Parametric Approach to Islamic Goemetric Patterns

Parametric Approach to re-creating Islamic Geometric Patterns.

Assignment 2: Extended Research Abstract K14DDF- Digital Architecture and Digital Fabrication Sanjay Somanath, Student ID - 4313018

1. Introduction & Research Aim

Figure 1 - Time chart of the evolution of IGP’s throughout history” (Abdullahi and Embi, 2013)

For centuries, Islamic artists used a simple compass and a straightedge to construct Islamic Geometric Patterns (IGP) . Hence the basic understanding is that all IGP originate from the regular subdivision of circles and repetition with a grid reference. Since the nature of geometric patterns (star shaped, rosette patterns, etc.. ) dictates only the final form, the originating guidelines to create this design may vary.

The four-pointed and eight-pointed geometric patterns are two of the simplest patterns that form the basis for many of the IGP (Dabbour, 2012).

Using the “Time chart of the evolution of IGP throughout history” (Abdullahi and Embi, 2013)

Islamic Geometric Patterns |1

It is understood that roughly during the year 836 - at the initial stages of IGP, the emergence of “sporadic geometric shapes” is seen. For example, the great mosque of Kairouan in Tunisia.

Using the principles laid out in both the papers by Dabbour, Abdullahi and Embi; it is possible to recreate the IGP with increasing orders of complexity using parametric tools.

2. Literature Review 2.1. Evolution of Islamic geometric patterns - Frontiers of Architectural Research The research documents and retraces the path taken on by the evolution of Islamic Geometric Patterns from the year 800 to the 18th century carried over by different rulers, dynasties and generations.

An interesting aspect of the documentation is how Abdullahi and Embi show the relationship of the different styles to the geographical and socio-political conditions of the the region.

“The relatively stable government and economy during the Mamluk period encouraged architects to design very fine and detailed ornaments that are unique in terms of complexity” - (Abdullahi and Embi, 2013)

2.2. Geometric proportions: The underlying structure of design process for Islamic geometric patterns. Frontiers of Architectural Research The paper discusses how the geometric proportions in a geometric pattern serve as both a self-guiding method of esthetically proven design as well as helps to regulate the order of patterns (Dabbour, 2012). Understanding the implications of the changes in proportions could prove to be insightful in appreciating the complexity of these designs. Since geometric proportions are deeply woven into the roots of IGP, with the help of parametric design tools these proportions may be varied parametrically and may lead to a new perspective into analyzing IGP

Islamic Geometric Patterns |2

2.3. Parquet deformation of IGP using Hankins method

Figure 2 - Tiles in a parquet deformation metamorphose. Illustration: Craig Kaplan

With the advent of parametric design the evolution of the IGP need not stop with traditional construction techniques. As demonstrated by Kaplan and Salesin using Hankins method to generate nonperiodic plane tiling patterns we can create IGP’s using the same basic principle but too complex to be derived using basic geometrical tools and calculation. (Kaplan, C. and Salesin, D., 2004).

In the 1960s an American architecture professor, William Huff, coined the term ‘parquet deformation’ to mean a regular pattern of tiles that transforms as you go from left to right whilst maintaining the regularity of the tiling.(Bellos, 2017)

William Huff did not attempt any parquet floorings in this fashion rather he was interested in the way that the patterns could be read from either sides due to their nonperiodic plane tiling. […] In this way, it makes the pattern a ‘temporal’ composition – and possibly the nearest that geometry comes to music, which is also appreciated temporally. (Bellos, 2017)

3. Methodology The methodology of this research is divided into two parts, the gathering of research data and analysis of the research data.

Islamic Geometric Patterns |3

The source for the research data is from historical documentation of Islamic architecture from the year 800 to the 18th century. This research builds on the information documented in the research paper by Abdullahi and Embi from 2013 (Evolution of Islamic geometric patterns Frontiers of Architectural Research) The analysis is done by breaking down the geometric patterns and experimenting with different techniques to recreate them Step 1 - Identify Category of Islamic Geometric Pattern Step 2 - Trace the Pattern to identify the basic unit as well as Grid type Step 3 - Research different techniques of construction and identify the most optimal method Step 4 - Apply optimal construction technique within Grasshopper and optimize script Step 5 - Repeat Basic unit on Grid Step 6 - Change Parameters to identify similarities to other patterns Step 7 - Use attractor curves to deform pattern.

4. Analysis 4.1. Sporadic Pattern Forming - A

Figure - Sporadic pattern using "The western method"

Figure - Sporadic pattern using the "Traditional method"

Figure 3 - Western and Traditional construction techniques How to properly draw Geometric Patterns - Introduction.

(2017)

A sporadic pattern is created from a simple and seemingly random geometric shape.

For example, as shown in fig. 3 an attempt to draw the same basic sporadic IGP using two methods can be seen. The first figure refers to the “Western Method� which involves an intricate series of 24 construction lines and a circle before one can even start drawing the Islamic Geometric Patterns |4

actual pattern, whereas the second figure refers to a “Traditional Method� to draw the same IGP that involves only 10 lines and 4 arcs.

