Topological and Fractal Modelling of Nagara Temple Architecture: A Comparative Mathematical Study of Kandariya Mahadeva and Konark Sun Temples

North Indian Nagara temple architecture exhibits remarkable geometric sophistication through recursive tower clustering, curvilinear verticality, radial organization, axial alignment, cyclic ordering, and hierarchical spatial planning. While these temples have been extensively studied from historical, archaeological, iconographic, and cultural perspectives, their mathematical interpretation using topology, graph theory, and fractal geometry remains comparatively underexplored.

This study proposes a reproducible mathematical framework for analysing selected architectural features of Nagara temple architecture using graph-theoretic abstraction, normalized connectivity measures, fractal-inspired modelling, symmetry analysis, and spatial topology. Architectural variables including shikhara clustering, spatial connectivity, and radial organization were identified from published architectural documentation and encoded into measurable parameters. The framework is applied to two representative North Indian temples: Kandariya Mahadeva Temple, Khajuraho, and Konark Sun Temple, Odisha. Kandariya Mahadeva Temple is analysed as an example of recursive vertical clustering, whereas Konark Sun Temple is examined for its radial geometry, cyclic ordering, and astronomical orientation.

A composite parameter termed the Nagara Temple Geometric Index (NTGI) is introduced to integrate recursive geometry, spatial topology, and radial symmetry within a normalized comparative framework. The resulting values are intended as comparative mathematical indicators derived from defined architectural features rather than measures of cultural, artistic, or spiritual significance.

The proposed framework contributes to interdisciplinary research linking mathematics, architecture, computational heritage studies, and Indian Knowledge Systems. A validation pathway based on architectural plans, photogrammetry, GIS analysis, image processing, and computational feature extraction is also outlined to support future refinement and empirical verification of the model.

Nagara Temple Architecture; Fractal Geometry; Graph Theory; Topology; Sacred Geometry; Radial Symmetry; Computational Heritage; Indian Knowledge Systems.

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