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For many well behaved fractals all these dimensions are equal; in particular, these dimensions coincide whenever the fractal satisfies the open set condition (OSC). [1] For example, the Hausdorff dimension, lower box dimension, and upper box dimension of the Cantor set are all equal to log(2)/log(3). However, the definitions are not equivalent.
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Dimensioners are weighing and volume measuring systems for measuring three-dimensional or cuboid-shaped objects such as packages, parcels, pallets, cartons and boxes. They are frequently used as part of a much larger logistical system in a distribution center , warehouse or trucking terminal facility.
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The boundary and the set itself have the same Hausdorff dimension. [27] 2: Julia set: For determined values of c (including c belonging to the boundary of the Mandelbrot set), the Julia set has a dimension of 2. [27] 2: Sierpiński curve: Every space-filling curve filling the plane has a Hausdorff dimension of 2.
The terms fractal dimension and fractal were coined by Mandelbrot in 1975, [16] about a decade after he published his paper on self-similarity in the coastline of Britain. . Various historical authorities credit him with also synthesizing centuries of complicated theoretical mathematics and engineering work and applying them in a new way to study complex geometries that defied description in ...