Figure 4 - Grasshopper logic showing the pattern creation for Sporadic geometric pattern - A

The same patterns can be recreated parametrically using Rhino 3d and Grasshopper using basic commands such as move, join, mirror and array.

It all begins with creating the reference geometry such as the square, diagonals of the squares, bisecting angles etc. to connect points to form the basic unit. This basic unit is then mirrored in the correct orientations to form the primary tiling unit.

Figure 5 - Sporadic pattern A.

Islamic Geometric Patterns |5

Figure 6 - Sporadic Pattern A - with change in point spacing.

Figure 7 - Sporadic Pattern A - with change in grid spacing.

This primary unit is then applied to a regular square grid and the pattern begins to emerge.

In addition to that changing the values of the radius of the arc from 1 to 4 units and grid from 30 to 0 and 15 give us different variations of the same motif.

4.2. Sporadic Pattern Forming - B In the next example for sporadic pattern formation, the Timurid infinity pattern starts off with a basic unit. This unit again is constructed from a simple square. Basic operations are once again applied on the square such as connecting the diagonals, bisecting the angles and drawing arcs from opposite diagonal points.

Islamic Geometric Patterns |6

Figure 8 - Grasshopper logic showing the creation of Sporadic pattern B

Figure 9 - Basic Unit.

Figure 10 - Primary repeating unit

This unit is mirrored and sampled into the primary unit. Once a simple grid repetition is added one can see the true pattern come out. It is important to know that all shapes must be symmetric and have regular predictable angles.

Figure 11- Grasshopper logic for pattern creation.

Islamic Geometric Patterns |7

Figure 12 - Sporadic pattern - B

Figure 13 - Sporadic pattern - B with point offset changed

Figure 14 - Overlapped patterns

Figure 15 - Overlapped patterns (zoomed)

The patterns can be infinitely manipulated by controlling simple parameters such as distance of point offsets that were defined in the initial stage, the smallest changes in the parameters result in completely new and unique patterns (fig. 14).

This pattern can be taken further by incorporating a secondary geometry within the shape and adding colors using a “recolor mesh� component (fig. 15).

Islamic Geometric Patterns |8

5. Findings & Conclusion The literature study and research in this abstract has led to different techniques of recreating IGP parametrically by trying to understand the basic principles of proportions and physical construction techniques behind the patterns. Due to the numerous types of patterns, even though the driving principles seem to be relatively similar, it may not be possible to recreate them parametrically using a single technique. Each of these patterns are unique, but using parametric tools to create them allows for a dynamic variation in these patterns using simple controls like sliders (that change initial basic values). This gives an interesting look into deformations of these patterns which would otherwise not be possible without the help of these tools.

The parametric deformations can further be explored by using Hankins method of nonperiodic tiling. This method stays more true to the original principles of IGP of creating a regular pattern of tiles that transforms sequentially without breaking the continuity of the lines.

Modern deformations of Islamic motifs are currently a form of pastiche, not paying attention to the roots of the design but using parametric tools to recreate these deformations seems to uphold the concepts held within the traditional IGP.

7. Further Research The potential of using parametric pattern creation opens up a numerous avenues for further research. One such interesting aspect of these techniques would be to extract the parametric geometry and create planar surfaces and further extrude them and implement them in 3-Dimensional forms.

Using a combination of true to form Islamic Geometric patterns with innovative and novel techniques of creation will allow for the creation of interesting architectural spaces. This movement has already been taking hold in the Middle East with architects like Jean Nouvel implementing IGP in mashrabiyas in projects like the Burj Doha in Qatar and The Louvre Abu Dhabi and even into building kinetic facades such as the Al- Bahar Tower - Abu Dhabi.

Islamic Geometric Patterns |9

8. References Abdullahi, Y. and Embi, M. (2013). Evolution of Islamic geometric patterns. Frontiers of Architectural Research, 2(2), pp.243-251.

Bellos, A. (2017). Crazy paving: the twisted world of parquet deformations. The Guardian.

[Online] Available at: https://www.theguardian.com/artanddesign/alexs-adventures-innumberland/2014/sep/09/crazy-paving-the-twisted-world-of-parquet-deformations [Accessed 22 Dec. 2017].

Critchlow, K. (1976). Islamic patterns. London: Thames and Hudson.

Dabbour, L. (2012). Geometric proportions: The underlying structure of design process for Islamic geometric patterns. Frontiers of Architectural Research, [online] 1(4), pp.380-391.

Available at: http://www.sciencedirect.com/science/article/pii/S2095263512000635 [Accessed 20 Dec. 2017].

How to properly draw Geometric Patterns - Introduction. (2017). [Online Video] http://www.alkatat.com/.

Kaplan, C. and Salesin, D. (2004). Islamic star patterns in absolute geometry. ACM Transactions on Graphics, 23(2), pp.97-119.

Islamic Geometric Patterns |10