What Is The Fractal Dimension Of The Sierpinski Carpet

Sierpinski used the carpet to catalogue all compact one dimensional objects in the plane from a topological point of view.

What is the fractal dimension of the sierpinski carpet.

Note that dimension is indeed in between 1 and 2 and it is higher than the value for the koch curve. The area of sierpinski s carpet is actually zero. Sierpinski s carpet also has another very famous relative. Whats people lookup in this blog.

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. The sierpinski carpet is self similar pattern with 8 non overlapping copies of itself. The carpet is one generalization of the cantor set to two dimensions. Another is the cantor dust.

Originally constructed as a curve this is one of the basic examples of self similar sets that is it is a mathematically generated. Here are 6 generations of the fractal. How to construct it. Whats people lookup in this blog.

Here s the wikipedia article if you d like to know more about sierpinski carpet. Next we ll apply this same idea to some fractals that reside in the space between 2 and 3 dimensions. The interior square is filled with black 0. 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 triangle i coded here. 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. This makes sense because the sierpinski triangle does a better job filling up a 2 dimensional plane. A very challenging extension is to ask students to find the perimeter of each figure in the task.

The sierpinski carpet is a fractal pattern first described by waclaw sierpinski in 1916. For instance subdividing an equilateral triangle. 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 technique of subdividing a shape into smaller copies of itself removing one or more copies and continuing recursively can be extended to other shapes.

This is divided into nine smaller squares. Fractal dimension of the menger sponge. An investigation of fractals and fractal dimension perimeter formula area polygon hexagon losange blue angle fractals.