Page 3161
www.rsisinternational.org
INTERNATIONAL JOURNAL OF LATEST TECHNOLOGY IN ENGINEERING,
MANAGEMENT & APPLIED SCIENCE (IJLTEMAS)
ISSN 2278-2540 | DOI: 10.51583/IJLTEMAS | Volume XV, Issue V, May 2026
Topological and Fractal Modelling of Nagara Temple Architecture: A
Comparative Mathematical Study of Kandariya Mahadeva and Konark
Sun Temples
Dr. Pratiksha Kadam
Statistics, K. C. College, HSNC University, Mumbai, Maharashtra, India
DOI: https://doi.org/10.51583/IJLTEMAS.2026.150500259
Received: 27 May 2026; Accepted: 01 June 2026; Published: 23 June 2026
ABSTRACT
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.
Keywords: Nagara Temple Architecture; Fractal Geometry; Graph Theory; Topology; Sacred Geometry; Radial
Symmetry; Computational Heritage; Indian Knowledge Systems.
INTRODUCTION
North Indian temple architecture, commonly known as the Nagara style, represents one of the most
mathematically expressive architectural traditions in India. Nagara temples are distinguished by vertically rising
curvilinear shikharas, clustered tower forms, axial organization, geometric ordering, and hierarchical spatial
progression. The visual and spatial organization of these temples suggests strong structural order, recursive
proportion, and systematic geometric planning.
While Nagara temples have been widely studied from historical, archaeological, iconographic, religious, and
cultural perspectives, relatively fewer studies have examined their architectural structure using modern
mathematical frameworks such as fractal geometry, topology, graph theory, radial symmetry, and spatial network
modelling.
Page 3162
www.rsisinternational.org
INTERNATIONAL JOURNAL OF LATEST TECHNOLOGY IN ENGINEERING,
MANAGEMENT & APPLIED SCIENCE (IJLTEMAS)
ISSN 2278-2540 | DOI: 10.51583/IJLTEMAS | Volume XV, Issue V, May 2026
The present study focuses on two major North Indian temple systems:
1. Kandariya Mahadeva Temple, Khajuraho
2. Konark Sun Temple, Odisha
These temples were selected because they represent two complementary mathematical tendencies within Nagara
architecture. Kandariya Mahadeva Temple demonstrates recursive vertical geometric clustering through grouped
shikharas, whereas Konark Sun Temple demonstrates radial geometry, cyclic organization, wheel-based spatial
ordering, and axial orientation.
The purpose of this study is not to suggest that the builders of Nagara temples explicitly employed modern
concepts such as graph theory, topology, or fractal geometry. Instead, these mathematical frameworks are used
as analytical tools for examining observable architectural characteristics including spatial connectivity, recursive
tower arrangements, radial organization, and geometric hierarchy. The selected features are translated into
measurable variables derived from documented architectural descriptions and plan-based interpretations,
allowing comparative mathematical analysis while remaining distinct from symbolic or religious interpretations.
Where possible, the selected architectural characteristics are represented through explicitly defined variables that
can be normalized and compared across temple systems.
The study focuses on two representative temple systems—Kandariya Mahadeva Temple and Konark Sun
Temple—which exhibit contrasting yet complementary geometric characteristics. Kandariya Mahadeva Temple
is examined primarily through recursive shikhara clustering and vertical hierarchy, whereas Konark Sun Temple
is analysed through radial wheel geometry, cyclic ordering, and spatial symmetry.
To facilitate systematic comparison, a composite measure termed the Nagara Temple Geometric Index (NTGI)
is proposed. The index integrates normalized measures of recursive geometry, topological connectivity, and
radial symmetry into a unified mathematical framework. Although the present work is exploratory in nature, the
framework is structured to support future empirical validation through architectural plans, photogrammetric
reconstruction, GIS-based measurements, and computational feature extraction.
LITERATURE REVIEW
The methodological emphasis of the study is on the definition, normalization, and comparison of architectural
variables rather than on aesthetic evaluation. Each mathematical parameter introduced in the subsequent sections
is associated with a clearly defined architectural feature and may be refined further as more detailed measurement
data become available.
