scholarly journals On distance sets, box-counting and Ahlfors-regular sets

2017 ◽  
Author(s):  
Pablo Shmerkin ◽  
Keyword(s):  
Box Counting ◽  
Regular Sets ◽  
Distance Sets

scholarly journals On the distance sets of Ahlfors–David regular sets

2017 ◽  
Vol 307 ◽  
pp. 1029-1045 ◽  
Author(s):  
Tuomas Orponen
Keyword(s):  
Regular Sets ◽  
Distance Sets

3D box-counting algorithm for calculating fractal dimension of cities

2010 ◽  
Vol 30 (8) ◽  
pp. 2070-2072
Author(s):  
Le-shan ZHANG ◽  
Ge CHEN ◽  
Yong HAN ◽  
Tao ZHANG
Keyword(s):  
Fractal Dimension ◽  
Box Counting ◽  
Counting Algorithm

scholarly journals Supramolecular Fractal Growth of Self-Assembled Fibrillar Networks

Gels ◽  
2021 ◽  
Vol 7 (2) ◽  
pp. 46
Author(s):  
Pedram Nasr ◽  
Hannah Leung ◽  
France-Isabelle Auzanneau ◽  
Michael A. Rogers
Keyword(s):  
Fractal Dimension ◽  
Crystallization Temperature ◽  
Cayley Tree ◽  
Fractal Dimensions ◽  
Self Similarity ◽  
Avrami Model ◽  
Cluster Aggregation ◽  
Box Counting ◽  
Self Assembled ◽  
Limited Diffusion

Complex morphologies, as is the case in self-assembled fibrillar networks (SAFiNs) of 1,3:2,4-Dibenzylidene sorbitol (DBS), are often characterized by their Fractal dimension and not Euclidean. Self-similarity presents for DBS-polyethylene glycol (PEG) SAFiNs in the Cayley Tree branching pattern, similar box-counting fractal dimensions across length scales, and fractals derived from the Avrami model. Irrespective of the crystallization temperature, fractal values corresponded to limited diffusion aggregation and not ballistic particle–cluster aggregation. Additionally, the fractal dimension of the SAFiN was affected more by changes in solvent viscosity (e.g., PEG200 compared to PEG600) than crystallization temperature. Most surprising was the evidence of Cayley branching not only for the radial fibers within the spherulitic but also on the fiber surfaces.

scholarly journals Prox-regular sets and Legendre-Fenchel transform related to separation properties

Optimization ◽  
2020 ◽  
pp. 1-33
Author(s):  
Samir Adly ◽  
Florent Nacry ◽  
Lionel Thibault
Keyword(s):  
Fenchel Transform ◽  
Regular Sets

scholarly journals Plenty of big projections imply big pieces of Lipschitz graphs

2021 ◽  
Author(s):  
Tuomas Orponen
Keyword(s):  
Lipschitz Graphs ◽  
Regular Sets ◽  
Big Pieces

AbstractI prove that closed n-regular sets $$E \subset {\mathbb {R}}^{d}$$ E ⊂ R d with plenty of big projections have big pieces of Lipschitz graphs. In particular, these sets are uniformly n-rectifiable. This answers a question of David and Semmes from 1993.

CT Image Analysis on the Meso-Damage of Construction Waste Recycled Brick

2012 ◽  
Vol 588-589 ◽  
pp. 1930-1933
Author(s):  
Guo Song Han ◽  
Hai Yan Yang ◽  
Xin Pei Jiang
Keyword(s):  
Fractal Dimension ◽  
Strain Curve ◽  
Ct Image ◽  
Stress Strain Curve ◽  
Crack Evolution ◽  
Construction Waste ◽  
Box Counting ◽  
Industrial Ct ◽  
Ct Image Analysis ◽  
Box Counting Method

Based on industrial CT technique, Meso-mechanical experiment was conducted on construction waste recycled brick to get the real-time CT image and stress-strain curve of brick during the loading process. Box counting method was used to calculate the fractal dimension of the inner pore transfixion and crack evolution. The results showed that lots of pore in the interfacial transition zone mainly resulted in the damage of the brick. With the increase of stress, the opening through-pore appeared and crack expanded, and the fractal dimension increased.

scholarly journals ASSESSMENT OF URBAN SPRAWL USING SHANNON’S ENTROPY AND FRACTAL ANALYSIS: A CASE STUDY OF ATAKUM, ILKADIM AND CANIK (SAMSUN, TURKEY)

2017 ◽  
Vol 25 (3) ◽  
pp. 264-276 ◽  
Author(s):  
Derya OZTURK
Keyword(s):  
Urban Sprawl ◽  
Fractal Analysis ◽  
Urban Form ◽  
Entropy Method ◽  
Shannon’S Entropy ◽  
Analysis Method ◽  
Maximum Likelihood Classification ◽  
Shannon's Entropy ◽  
Box Counting

Urban sprawl is one of the most important problems in urban development due to its negative environmental and societal impacts. Therefore, the spatial pattern of urban growth should be accurately analyzed and well understood for effective urban planning. This paper focuses on urban sprawl analysis in the Atakum, Ilkadim and Canik districts of Samsun, Turkey. In this study, urban sprawl was examined over a period of 24 years using Shannon's entropy and fractal analysis based on remote sensing and Geographic Information System (GIS). The built-up areas in 1989, 2000 and 2013 were extracted from Landsat TM/ETM+/OLI images using the maximum likelihood classification method, and urban form changes in the 1989–2013 period were investigated. The Shannon's entropy method was used to determine the degree of urban sprawl, and a fractal analysis method based on box counting was used to characterize the urban sprawl. The results show that Atakum, Ilkadim and Canik experienced important changes and have considerable sprawl and complex characteristics now. The study also revealed that there is no monotonic relationship between Shannon's entropy and fractal dimension.

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