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Islamic geometric patterns (IGP) have been an integral component of Islamic art for centuries. Developed using traditional techniques and tools, these patterns have been profoundly influenced by them. However, the emergence of digital tools has posed novel challenges to the creation and preservation of these intricate designs, leading to compatibility issues between original methodologies and new technologies. Consequently, the process of generating new patterns based on the same syntax has become notably more intricate. This paper delves into the application of Formal Grammar Methodology (FGM), specifically the string rewriting system (SRS), for digital modeling of star patterns that originated in historical Iran, substantiated by existing evidence. We assess the potential of adapting these patterns to the digital realm while respecting their cultural context for design and production purposes. Our study draws upon both historical and contemporary sources to gather, scrutinize, and analyze patterns utilizing both traditional and innovative approaches. The outcomes reveal an 85% success rate for the introduced method, as opposed to 55% for the traditional approach in production.