Famous Fractals   

Levy Tapestry

The Levy Tapestry is formed the same way as the Levy Curve, only a square is used for the base instead of a line segment. We can form two different fractals using this base, depending on whether we place the motif inside or outside the square.

In the first step, we take the square and substitute every side with the motif. We then continue substituting line segments with the motif. With increasing number of iterations, the fractals becomes amazingly complex. After a very large number of iterations, the two fractals are the following:

FRACTAL DIMENSION

The fractal dimension of the Levy Tapestry can be calculated very easily using the similarity method. There are 2 identical line segments in the motif, each of which has to be magnified sqr(2) times to become the same size as the base line segment. The dimension is, thus, log 2 / log(sqr(2)), which is equal to 2. This means that both of the above fractals are Peano curves.

LENGTH

At every iteration, the fractal becomes sqr(2) times longer. This means that after an infinite number of iterations the fractal will become infinitely long, just like all fractal curves do.