Analysis of Symmetry Groups in Temple Layouts and Mandalas Using Group Theory and Fractal Geometry - PRATHEEK RAI N; PADUVALAPATTANA KEMPEGOWDA MAMATHA (Utilitas Mathematica, 2025)
This paper discusses the mathematical bases of symmetry groups and fractal geometry in Hindu temple architecture and Hindu mandalas. Using group theory, crystallographic theory, and computational fractal modeling, we show how sacred buildings in India encode cosmic principles through precise geometric order. The framed case studies of the Kandariya Mahadeva Temple, Modhera Sun Temple, and Sri Yantra mandala demonstrate clearly deterministic fractals (box dimensions: 1.6–1.9) based on wallpaper groups and other dihedral symmetries. The computation of these structures through iterated function systems (IFS) in Python supports the notion of strict rules practiced by builders, revealing some previously unrecognised mathematical capabilities from ancient India.