Mathematical Interpretation of Indian Temple Architecture
Indian temple architecture has historically been studied through religious symbolism, iconography, sculpture,
ritual systems, and dynastic development. However, the geometric and mathematical dimensions embedded
within temple architecture have also attracted scholarly attention. Traditional Indian architectural treatises such
as the Shilpa Shastras and Vastu Shastras emphasize proportion, orientation, symmetry, axiality, and sacred
measurement systems.
Kramrisch interpreted temple architecture as a symbolic representation of the cosmic mountain and sacred spatial
order [1]. Hardy discussed structural transformation and geometric organization within Indian temple forms [2].
Michell examined temple planning and symbolic architectural hierarchy [3]. Nevertheless, comparatively fewer
studies examine temple structures using modern mathematical frameworks such as graph theory, fractal
geometry, topology, and computational modelling.
Consequently, there remains significant scope for developing quantitative approaches that complement
traditional historical and architectural interpretations while providing measurable descriptors of structural
organization and spatial hierarchy.
Page 3163
www.rsisinternational.org
INTERNATIONAL JOURNAL OF LATEST TECHNOLOGY IN ENGINEERING,
MANAGEMENT & APPLIED SCIENCE (IJLTEMAS)
ISSN 2278-2540 | DOI: 10.51583/IJLTEMAS | Volume XV, Issue V, May 2026
Fractal Geometry in Architectural Studies
Fractal geometry provides mathematical tools for studying recursive structures, scale hierarchy, and self-similar
organization. Mandelbrot introduced the mathematical theory of fractals for analysing irregular geometric
systems [4]. In architecture, repetitive scaling and recursive ornamentation frequently demonstrate fractal-like
characteristics.
Bovill applied fractal geometry to architectural analysis and demonstrated how recursive scaling can be
identified in historical monuments and traditional architectural systems [5]. Nagara temple architecture,
particularly clustered shikhara systems, visually resembles recursive hierarchical organization where smaller
towers repeat around a dominant central structure.
Topology and Spatial Connectivity
Topology and graph theory are increasingly used in urban analysis, spatial modelling, circulation systems, and
architectural network studies. Temple spaces may be interpreted as graphs in which nodes represent architectural
units and edges represent movement pathways or visual connections.
Diestel developed foundational graph-theoretic methods applicable to spatial connectivity [6]. Batty discussed
spatial networks and urban topology in architectural systems [7]. Nagara temples exhibit hierarchical movement
pathways, axial progression, mandapabased circulation, and structured spatial transitions suitable for topological
modelling.
Beyond qualitative interpretation, graph-based approaches offer the advantage of converting architectural
layouts into measurable network structures. Such representations enable the computation of connectivity indices,
node centrality measures, and spatial density parameters that can be compared across different architectural
systems. This characteristic makes graph-theoretic methods particularly suitable for comparative studies of
temple layouts.
Astronomical and Symbolic Geometry
Several North Indian temples exhibit astronomical alignment and symbolic geometric planning. Konark Sun
Temple is particularly significant because of its radial wheel geometry, solar symbolism, cyclic representation
of time, and eastward orientation [9]. The monumental wheels of Konark may be interpreted mathematically
through radial symmetry, circular partitioning, angular division, and periodic spatial symbolism.
Computational Heritage and Digital Documentation
Recent developments in computational heritage studies have enabled the quantitative analysis of historical
monuments through digital documentation techniques such as photogrammetry, laser scanning, GIS mapping,
image segmentation, and three-dimensional modelling [10, 11]. These approaches facilitate the extraction of
measurable geometric features from architectural structures and provide reproducible datasets for mathematical
and computational analysis.
In architectural research, digital methods have increasingly been used to investigate spatial organization,
symmetry, geometric proportions, connectivity networks, and structural complexity [10, 11]. Such approaches
are particularly relevant for temple architecture, where large-scale geometric forms and hierarchical spatial
arrangements can be studied through computational techniques. The present study adopts a conceptual
mathematical framework while identifying potential pathways for future validation using digital heritage
documentation and computational feature extraction methods.
