Hey muchof.

What kind of iteration scheme are you using? How do you construct the object using your iteration scheme?

Fractals are characterized by this property of iterative-ness which contributes to the quantitative characteristic known as the Hausdorff dimension which should be fractional in the case of a fractal, and a major part of this is related to the self-similarity since this self-similarity creates weird dependencies in the actual information content of the object itself.

This is how you can show something is a fractal.