Sandbox method for factorial moments and anomalous fractal dimensions

Kun, Ferenc; Sorge, H.; Sailer, K.; Bardos, G.; Greiner, Walter

doi:10.1016/0370-2693(95)00697-j

Cited by 5 publications

(3 citation statements)

References 15 publications

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“…The method is based on circles of radius R centred on each randomly selected event, i, or points belonging to the structure and counting the number of events (points or pixels) inside the circle, R. The fractal dimension d is estimated from the growth curve <N(R)>~(R) d where <N(R)> is a mean over all points with a fixed radius R (Lopes and Betrouni 2009). Limitations and advantages of each of these methods are discussed in many previous studies (Dombrádi et al 2007;Kun et al 1995;Lopes and Betrouni 2009).…”

Section: Preliminary Exploratory Spatial Analysis and Global Fractal/...mentioning

confidence: 99%

“…The conventional sandbox method have been used to assess fractal or multifractal analysis in many different areas such as microvasculature in health and disease (Ward and Bai 2013), heavy metals contamination (Hakamata et al 1998), spatial structure of population distribution (Orozco et al 2013), drainage (Dombrádi et al 2007) and natural river networks (De Bartolo et al 2004), fracture network permeability (Jafari and Babadagli 2008), intermittency analysis of high-energy heavy-ion data (Kun et al 1995) and in temperature-dependent properties of resistivity and thermoelectric power properties in bilayer films (Li et al 2011;Tian et al 1999).…”

Section: 3local Sandbox-countingmentioning

confidence: 99%

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Local fractality: The case of forest fires in Portugal

Kanevski

Pereira

2017

Physica A: Statistical Mechanics and its Applications

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The research deals with a study of local fractality in spatial distribution of forest fires in Portugal using the sandbox method. The general procedure is the following: (a) define a circle centred in each and all events with increasing radius R; (b) count the number of other events located within the circle of radius R, N(R); (c) plot the growth curve which is the functional dependence of N(R) versus R; and (d) estimate the local fractal dimension as the slope on log[N(R)] versus log[R]. The computation is carried out by using the location of every fire event as a centre but without the final averaging over all the fires for a given R, which is usually performed to get a global fractal dimension and to estimate global clustering. Sandbox method is widely used in many applications in physics and other subjects. The local procedure has the ability to provide the most complete information regarding the spatial distribution of clustering and avoiding non-homogeneity and non-stationarity problems. Most of the analysis was performed using the National Mapping Burnt Area (NMBA) database which accounts for 32 156 fires during the 1975 -2013 period. The results of local analysis are compared with a randomly generated pattern in forest zones (validity domain). The results demonstrate interesting local spatial patterns of clustering. Some results on global measures are reported as well.

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Section: Preliminary Exploratory Spatial Analysis and Global Fractal/...mentioning

confidence: 99%

Section: 3local Sandbox-countingmentioning

confidence: 99%

Local fractality: The case of forest fires in Portugal

Kanevski

Pereira

2017

Physica A: Statistical Mechanics and its Applications

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“…Scaled factorial moments have found widespread use in high-energy physics for detecting intermittency in particle production [1][2][3][4][5][6][7][8][9][10]. The presence of jet-like structures and perhaps quark-gluon plasma phase in particle production can result in clustering of data in bins leading to holes and spikes in the rapidity distribution.…”

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confidence: 99%