Famous Fractals   

Minkowski Sausage

Minkowski Sausage is a base-motif fractal formed with a very simple base and motif:

To form it, you first substitute the line segment with the motif. Then, every one of the 8 line segments is substituted with the motif again and the process is continued.

At the end, you get the Minkowski Sausage. If you do the same with a square instead of a line segment for the base, you will get one of the quadric Koch Islands.

FRACTAL DIMENSION

In the Minkowski Sausage, there are 8 identical figures, each of which is 1/4 of the entire figure. Using the similarity method, you can find the fractal dimension of this fractal to be log 8 / log 4, which is equal to 1.5.

LENGTH

Since the Minkowski Sausage is a fractal curve, its length must be infinite. You can verify this by realizing that with every iteration, the length of the curve doubles.