I suggest reading this:

The Fractal Urban Fabric. Emptiness as an Urban Planning Item

By Cîrnu, Lilian published in Geopolitics, History and International Relations, January 1, 2014

 شكرا جزيلا

Thank you for the recomendation , very kind. now i'm searching for the paper.

Cirnu Lilian analysed romanian suburban areas by using P.FRANKHAUSER's method, a strong method to analyse the urban sprawl .

The box-counting method is too mechanistic. Instead, I would suggest some organic or natural ways of determining fractals; see the related papers on the new definition of fractal:

Article Ht-Index for Quantifying the Fractal or Scaling Structure of...

Article A Topological Representation for Taking Cities as a Coherent Whole

Dear PR JIANG,

thanks so much for the suggestions and for the papers, i'm reading exhaustively .

Iam really grateful.

Best regards,

BEKHELIFI A.A.

@ Ahmed El Amine Bekhelifi Thank you for your stimulating question first!

The fractal geometry I referred to is a new kind of fractal geometry, which is defined from the bottom up, instead of Mandelbrot's fractal geometry essentially from the top down. This new fractal geometry is more in line with Alexander's living geometry, characterized by the 15 fundamental properties. It aims, first and foremost, for creating fractal or living structure, and in the mean time, for better understanding complexity of natural and societal phenomena; see my recent talk Presentation Geospatial Big Data and Living Structure For better Understa...

Dear PR JIANG,

I don't know how to thank you for the kindness and for the generosity,

I Am really grateful.

Best regards,

BEKHELIFI A.A.

@ Ahmed El Amine Bekhelifi

Along the line of what I suggested above on new fractal geometry, two tools we developed are of great use for in-depth research: Axwoman and head/tail breaks. These two tools are particularly useful for extracting natural cities and natural streets. Herewith some links:

http://www.arcgis.com/home/item.html?id=47b1d6fdd1984a6fae916af389cdc57d

http://fromto.hig.se/~bjg/axwoman/

https://en.wikipedia.org/wiki/Head/tail_Breaks

This call for papers might be of your interest:

Poster CALL FOR PAPERS Fractal Geometry in Cartography and Geograph...

The log-log plot gives an excellent power law fit, but I still encourage you to try the binned method. In the mean time, calculate the ht-index, which is a better indicator for scaling hierarchy.