Dimension Of Sierpinski Carpet

Therefore the similarity dimension d of the unique attractor of the ifs is the solution to 8 k 1rd 1 d log 1 8 log r log 1 8 log 1 3 log 8 log 3 1 89279.

Dimension of sierpinski carpet.

This tool draws the sierpinski carpet fractal with three different sizes of squares as the number of iterations is equal to 3. Sierpiήski carpetrform 2 n 3 andr 0 0 1 1 2 0. Let s see if this is true. Possible sizes are powers of 3 squared.

Here bright colors are used on a canvas size of 558x558px. Whats people lookup in this blog. The hausdorff dimension of the carpet is log 8 log 3 1 8928. The sierpinski carpet is self similar with 8 non overlapping copies of itself each scaled by the factor r 1.

First take a rough guess at what you might think the dimension will be. In these type of fractals a shape is divided into a smaller copy of itself removing some of the new copies and leaving the remaining copies in specific order to form new shapes of fractals. 3x3 9x9 27x27 or 81x81. A very challenging extension is to ask students to find the perimeter of each figure in the task.

In section 3 we recall the. 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. Between 1 and 2. The metric dimension of r is given by.

1 the theorem is proved in section 2. Remember it is a 2d fractal. The sierpinski carpet is a plane fractal curve i e. A curve that is homeomorphic to a subspace of plane.

Sierpiński demonstrated that his carpet is a universal plane curve. Let s use the formula for scaling to determine the dimension of the sierpinski triangle fractal. The sierpinski carpet 1 is a well known hierarchical decomposition of the square plane tiling associated with that is pairs of integers consider the sierpinski graph 2 which is the adjacency graph of the complement of in where is one of the hierarchical subsets of gray squares are used to depict the intersection of with a subset of. Solved now we can apply this formula for dimension to fra 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.

First you have to decide which scale your sierpinski carpet should be. 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. Notion of metric dimension and discuss the following result.