The application of computational methods to architectural heritage has demonstrated that complex spatial and
geometric characteristics can be represented through quantitative descriptors. Measures of connectivity,
symmetry, hierarchy, and geometric repetition have been successfully employed in studies of historical buildings,
urban layouts, and cultural monuments. These developments provide a methodological foundation for extending
Page 3164
www.rsisinternational.org
INTERNATIONAL JOURNAL OF LATEST TECHNOLOGY IN ENGINEERING,
MANAGEMENT & APPLIED SCIENCE (IJLTEMAS)
ISSN 2278-2540 | DOI: 10.51583/IJLTEMAS | Volume XV, Issue V, May 2026
similar analytical approaches to Nagara temple architecture, where hierarchical tower arrangements, radial
structures, and spatial organization offer suitable candidates for mathematical modelling.
Research Gap
Existing studies on Nagara temple architecture primarily focus on archaeological interpretation, religious
symbolism, iconography, historical development, and artistic expression. Although several works discuss
geometric planning and proportional systems, comparatively few studies attempt to represent temple architecture
using quantitative frameworks based on graph theory, topology, fractal-inspired modelling, or spatial
connectivity analysis. Furthermore, limited attention has been given to the development of reproducible
mathematical indicators that can be derived from observable architectural characteristics and subsequently
validated through computational methods. The present study seeks to address this gap by proposing a normalized
mathematical framework for analysing selected geometric and topological characteristics of Nagara temple
architecture and by introducing a composite index for comparative evaluation of architectural organization.
Objectives of the Study
The objectives of the study are:
1. To analyse recursive vertical clustering in Nagara temple architecture.
2. To examine radial geometry and cyclic symbolism in North Indian temple systems.
3. To investigate spatial topology and architectural connectivity.
4. To construct graph-theoretic abstractions of temple layouts.
5. To develop a normalized mathematical framework for Nagara temple analysis.
6. To propose the Nagara Temple Geometric Index.
7. To compare recursive geometry and radial organization between Kandariya Mahadeva Temple and
Konark Sun Temple.
Figure 1: Proposed mathematical framework for analysing selected features of Nagara temple architecture.
Architectural Background of the Selected Temples
Kandariya Mahadeva Temple
Kandariya Mahadeva Temple, located in the Khajuraho Group of Monuments in Madhya Pradesh, is one of the
finest examples of mature Nagara temple architecture. The temple is dedicated to Shiva and is known for its high
central shikhara, clustered miniature spires, sculptural abundance, and strong vertical movement. It belongs to
the Chandela period and is generally dated to the eleventh century CE [8, 2, 3].
NagaraTemple
Architecture
Recursive
FractalGeometry
Topologyand
GraphTheory
Radialand
CyclicSymmetry
NagaraTemple
GeometricIndex
Page 3165
www.rsisinternational.org
INTERNATIONAL JOURNAL OF LATEST TECHNOLOGY IN ENGINEERING,
MANAGEMENT & APPLIED SCIENCE (IJLTEMAS)
ISSN 2278-2540 | DOI: 10.51583/IJLTEMAS | Volume XV, Issue V, May 2026
Parameter
Value
Location
Khajuraho, Madhya Pradesh
Approximate period
c. 1025–1050 CE
Dynasty
Chandela
Architectural style
Nagara
Main deity
Shiva
Main shikhara height
Approximately 31 m
Main mathematical feature
Recursive clustered shikhara system
Orientation
East-facing
Table 1: Kandariya Mahadeva Temple Details
The temple exhibits vertical hierarchy, recursive clustering, axiality, progressive elevation, and repeated
miniature shikhara forms. Smaller tower elements cluster around the main tower, creating an impression of
geometric growth toward a central vertical peak.
Konark Sun Temple
Konark Sun Temple, located in Odisha, is one of the most celebrated examples of KalingaNagara architecture.
