What Is The Fractal Dimension Of The Sierpinski Carpet

The carpet is one generalization of the cantor set to two dimensions.

What is the fractal dimension of the sierpinski carpet. It starts with a solid white 255 square in this case a 513 513. Here s the wikipedia article if you d like to know more about sierpinski carpet. 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. The area of sierpinski s carpet is actually zero.

An investigation of fractals and fractal dimension perimeter formula area polygon hexagon losange blue angle fractals. Note that dimension is indeed in between 1 and 2 and it is higher than the value for the koch curve. The interior square is filled with black 0. The sierpinski triangle i coded here.

For instance subdividing an equilateral triangle. Area and perimeter of a sierpinski triangle you solved finding the perimeter of a sierpinski carpet see exer sierpinski triangle perimeter you area and perimeter of a sierpinski triangle you. The technique of subdividing a shape into smaller copies of itself removing one or more copies and continuing recursively can be extended to other shapes. Whats people lookup in this blog.

Fractal dimension of the menger sponge. This makes sense because the sierpinski triangle does a better job filling up a 2 dimensional plane. Here are 6 generations of the fractal. How to construct it.

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. The sierpinski carpet is self similar pattern with 8 non overlapping copies of itself. What this basically means is the sierpinski carpet contains a topologically equivalent copy of any compact one dimensional object in the plane. The sierpiński carpet is a plane fractal first described by wacław sierpiński in 1916.

This is divided into nine smaller squares. Sierpinski s carpet also has another very famous relative. Next we ll apply this same idea to some fractals that reside in the space between 2 and 3 dimensions. The sierpinski carpet is a fractal pattern first described by waclaw sierpinski in 1916.

The sierpiński triangle sometimes spelled sierpinski also called the sierpiński gasket or sierpiński sieve is a fractal attractive fixed set with the overall shape of an equilateral triangle subdivided recursively into smaller equilateral triangles. Whats people lookup in this blog. A very challenging extension is to ask students to find the perimeter of each figure in the task.