Box Counting Dimension Sierpinski Carpet

4 2 box counting method draw a lattice of squares of different sizes e.

Box counting dimension sierpinski carpet.

Note that dimension is indeed in between 1 and 2 and it is higher than the value for the koch curve. 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. But not all natural fractals are so easy to measure. Random sierpinski carpet deterministic sierpinski carpet the fractal dimension of therandom sierpinski carpet is the same as the deterministic.

The hausdorff dimension of the carpet is log 8 log 3 1 8928. Box counting analysis results of multifractal objects. 111log8 1 893 383log3 d f. Next we ll apply this same idea to some fractals that reside in the space between 2 and 3 dimensions.

Fractal dimension of the menger sponge. We learned in the last section how to compute the dimension of a coastline. This makes sense because the sierpinski triangle does a better job filling up a 2 dimensional plane. This leads to the definition of the box counting dimension.

Fractal dimension box counting method. To show the box counting dimension agrees with the standard dimension in familiar cases consider the filled in triangle. Sierpiński demonstrated that his carpet is a universal plane curve. A for the bifractal structure two regions were identified.

For the sierpinski gasket we obtain d b log 3 log 2 1 58996. It is relatively easy to determine the fractal dimension of geometric fractals such as the sierpinski triangle. 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.