geometry — the Assouad dimension is a definition of fractal dimension for subsets of a metric space. It was introduced by Patrice Assouad in his 1977 PhD...
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In mathematics, the Assouad–Nagata dimension (sometimes simply Nagata dimension) is a notion of dimension for metric spaces, introduced by Jun-iti Nagata...
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Hausdorff dimension Examples of deterministic fractals, random and natural fractals. Assouad dimension, another variation of fractal dimension that, like...
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}(X):=\inf\{d\geq 0:C_{H}^{d}(X)=0\}.} Packing dimension Assouad dimension Local connected dimension Degree dimension: describes the fractal nature of the degree...
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dimension and Assouad–Nagata dimension of a space: a space with asymptotic dimension n is n-dimensional "at large scales", and a space with Assouad–Nagata...
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Doubling space (redirect from Doubling dimension)
531–534. doi:10.1090/s0002-9939-98-04201-4. Jouni, Luukkainen (1998). "ASSOUAD DIMENSION: ANTIFRACTAL METRIZATION, POROUS SETS, AND HOMOGENEOUS MEASURES"....
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Nagata–Biran conjecture, an algebraic formula Nagata dimension or Assouad-Nagata dimension, a notion of dimension for metric spaces Nagata ring, an integral domain...
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is a fractal curve. It is a three-dimensional generalization of the one-dimensional Cantor set and two-dimensional Sierpinski carpet. It was first described...
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differentiability is usually given in terms of fractal dimension, with the Hausdorff dimension the most popular choice. This line of research was started...
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Zürich, 2006; ISBN 978-3-03719-022-7. S. Keith, T. Laakso, Conformal Assouad dimension and modulus. Geometric and Functional Analysis, vol 14 (2004), no...
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Box counting (category Dimension theory)
box counting algorithms have been applied to patterns in 1-, 2-, and 3-dimensional spaces. The technique is usually implemented in software for use on patterns...
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independently by Nagata in 1950 and by Smirnov in 1951, as well as the Assouad–Nagata dimension of a metric space, which he introduced in a 1958 article. Nagata...
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factor 1/2 will create a display of a "Sierpinski Tetrahedron", the three-dimensional analogue of the Sierpinski triangle. As the number of points is increased...
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compute the box-counting dimension of the Cantor set. This notion of fractal dimension can be generalized to that of complex dimension, which may be used to...
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drawing of the boundary, the distance function can be introduced as a 3rd dimension to create a solid fractal landscape. Wikimedia Commons has media related...
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