Surah Yusuf’s sinusoidal narrative: cyclical form, character development, thematic oscillation, and computational analysis

Abstract Narrative structure plays a central role in shaping thematic development, rhetorical strategy, and reader engagement. While existing studies on Surah Yūsuf have emphasized coherence, semantic organization, and rhetorical design, approaches that explicitly model cyclical narrative movement and thematic recurrence, particularly through computational methods, remain limited. This study addresses this gap by proposing an analytical framework for examining the internal structure of the surah. The main objective is to analyze the sinusoidal narrative structure of Surah Yūsuf, understood as a pattern of alternating phases of hardship and relief, and to examine how this organization contributes to moral and spiritual engagement. The study does not aim to establish a comparative evaluation between sacred and Western texts; rather, references to linear narratives are used solely for methodological clarification. A descriptive-analytical approach is adopted, combining literary interpretation with computational tools. The methodology includes thematic frequency analysis and the use of oscillation indices implemented in Matlab to identify and quantify narrative patterns related to divine references, moral concepts, and emotional dynamics. The findings reveal a structured oscillatory pattern characterized by cycles of betrayal, patience, forgiveness, and resolution. This wave-like progression reinforces thematic continuity and supports sustained moral and ethical reflection. The study demonstrates that the sinusoidal structure of Surah Yūsuf provides a measurable and reproducible model of narrative organization, in which cyclical progression plays a key role in shaping moral, emotional, and pedagogical engagement, while preserving the specificity of the sacred text.