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  2. Minkowski–Bouligand dimension - Wikipedia

    en.wikipedia.org/wiki/Minkowski–Bouligand...

    Estimating the box-counting dimension of the coast of Great Britain. In fractal geometry, the Minkowski–Bouligand dimension, also known as Minkowski dimension or box-counting dimension, is a way of determining the fractal dimension of a bounded set in a Euclidean space, or more generally in a metric space (,).

  3. Sphere packing - Wikipedia

    en.wikipedia.org/wiki/Sphere_packing

    In three dimensions the Böröczky bound is approximately 85.327613%, and is realized by the horosphere packing of the order-6 tetrahedral honeycomb with Schläfli symbol {3,3,6}. [30] In addition to this configuration at least three other horosphere packings are known to exist in hyperbolic 3-space that realize the density upper bound.

  4. Minimum bounding box algorithms - Wikipedia

    en.wikipedia.org/wiki/Minimum_bounding_box...

    In computational geometry, the smallest enclosing box problem is that of finding the oriented minimum bounding box enclosing a set of points. It is a type of bounding volume. "Smallest" may refer to volume, area, perimeter, etc. of the box. It is sufficient to find the smallest enclosing box for the convex hull of the objects in question. It is ...

  5. Hausdorff dimension - Wikipedia

    en.wikipedia.org/wiki/Hausdorff_dimension

    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.

  6. Fractal dimension - Wikipedia

    en.wikipedia.org/wiki/Fractal_dimension

    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 ...

  7. Minimum bounding box - Wikipedia

    en.wikipedia.org/wiki/Minimum_bounding_box

    A sphere enclosed by its axis-aligned minimum bounding box (in 3 dimensions) In geometry, the minimum bounding box or smallest bounding box (also known as the minimum enclosing box or smallest enclosing box) for a point set S in N dimensions is the box with the smallest measure (area, volume, or hypervolume in higher dimensions) within which all the points lie.

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