Figure 1. A 32-segment quadric fractal viewed through "boxes" of different sizes. The pattern illustrates self similarity.
Box counting is a method of gathering data for analyzing complex patterns by breaking a dataset, object, image, etc. into smaller and smaller pieces, typically "box"-shaped, and analyzing the pieces at each smaller scale. The essence of the process has been compared to zooming in or out using optical or computer based methods to examine how observations of detail change with scale. In box counting, however, rather than changing the magnification or resolution of a lens, the investigator changes the size of the element used to inspect the object or pattern (see Figure 1). Computer based box counting algorithms have been applied to patterns in 1-, 2-, and 3-dimensional spaces.[1][2] The technique is usually implemented in software for use on patterns extracted from digital media, although the fundamental method can be used to investigate some patterns physically. The technique arose out of and is used in fractal analysis. It also has application in related fields such as lacunarity and multifractal analysis.[3][4]
^Liu, Jing Z.; Zhang, Lu D.; Yue, Guang H. (2003). "Fractal Dimension in Human Cerebellum Measured by Magnetic Resonance Imaging". Biophysical Journal. 85 (6): 4041–4046. Bibcode:2003BpJ....85.4041L. doi:10.1016/S0006-3495(03)74817-6. PMC 1303704. PMID 14645092.
^Smith, T. G.; Lange, G. D.; Marks, W. B. (1996). "Fractal methods and results in cellular morphology — dimensions, lacunarity and multifractals". Journal of Neuroscience Methods. 69 (2): 123–136. doi:10.1016/S0165-0270(96)00080-5. PMID 8946315. S2CID 20175299.
^Mandelbrot (1983). The Fractal Geometry of Nature. Henry Holt and Company. ISBN 978-0-7167-1186-5.
^Iannaccone, Khokha (1996). Fractal Geometry in Biological Systems. CRC Press. p. 143. ISBN 978-0-8493-7636-8.
approach to boxcounting is to move the box according to some feature related to the pixels of interest. In local connected dimension boxcounting algorithms...
restore and modify classic automobiles and motorcycles. Counting Cars debuted on August 13, 2012. Counting Cars is an American reality-television series, shown...
calculated from the box-counting pixel distribution as in Eq.2.0. ϵ {\displaystyle \epsilon } = an arbitrary scale (box size in boxcounting) at which the set...
laid down, the number of pixels that fall within the box is recorded. In standard boxcounting, the box for each ε {\displaystyle \varepsilon } in E {\displaystyle...
using methods such as the boxcounting method or the cluster growing method. Let N B {\displaystyle N_{B}} be the number of boxes of linear size l B {\displaystyle...
Vote counting is the process of counting votes in an election. It can be done manually or by machines. In the United States, the compilation of election...
self-similarity all these dimensions coincide, in general they are not equivalent: Boxcounting dimension: D is estimated as the exponent of a power law. D 0 = lim ε...
Hausdorff dimension is a successor to the simpler, but usually equivalent, box-counting or Minkowski–Bouligand dimension. The intuitive concept of dimension...
gonna happen or come to pass? So, instead of counting sheep, we're counting stars." Sheet music for "Counting Stars" is in the key of C♯ minor with a tempo...
commonly played in a group of two to four for stakes. Traditionally, a countingbox is used with tiles numbered 1 to 9 where each can be covered with a hinged...
(or Higuchi fractal dimension (HFD)) is an approximate value for the box-counting dimension of the graph of a real-valued function or time series. This...
of the voting period. A ballot drop box allows voters who have received a ballot by mail to submit it for counting in a self-service fashion. It will usually...
two-dimensional Vicsek fractal. Wikimedia Commons has media related to Box fractals. Box-counting dimension Cross crosslet List of fractals by Hausdorff dimension...
other methods of measuring dimension (e.g. the Hausdorff dimension, the box-counting dimension, and the information dimension) but the correlation dimension...
quartiles. In addition to the box on a box plot, there can be lines (which are called whiskers) extending from the box indicating variability outside...
\varepsilon }}} The uncertainty exponent can be shown to approximate the box-counting dimension as follows: D 0 = N − γ {\displaystyle D_{0}=N-\gamma \,} where...
omer still has a purpose as a remembrance of the counting up to Sinai. One explanation for the Counting of the Omer is that it shows the connection between...
Box jellyfish (class Cubozoa) are cnidarian invertebrates distinguished by their box-like (i.e. cube-shaped) body. Some species of box jellyfish produce...
century. Chinese arithmeticians used counting rods well over two thousand years ago. In 1954, forty-odd counting rods of the Warring States period (5th...
common boxes: Cabinet selection, slid-lid or hinged lid, typically storing 25 or 50 cigars; 8-9-8, round-sided box with three layers, counting 8, 9 and...
David Parker Ray (November 6, 1939 – May 28, 2002), also known as the Toy-Box Killer, was an American kidnapper, torturer, serial rapist and suspected...
Mathematics and the Built Environment book series. The book applies the boxcounting method for computing fractal dimension, via the ArchImage software system...
star.text.TextDocument") Then MsgBox "This macro must be run from a text document", 64, "Error" Exit Sub End If Count = 0 ' Examine each component - paragraph...
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