A computational interpretative design model for exploring Iranian geometrical patterns

Abstract

Geometry is one of the distinguishing characteristics of Iranian art and architecture. This valuable art is endangered because the original designers did not provide comprehensive documentation. To preserve this invaluable cultural heritage, designers must understand these geometrical patterns' underlying principles and rules. This knowledge will enable them to generate new patterns accurately and restore damaged ones. As the patterns are complex and contain many mathematical rules, generating them necessitates a transferable knowledge of computational methods. Today, with the development of technology, especially computer science, it is possible to draw complicated geometries, analyze existing geometries, and generate entirely new ones. This research explores the historical and cultural significance of Islamic geometrical patterns, with examples from Iranian architecture, analyzing their traditional design rules and their evolution through time. To address this, computational design techniques as a modern approach to reinterpret and expand the potential of geometric patterns are adopted. Iranian geometrical patterns are categorized into two layers of 2-dimensional and 3-dimensional patterns. From 2-dimensional patterns, some prominent patterns in Iranian architecture are analyzed and generated with computational design methods. The methodology involves identifying the underlying rules of these patterns. An algorithmic design method is employed to generate patterns by automating their intricate relationships and modular structures. This method allowed for the precise reproduction of selected patterns and experimentation with new configurations while adhering to traditional rules. In parallel, a graph-theory approach is introduced as a novel method for pattern generation. This method redefines patterns as networks of nodes and edges, offering a highly flexible and abstract framework for pattern design. The graph-based approach enables a generative and parametric workflow, allowing for more creative and complex variations. The study also compares the effectiveness of these two computational methods, evaluating their strengths and weaknesses. To evaluate these methods, a comparative study using the Analytic Hierarchy Process (AHP) with expert feedback is conducted. The results revealed that while algorithmic design is effective in maintaining traditional integrity, the graph-theory approach allows for greater creative freedom by breaking away from strict rule-based constraints. Both approaches not only faithfully reproduce existing patterns but also enable the creation of entirely new designs, contributing to the preservation and innovation of this valuable heritage. Building on this, the study extended the application of graph theory to explore its potential for generating 3-D patterns for future works. A 3-D Muqarnas was successfully designed using graph-theory algorithms, demonstrating the method's versatility and capability in creating complex, generative 3-D structures. This finding highlights the adaptability of graph theory in pattern generation, offering a robust framework for computational design. This work contributes to the growing intersection of mathematics, architecture, and computational design, offering new pathways for preserving cultural heritage while fostering creative exploration in the digital era. The dissertation shows that cultural heritage could be preserved with computational techniques and encourages designers to use computational tools and methods in their design. Yet, designers should search for ways to expand existing implementations by active participation.