Analysis of Symmetry Groups in Temple Layouts and Mandalas Using Group Theory and Fractal Geometry
Keywords:
Hindu Temple Architecture, Symmetry Groups, Group Theory, Fractal Geometry, Wallpaper Groups, Dihedral Symmetry, Crystallographic Groups, Iterated Function Systems (IFS), Multifractal Analysis, Hausdorff Dimension, Vedic Cosmology, Sri Yantra Mandala, Kandariya Mahadeva Temple, Modhera Sun Temple, Computational Modeling, Python IFS Reconstruction, LIDAR Validation, Trimurti Symbolism, Vastupurusha Mandala, Sacred GeometryAbstract
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.
