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 (related to the Cantor triadic set): 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 the first objects of this family (including this one):

The Sierpinski Carpet -iteration 0- 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 Empty The Sierpinski Carpet -iteration 1 to 5-  
Empty 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 07/07/2024 12:20:09 -CEST-)



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