click to view the MPEG movie (cliquez pour voir le film MPEG)

The construction process of the Sierpinski carpet [Le processus de construction du tapis de Sierpinski].




Definition of the Sierpinski carpet: A square is cut into 3x3=9 identical smaller squares. Then the central subsquare -grey- is removed. At last this process is iterated recursively with the 9-1=8 remaining subsquares. The fractal dimension of the Sierpinski carpet is equal to:
                     log(8)
                    -------- = 1.892789260714372
                     log(3)


See some related pictures (possibly including this one):

The Sierpinski carpet -iteration 1- The Sierpinski carpet -iteration 2- The Sierpinski carpet -iteration 3- The Sierpinski carpet -iteration 4- The Sierpinski carpet -iteration 5-  
Empty Empty Empty Empty The Sierpinski carpet -iteration 5-  
Empty Empty The Sierpinski carpet -iteration 3- with colors -a tribute to Karl Menger and Piet Mondrian- Empty Empty


(CMAP28 WWW site: this page was created on 02/11/2018 and last updated on 07/15/2018 11:51:15 -CEST-)



[See all related pictures (including this one) [Voir toutes les images associées (incluant celle-ci)]]

[Please visit the related ImagesDidactiques picture gallery [Visitez la galerie d'images ImagesDidactiques associée]]
[Go back to AVirtualSpaceTimeTravelMachine [Retour à AVirtualSpaceTimeTravelMachine]]
[The Y2K bug [Le bug de l'an 2000]]

[Site Map, Help and Search [Plan du Site, Aide et Recherche]]
[Mail [Courrier]]
[About Pictures and Animations [A Propos des Images et des Animations]]


Copyright (c) Jean-François Colonna, 2018.
Copyright (c) CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / Ecole Polytechnique, 2018.