Traditional built environments are surely complex adaptive systems. To prove it, one needs to use a topological representation of wholeness based on either natural streets or natural cities, e.g.

Article A Topological Representation for Taking Cities as a Coherent Whole

Chapter A City Is a Complex Network

Dear Professor Jiang,

Really grateful, if there is a real generous researsher on resarchgate, is you, many thanks.

Best regards,

My thesis deals with the continuation of hypotheses presented by Pr. Benhamouche, which were introduced in two of his papers published in Nexus Netowrk Journal (papers attached below).

In other words, I aim to verify the hypotheses using a quantitative approach. 

My goal is to demonstrate:

- That the fabrication of traditional urban tissues  in Algeria is a process, (such as traditional carpets) produced by Islamic rules?

- Which morphogenesis of traditional tissues? Is this processes that follows Islamic rules based on: emergence? Fractals? Chaos?

- Whether the Islamic city is a complex system? or and adaptive complex system?

- What modeling is more accurate in this context: cellular automata? Agent Based modeling? Network analysis? .....????

I suggest fractal geometry under the third definition: a set or pattern is fractal if the scaling of far more smalls than larges recurs at least twice:

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

Instead of fractal dimension, you could use ht-index or fht-index to characterize fractal or complexity of a fractal:

Article How Complex Is a Fractal? Head/tail Breaks and Fractional Hierarchy

The reason I suggest ht-index or fht-index is that box-counting fractal dimension is a bit too mechanical; see this editorial:

Article Editorial: Spatial Heterogeneity, Scale, Data Character, and...

https://youtu.be/pVUquwnwcvc

Thanks, it need a real deep lecture.

https://twitter.com/binjiangxp/status/1009506398571515904

After a large study of different complex systems based methods I'm considering to use graph theory and network theory to analyze urban street patterns (based on toplogical indicators).

Among these software tools ArcGIS and NetworkX which do you recommand to use?, what are your suggestions beyond this set ?

AXWOMAN: http://giscience.hig.se/binjiang/axwoman/

Presentation AXWOMAN: Towards a Design Tool for Smart Cities

Note that none of GIS tools such as ArcGIS is able to develop insight into CAS. The reason is well explained in the following papers or presentations:

Presentation A Geospatial Perspective on Sustainable Urban Mobility in th...

Article Spatial heterogeneity, scale, data character, and sustainabl...

Article New Paradigm in Mapping: A Critique on Cartography and GIS

Presentation New Paradigm in Mapping: A Critique on Cartography and GIS

We are all the prisoner of Descarte's mechanistic thinking. To make smart built environments as well as beautiful artifacts, we should get out of the prison, and re-think under Alexander's organic thinking:

https://www.researchgate.net/publication/331431075_Christopher_Alexander_and_His_Life's_Work_The_Nature_of_Order