# The Islamic Star Pattern

**Study of the Control of Geometric Pattern Using Digital Algorithm (with Focus on Analysis and Application of the Islamic Star Pattern)**

##### Jin-Young Lee^{1}, Sung-Wook Kim^{2}, and You-Chang Jeon^{2}

^{1}aDLab+, Suwon-si 16499, Republic of Korea

^{1}aDLab+, Suwon-si 16499, Republic of Korea^{2}Department of Architecture, Ajou University, Suwon-si 16499, Republic of Korea

^{2}Department of Architecture, Ajou University, Suwon-si 16499, Republic of Korea**Figure 1: Basic formation and combination formula of a tessellation.**

This paper presents a study to analyze and modify the Islamic star pattern using digital algorithm, introducing a method to efficiently modify and control classical geometric patterns through experiments and applications of computer algorithms.

**Figure 2: Equilateral polygon combinations.**

This will help to overcome the gap between the closeness of classical geometric patterns and the influx of design by digital technology and to lay out a foundation for efficiency and flexibility in developing future designs and material fabrication by promoting better understanding of the various methods for controlling geometric patterns.

**Figure 3: Islamic strapwork.**

With the advance of digital technology, the development of surfaces in modern structures enjoys an unprecedented freedom of expression.

**Figure 4: Owen Jones, 1856.**

The various ability of computer programs, in tune with the will of designers to discover a new design, accelerates the speed of “limitless” design through proliferation, modification, and trajectory tracking.The rapid development of computer technology results in a tendency to perform unpredictable calculations with the computer using an algorithm beyond the control of the artist.

**Figure 5: Arabic pattern development (Lewis F. Day).**

The development of manufacturing technology has also enabled the construction of various experimental shapes, which provides a good justification as meaningful construction work.

**Figure 8: Variations of patterns using Hankin’s method (Craig S. Kaplan).**

These phenomena try to differentiate themselves from the rules of classical geometry by using terminologies such as “Digital Geometry” and “Digital Materiality.”

**Figure 9: Unit module. Figure 10: 4.8.8 combination.**

To counter this rapid trend, some architects severely limit the role of the computer, refuse designs made by digital programs, and instead produce designs based on the tradition and history of the sense of geometry.

**Figure 11: Transformation of 4.8.8 combination.**

This study will focus on the disparity of such an extreme position regarding the use of computer algorithms in design. The purpose of this study is to identify a connection point of classic geometry and algorithmic design.

**Figure 12: Types of controlling method.**

In other words, to overcome the closeness of classic patterns through studies on the patterns produced by designers and also overcome the influx of design by digital technology, the objective of this study is to introduce a method to efficiently modify and control classical geometric patterns through experiments and applications of computer algorithms.

**Figure 14: Radius control diagram (Type B). Figure 16: Side on segment control diagram (Type D).**

As the analysis object of this study, we used the Islamic star pattern. Specifically, this study selected the 4.8.8 pattern among the modified star pattern examples used in Hankin’s method.

**Figure 17: Basic geometry from diagrid.**

For analysis and experiment control of this pattern, we utilized “Grasshopper” and “Rhinoscript,” which are plugins for the Rhinoceros program by Robert McNeel and Associates, and “Processing” developed by Ben Fry and Casey Reas.

**Figure 18: Algorithmic formula.**

“Tessellation” can be defined as a pattern of more than one shape which completely covers a certain plane. The regular splitting method of a plane is a method which leaves no gaps by using a certain shape, completely fills out the space without overlapping, and does not allow for overlapping of shapes or gaps.

**Figure 23: Type A patterning.**

**Figure 28: Type C patterning.**

Tessellation is typically composed of closed shapes or closed curves, and the simplest kind of closed curve is a polygon. It is possible to develop a polygon into a tessellation composed of complex shapes.

**Figure 31: Pattern variations using Attractor Algorithm.**

The patterns which appear on the Islamic buildings and tiles of the Middle Ages started from simple designs and developed into complex designs with mathematical symmetry over centuries. These complex patterns were modified by the strapwalk method using circles and rectangles in overlapping lattice patterns and were further improved to produce more complicated forms of symmetric patterns.

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