Finding Fractal Behavior - Methods & Statistical Analysis

[Vaal]

Hi, I have been looking for fractal behavior in a data set. I've used the box method to determine fractal dimension by looking at the inverse of box size and the number of boxes needed to enclose the object. These two variables seem to be fairly accurately predicted by a power law (exponent/fractal dimension around 1.85) but I was hoping for a simple statistical method that explicitly looks for self similarity on different scales. Does anyone have any ideas here?

Thanks in advance for any help.

 

[chiro]

Hey Vaal.

I don't know much about factal dimensions so maybe you could fill in the missing blanks.

If you want to get some kind statistical answer you need to explain the variation involved in terms of a distribution.

What kinds of possible things are you trying to measure (i.e. boxes or areas or lengths with a distribution)? Are you only measuring properties related to boxes? If so do you have a distribution for the sides or the area of the box?

 

[Vaal]

The data is a scalar value for all points in a 2D plane. I am most interested in seeing if patterns that are evident on large scales repeat themselves on smaller scales, like is seen in fractals. I'm interested in both 1D and 2D patterns.

Thanks.