TERMIUM Plus®

The Government of Canada’s terminology and linguistic data bank.

APPENZELL SWISS CHEESE [1 record]

Record 1 1995-10-16

English

Subject field(s)
  • Mathematics
  • Computer Graphics
DEF

A lacunary fractal named by Mandelbrot after the Swiss cheese it resembles most.

CONT

Smallish round tremas, in white, and random slices of "swiss cheese" (Dimension D=1.9900 and D=1.9000). The tremas are white circular discs. Their centers are distributed at random on the plane. For the disc of rank p, the area is K(2-D)/p, the numerical constant then being chosen suitably to fit the trema model described in the text. Plate 306 shows a sort of Appenzeller wherein the black portion is of dimension D=1.9900, and Plate 307 a sort of Emmenthaler with a black portion of dimension D=1.9000.

French

Domaine(s)
  • Mathématiques
  • Infographie
CONT

Tranches de "fromage fractal d'Appenzell", à trous ronds aléatoires. On retranche du plan une série de trémas circulaires, marqués en blanc, ayant des centres distribués au hasard (distribution de Poisson) et des rayons choisis de façon à assurer l'homothétie interne statistique [...]. On permet à un petit tréma d'intersecter un autre plus grand. Il n'est pas étonnant d'apprendre que, si la construction ci-dessus est poussée à l'infini, le reste sera de surface nulle, mais notre intuition ne nous dit pas si réellement quoi que ce soit va rester et, dans l'affirmative, si le reste sera fait de fils connexes ou d'une poussière de points.

Spanish

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