Construction
The basic square is decomposed into nine smaller squares in the 3-by-3 grid. The four squares at the corners and the middle square are left, the other squares being removed. The process is repeated recursively for each of the five remaining subsquares. The Vicsek fractal is the set obtained at the limit of this procedure. The Hausdorff dimension of this fractal is ≈ 1.46497.
An alternative construction (shown below in the left image) is to remove the four corner squares and leave the middle square and the squares above, below, left and right of it. The two constructions produce identical limiting curves, but one is rotated by 45 degrees with respect to the other.
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Self-similarities I — removing corner squares.
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Self-similarities II — keeping corner squares.
Read more about this topic: Vicsek Fractal
Famous quotes containing the word construction:
“When the leaders choose to make themselves bidders at an auction of popularity, their talents, in the construction of the state, will be of no service. They will become flatterers instead of legislators; the instruments, not the guides, of the people.”
—Edmund Burke (1729–1797)
“No construction stiff working overtime takes more stress and straining than we did just to stay high.”
—Gus Van Sant, U.S. screenwriter and director, and Dan Yost. Bob Hughes (Matt Dillon)
“There is, I think, no point in the philosophy of progressive education which is sounder than its emphasis upon the importance of the participation of the learner in the formation of the purposes which direct his activities in the learning process, just as there is no defect in traditional education greater than its failure to secure the active cooperation of the pupil in construction of the purposes involved in his studying.”
—John Dewey (1859–1952)