Famous Fractals

Snowflake Sweep

Snowflake Sweep is a name given to any fractal which fills the Koch Snowflake:

All of the Snowflake Sweeps are base-motif fractal that use a line segment for the base and one of the following motifs:

Since the Snowflake Sweeps are sweeps, you have to flip the motif upside-down at certain times during iteration. At any point in iteration, you can also use either the original motif, or its mirror image. Using different sequences of these two versions of the motif, you can create an infinite variety of Snowflake Sweeps. The following is an example of a Snowflake Sweep formed using the first one of the above motifs. Notice how it fills the Koch Snowflake:

This is another example, now using the second motif:

FRACTAL DIMENSION

Since all Snowflake Sweeps fill a 2-dimensional figure, they can be considered to be Peano Curves. Because of this, their fractal dimension must be equal to 2.

LENGTH

Since a Snowflake Sweep is fractal curve, its length must be infinite. This is true of all fractal with fractal dimension greater than 1.