

University of Washington
Department of Architecture, Spring 2001
[Computational] Geometry in Islamic Architecture
Instructor: Mamoun Sakkal, PhD


Muqarnas, part 1: The basics.
Muqarnas is the Arabic word that describes a traditional element unique
to Islamic architecture, in which small nichlike components are combined
with each other in successive layers to enclose a space and produce surfaces
rich in threedimensional geometric compositions.
Fig. 1. Parts of the Muqarnas block 
I call these components "Muqarnas Blocks."
These blocks change the surface of a space enclosure in a threedim en ti on al
way due to their unique geometry. Although they can take many different
variations in shape, it is possible to simplify the typical block
into basic parts that represent its geometrical function as shown in fig. 1.
This model is produced in FormWriter, a 3D program developed at the University of Washington Architecure school's computer lab. I used the triangle primitive,
and combined the triangles to form pyramids and prisms.
All images on this website were produced by importing the models
created in FormWriter to InfiniD software for final rendering.

Fig. 2. Muqarnas blocks families 
The blocks used in a composition are related to each other in precise geometry.
In regular compositions, the angle of the block's base is increased by increments of one full angle in each successive
block. For example, the 45 degrees family of muqarnas blocks has
three blocks with 45, 90, and 135 degrees as shown in figure 2 from left to right.


Fig. 3. Muqarnas blocks interior surface variations
Each block can have different interior surface configuration without
affecting the basic geometry of the block. The FormWriter program that generates
the blocks allows one to obtain all blocks in a family by defining only one variable, the smallest angle in the family, and to obtain all interior surface variations
by changing another variable. Fig. 3 shows the different variations of interior surfaces in the 45 degrees family if we change the shape of the middle base of each block in regular increments of 11degrees 15 seconds (45/4).

Fig. 4. Muqarnas dome 
The members of each family of muqarnas blocks will fit with each
other to completely enclose space, usually in a domelike structure. The smaller blocks are at the
top of the dome. In each successive layer, the angle of the blocks
is increased. Model of the 30 degrees family dome is shown in fig. 4.
The above program will produce all possible families
of muqarnas blocks simply by entring the value of the smallest angle
in the family.

The blocks are also composed with each other according to rules that
changed from region to region. In part two
I show 2 related examples from Turkey and Armenia.
Revised 05/23/2016 