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BOULIGAND DIMENSION [1 record]

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Record 1 1995-10-16

English

Subject field(s)
  • Mathematics
  • Computer Graphics
DEF

A nontrivial dimension introduced by H. Minkowski for different purposes and extended to fractals by G. Bouligand.

CONT

The definition of length based on the coastline being covered by a tape of width 2 implements an idea of Cantor and Minkowski, and the corresponding dimension is due to Bouligand.

French

Domaine(s)
  • Mathématiques
  • Infographie
CONT

Il y a équivalence de la dimension de Bouligand globale avec la capacité supérieure de Kolmogorov. Lorsque la dimension de Bouligand locale prend une valeur unique sur tout l'ensemble A, cette valeur est la dimension de Hausdorff de A.

CONT

La méthode des mailles utiles de Bouligand se prête le mieux à l'évaluation de l'étendue des courbes irrégulières. La dimension de Bouligand (ou de Kolmogorov, qui lui est équivalente) peut s'estimer simplement par cette méthode.

Spanish

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