Fractal geometry in crumpled paper

[rafael_01]

I've made an experiment similar to the one found here:

http://classes.yale.edu/fractals/fracanddim/boxdim/PowerLaw/CrumpledPaper.html

The result was: the mass of crumpled paper balls is proportional to $$D^n$$, being D their mean external diameter, and n ≈ 2,5.

As $$n$$ is not an integer, the balls are fractals. But I cannot see, exactely, what caracterizes them as fractals.

If you look at a Koch snowflake, for example, it is easy to see that it is self-similar, and that it is not a regular euclidean object, as it's perimeter is infinite.

How can a Koch snowflake and a crumpled paper ball be similar kinds of object?

 

[marcusl]

You are looking at a very interesting and surprisingly complex physical system. (Fun, too!).

Open the ball and look at the pattern of ridges. The ridge lengths are fractal in several senses: first, as you look at the ridges from balls of decreasing diameter, you'll see that the ridge patterns look similar even though they are of different overall lengths (like looking at trees of different sizes, but noticing that the pattern of branches and twigs is scale-free). Second, the ridges in a single sheet also look like a branching tree with similar pattern behavior at the largest and smallest scales.

Here is some related student work with a list of references to the professional literature on crumpled paper:
http://www.maa.org/mathland/mathtrek_05_26_03.html"