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ARNOLDS CAT [1 record]

Record 1 2012-01-26

English

Subject field(s)
  • Mathematics
  • Computer Graphics
DEF

A two-dimensional map used for the description of Hamiltonian nonlinear systems. The distortion engendered by this transformation is reminiscent of a maladjusted out-of-sync television set. The map is expanding in one direction and contracting in the orthogonal direction.

CONT

Dr. Arnold’s math explanations also exhibited playfulness. In one of his books, he explained a simple algorithm that stretches and rearranges an image, shredding it into a chaotic mess. In the book, Dr. Arnold illustrated the idea with a sketch of a cat’s head that is now known as Arnold’s Cat Map.

OBS

A word about spelling: we use "Arnold", as opposed to "Arnol'd"; the latter is closer to the Russian pronunciation, but Vladimir Arnold preferred the former (it is used in numerous translations of his books into English) ...

Key term(s)
  • Arnol'd's cat map
  • Arnol'd's cat

French

Domaine(s)
  • Mathématiques
  • Infographie
DEF

Transformation discontinue inversible caractérisée par une conservation des aires : la contraction d'un facteur 1/2 le long de l'axe vertical est compensée par une dilatation d'un facteur 2 le long de l'axe horizontal.

Spanish

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