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Examples of ball packing, ball covering, and box covering. It is possible to define the box dimensions using balls, with either the covering number or the packing number. The covering number () is the minimal number of open balls of radius required to cover the fractal, or in other words, such that their union contains the fractal.
de Bruijn's theorem: A box can be packed with a harmonic brick a × a b × a b c if the box has dimensions a p × a b q × a b c r for some natural numbers p, q, r (i.e., the box is a multiple of the brick.) [15]
The Hausdorff dimension is defined for all metric spaces and, unlike the dimensions considered above, can also have non-integer real values. [6] The box dimension or Minkowski dimension is a variant of the same idea.
There are a number of box types to select from when deciding to make a userbox. The most commonly used design is the "Standard box". It has one square shaped area on the left ("id label") and a larger rectangular space on the right ("info area"). For ease of use, userboxes are typically made using maker-templates that have a number of parameters.
This equation is easily solved for D, yielding the ratio of logarithms (or natural logarithms) appearing in the figures, and giving—in the Koch and other fractal cases—non-integer dimensions for these objects. The Hausdorff dimension is a successor to the simpler, but usually equivalent, box-counting or Minkowski–Bouligand dimension.
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This is a standard size userbox created with Template:Userbox. ... This user provides information using user boxes for religious reasons. User: Rursus ...
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