, and box-counting analysis is proved to be an effective and appropriate method for fractal dimension estimation which is widely used.
Jiaxin Wu, Xin Jin, Shuo Mi, Jinbo Tang
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Approximate resolutions and box-counting dimension [PDF]
Topology and its Applications, 2003 The notion of approximate resolution was introduced and investigated in earlier papers of S. Mardešić and the authors [\textit{S. Mardešić} and \textit{T. Watanabe}, Glas. Mat., III. Ser. 24(44), 587--637 (1989; Zbl 0715.54009); \textit{T. Miyata} and \textit{T. Watanabe}, Topology Appl. 113, No. 1--3, 211--241 (2001; Zbl 0986.54033); \textit{T. Miyata}
Miyata, Takahisa, Watanabe, Tadashi
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A Box-Counting Method with Adaptable Box Height for Measuring the Fractal Feature of Images [PDF]
Radioengineering, 2013 Most of the existing box-counting methods for measuring fractal features are only applicable to square images or images with each dimension equal to the power of 2 and require that the box at the top of the box stack of each image block is of the same ...
Min Long, Fei Peng
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Box-counting measure of metric spaces [PDF]
Physica Scripta, 2022 Abstract In this paper, we introduce a new notion called the box-counting measure of a metric space. We show that for a doubling metric space, an Ahlfors regular measure is always a box-counting measure; consequently, if E is a self ...
Liang-yi Huang +3 more
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Box-Counting Dimension in One-Dimensional Random Geometry of Multiplicative Cascades. [PDF]
Commun Math Phys, 2023 We investigate the box-counting dimension of the image of a set $E \subset \mathbb{R}$ under a random multiplicative cascade function $f$. The corresponding result for Hausdorff dimension was established by Benjamini and Schramm in the context of random ...
Falconer KJ, Troscheit S.
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The microscopic characteristics of particle matter and image algorithm based on fractal theory [PDF]
E3S Web of Conferences, 2022 The effects of ash and sulfur content on the morphology of particulate matter (PM) in diesel particle filter (DPF) were investigated with five different components of lubricants. The aggregate morphology of primary particles in diesel were analyzed using
Tan Piqiang +4 more
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IEEE Access, 2022 The box-counting dimension, which can effectively reflect the complexity and self-similarity of models, is an important method for calculating the fractal dimension of models.
Chong Wang, Weiqiang An
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