Formal grammar methodology for digital visualization of Islamic geometric patterns

Abstract

In the oriental practice of art and architecture, and among the regions under their influence, Islamic geometric patterns (IGPs) have been widely used, not only due to aesthetics and decoration but also to make it possible to cover wide flat surfaces, curved surface of domes, and perforated surfaces of window and partitions, with perfectly tessellated shapes. However, with advances in time and technology, these techniques could not connect to the new technologies and benefit from the capacities of digitalization. Recent progress in science and technology tends to open new doors to study geometrical patterns by digitalizing the old ones and developing new variations. This study looks at formal grammar and computer science to introduce a new approach to digital visualization of available IGPs, particularly, star patterns. We investigate the potentials of developing a re-writing system for simulation of IGPs to provide a flexible platform, which allows introducing IGP to CAD/CAM software without previous knowledge on their design or drawing techniques. This methodology allows designers to directly develop various scenarios of IGP applications and implement them on related CAD/CAM tools. Formal language and grammar theories, based on applied mathematics are contributing to the advancements of computer science and digital modeling. They can provide an opportunity to express relational definition and written equivalents of the geometries by using strings and symbols. It is supposed that by using the formal grammar frameworks, certain languages could be developed to visualize IGPs in a machine-friendly way, and consequently, this computational interpretation of IGPs facilitates their application and further developments, for example, regards to digital fabrication. The presented method of IGP visualization is developed as a C#-based add-on for Grasshopper in Rhino3D, one of the main modeling tools used by architects and product designers.

Application-based principles of islamic geometric patterns; state-of-the-art, and future trends in computer science/technologies: a review

“…Nasri and Benslimane [127] automatically generated original and new forms of periodic Moorish geometric patterns utilizing underlying grid-based, symmetry-based approaches and shape grammar formalism. More recently, Refalian et al [128] introduced a new approach to digital visualization of available IGPs, particularly star patterns, focusing on formal grammar and computer science.…”

From Sacred Traditions to Digital Syntax: Navigating Formal Grammar's Role in Modelling Contemporary Islamic Geometric Patterns

“…Paul Bourke (1991) extended this to recursive tiling. Refalian et al (2021) explored rewriting systems for modeling Islamic geometric patterns (IGPs), employing specific rules in a step-by-step process. Each step builds patterns using axioms and production rules.…”

Generation of Ceiling Rose Patterns by Shape Grammar Approaches in Safranbolu Traditional Houses

“…It also provides important opportunities for the development of new variations by examining existing geometric patterns. In particular, the use of contemporary techniques has an important place in understanding the geometric logics of the existing cultural heritage and transferring them to the future (Refalian et al, 2021). For this reason, the sustainability of crafts depends on their openness to innovation and similarly, it is a need to use technology for the continuity of ceiling decorations.…”