<p>This study examines rhythmic repetition in the historic façades of Isfahan through a computational framework based on Fourier series analysis. Nine representative monuments along the city’s central north–south corridor were analyzed, yielding a dataset of 98 repetitive modules extracted from archival elevation drawings. Spectral decomposition and clustering revealed a dominant harmonic profile with a wavelength of λ = 2π/1.8365, corresponding closely to the modular spacing of Safavid compositions such as Si–o–Se Pol, Khajoo Bridge, and Naqsh-e Jahan Square. The alignment between Fourier-derived coefficients and measured architectural intervals indicates that harmonic modulation underlies both rhythmic legibility and proportional coherence. Furthermore, the normalized mean Fourier function was implemented in a parametric interface, demonstrating its generative capacity for façade design. The study demonstrates that Fourier-based analysis offers both a diagnostic lens for heritage rhythms and a generative tool for contemporary computational design.</p>

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Fourier Spectral Analysis of Architectural Rhythms: Case Study of Historic Isfahan

  • Yasaman Daram,
  • Seyyed Mostafa Mokhtabad Amrei,
  • Hossein Zabihi

摘要

This study examines rhythmic repetition in the historic façades of Isfahan through a computational framework based on Fourier series analysis. Nine representative monuments along the city’s central north–south corridor were analyzed, yielding a dataset of 98 repetitive modules extracted from archival elevation drawings. Spectral decomposition and clustering revealed a dominant harmonic profile with a wavelength of λ = 2π/1.8365, corresponding closely to the modular spacing of Safavid compositions such as Si–o–Se Pol, Khajoo Bridge, and Naqsh-e Jahan Square. The alignment between Fourier-derived coefficients and measured architectural intervals indicates that harmonic modulation underlies both rhythmic legibility and proportional coherence. Furthermore, the normalized mean Fourier function was implemented in a parametric interface, demonstrating its generative capacity for façade design. The study demonstrates that Fourier-based analysis offers both a diagnostic lens for heritage rhythms and a generative tool for contemporary computational design.