Area Of Sierpinski Carpet

A sierpinksi carpet is one of the more famous fractal objects in mathematics.

Area of sierpinski carpet.

It was first described by waclaw sierpinski in 1916. The sierpinski carpet is a plane fractal curve i e. The sierpinski carpet is a compact subset of the plane with lebesgue covering dimension 1 and every subset of the plane with these properties is homeomorphic to some subset of the sierpiński carpet. As with the gasket the area tends to zero and the total perimeter of the holes tend to infinity.

A very challenging extension is to ask students to find the perimeter of each figure in the task. We have proved that the white portion s area is 1 and being the area of the whole square 1 the are of the black portion must be 1 1 0 so when infinitely many iterations are made the black part doesn t exist and the surface of the sierpinski s carpet is 0. But of course there are many points still left in the carpet. The figures students are generating at each step are the figures whose limit is called sierpinski s carpet this is a fractal whose area is 0 and perimeter is infinite.

Creating one is an iterative procedure. The sierpinski triangle area and perimeter of a you fractal explorer solved finding carpet see exer its decompositions scientific sierpiński sieve from wolfram mathworld oftenpaper net htm as constructed by removing center. Sierpiński demonstrated that his carpet is a universal plane curve. The hausdorff dimension of the carpet is log 8 log 3 1 8928.

There are no ads popups or nonsense just an awesome sierpinski carpet generator. Instead of removing the central third of a triangle the central square piece is removed from a square sliced into thirds horizontally and vertically. Notice that these areas go to 0 as n goes to infinity. This means that the area of c n is 8 9 n for all n.

Start with a square divide it into nine equal squares and remove the central one. Closely related to the gasket is the sierpinski carpet. Created by math nerds from team browserling. Just press a button and you ll automatically get a sierpinski carpet fractal.

Press a button get a sierpinski carpet. That is one reason why area is not a useful dimension for this. A curve that is homeomorphic to a subspace of plane. This means that we have removed all of the area of the original square in constructing the sierpinski carpet.