Islamic Architecture by Dxx : Patterns

Imam Mosque in Isfahan, Iran

Muqarnas :
the Muqarnas is basically a three-dimensional decoration of Islamic architecture.It was initially built to be structural in purpose made out of stone, but later on it became of a more crafted decoration and made of plaster, these clusters niches were used to decorate the area between the wall and the dome in Islamic architecture.
it can also be defined as : Honeycomb or stalactite vaulting.

The main pieces used for muqarnas and their flat projections
reference website : http://castera.net/entrelacs/public/articles/Z-M-Q.htm

Professor Shiro Takahashi has thoroughly documented the architectural records of the Muqarans with hundereds of details of its geometric plan views, in his documentation he has calssified them into three categories in attempt to clarify the formative styles of Muqarnas.

The three basic classifications are :
1) Square Style:

2) Pole table Style:

3) Other styles :

I would highly recommend going to his website for a complete database of detailed plans for all the types of muqarnas in Islamic architecture thoroughly researched and analyzed.

A snapshot of Professor Shiro Takahashi's website

On the www.designcoding.net website you will also be able to find a simple grasshopper definition and a rhino file where these patterns are created. The design in simple but it is useful to understand the basics of creating these geometries in 3D.
http://www.designcoding.net/parametric-muqarnas/

If you are interested in creating some of these geometries yourself, you can find a research paper in www.academia.edu called (MUQARNAS RECONCEIVED - A BRIEF SURVEY: An Islamic Space-enclosing System - Techniques for Designing Muqarnas Forms), the paper explains the techniques and geometrical basis on how to design a Muqarnas.

Link of the pdf file here :
https://www.academia.edu/5734042/MUQARNAS_RECONCEIVED_-_A_BRIEF_SURVEY_An_Islamic_Space-enclosing_System_-_Techniques_for_Designing_Muqarnas_Forms