Box Counting Dimension Sierpinski Carpet

The hausdorff dimension of the carpet is log 8 log 3 1 8928.

Box counting dimension sierpinski carpet.

To show the box counting dimension agrees with the standard dimension in familiar cases consider the filled in triangle. Fractal dimension of the menger sponge. A for the bifractal structure two regions were identified. This leads to the definition of the box counting dimension.

Sierpiński demonstrated that his carpet is a universal plane curve. Fractal dimension box counting method. Random sierpinski carpet deterministic sierpinski carpet the fractal dimension of therandom sierpinski carpet is the same as the deterministic. The gasket is more than 1 dimensional but less than 2 dimensional.

For the sierpinski gasket we obtain d b log 3 log 2 1 58996. 4 2 box counting method draw a lattice of squares of different sizes e. To calculate this dimension for a fractal. This makes sense because the sierpinski triangle does a better job filling up a 2 dimensional plane.

It is relatively easy to determine the fractal dimension of geometric fractals such as the sierpinski triangle. But not all natural fractals are so easy to measure. The values of these slopes are 1 8927892607 and 1 2618595071 which are respectively the fractal dimension of the sierpinski carpet and the two dimensional cantor set. 111log8 1 893 383log3 d f.

We learned in the last section how to compute the dimension of a coastline. Next we ll apply this same idea to some fractals that reside in the space between 2 and 3 dimensions. Note that dimension is indeed in between 1 and 2 and it is higher than the value for the koch curve.