Famous Fractals   

Sierpinski Curve (also: Sierpinski Arrowhead)

The Sierpinski Curve is a base-motif fractal formed using the following base and motif:

In the first iteration, we simply substitute the line segment with the motif. In the second iteration, however, we flip the motif for every other segment, which makes the Sierpinski Curve a sweep. After an infinite number of iterations, we get a figure which is identical to the Sierpinski Triangle:

FRACTAL DIMENSION

Since the final figure is identical to the Sierpinski Triangle, it is most likely that the fractal dimension is the same. Indeed, if we use the similarity method to calculate it, we will see that there are 3 identical line segments in the motif, the size of each of which is 1/2. The fractal dimension will then be log 3 / log 2, which is approximately 1.58.

LENGTH