It was constructed in the thirteenth century CE and is dedicated to Surya, the Sun God. The temple is conceived
as a monumental solar chariot with twelve pairs of elaborately carved wheels and symbolic horses [9, 3, 2].
Parameter
Value
Location
Konark, Odisha
Approximate period
13th century CE
Dynasty
Eastern Ganga
Architectural style
Kalinga-Nagara
Main deity
Surya
Wheel structures
24 monumental wheels
Symbolic form
Solar chariot
Main mathematical feature
Radial geometry and cyclic symbolism
Orientation
East-facing
Table 2: Konark Sun Temple Details
The temple exhibits radial geometry, cyclic symbolism, solar orientation, axial planning, and mathematical
ordering through its wheel structures. The wheels may be interpreted as geometric representations of time,
periodicity, circular symmetry, and solar movement.
Page 3166
www.rsisinternational.org
INTERNATIONAL JOURNAL OF LATEST TECHNOLOGY IN ENGINEERING,
MANAGEMENT & APPLIED SCIENCE (IJLTEMAS)
ISSN 2278-2540 | DOI: 10.51583/IJLTEMAS | Volume XV, Issue V, May 2026
Sources of Architectural Data
The architectural information used in this study was compiled from authenticated heritage documentation,
UNESCO World Heritage records, published architectural literature, and standard reference works on Indian
temple architecture [8, 9, 3, 2, 1]. Particular attention was given to documented descriptions of temple layouts,
shikhara organization, wheel geometry, spatial sequencing, and architectural hierarchy.
For Kandariya Mahadeva Temple, architectural information regarding shikhara clustering, vertical composition,
plan organization, and spatial progression was obtained from UNESCO documentation and published studies of
Nagara temple architecture [8, 2, 3]. For Konark Sun Temple, information regarding wheel geometry, radial
organization, symbolic chariot planning, and orientation was obtained from UNESCO documentation and
architectural analyses [9, 3].
To facilitate mathematical modelling, architectural features were converted into measurable variables. These
variables were derived from documented architectural descriptions, published plans, elevation drawings, and
visually identifiable structural components reported in the literature [2, 3, 8, 9]. The conversion process was
designed to provide a consistent basis for comparative analysis across the selected temples.
Architectural Variable Definition and Coding
For reproducibility, each mathematical component used in the NTGI framework was associated with a specific
architectural feature. Table 3 summarizes the variables and their interpretation.
Variable
Symbol
Architectural Interpretation
Recursive shikhara units
Number of visually identifiable subsidiary
shikharas participating in clustered tower
formation
Total structural units
Total number of major and minor tower
elements considered in the analysis
Number of graph nodes
Distinct architectural spaces such as sanctum,
mandapas, gateways, platforms, and corridors
Number of graph edges
Physical or functional connections between
architectural spaces
Symmetric radial sectors
Radial sectors exhibiting geometric symmetry
Total radial sectors
Total number of radial sectors considered in
the analysis
Table 3: Variables and their interpretation
The coding procedure was based on published architectural descriptions, plan-based interpretation, and
documented structural features. All variables were normalized before inclusion in the NTGI framework to
facilitate comparison between temple systems of different scales and architectural complexity.
The variables selected for the present study do not represent exhaustive architectural measurements. Rather, they
were chosen to capture specific characteristics associated with recursive hierarchy, spatial connectivity, and
radial organization. Future studies may refine these variables through direct architectural measurement, image-
based extraction, or computational geometry techniques.
Page 3167
www.rsisinternational.org
INTERNATIONAL JOURNAL OF LATEST TECHNOLOGY IN ENGINEERING,
MANAGEMENT & APPLIED SCIENCE (IJLTEMAS)
ISSN 2278-2540 | DOI: 10.51583/IJLTEMAS | Volume XV, Issue V, May 2026
Model Assumptions and Validation Scope
The proposed framework is intended as a quantitative interpretation of selected architectural characteristics
observed in Nagara temple systems. The mathematical parameters are derived from architectural features that
can be identified from published plans, documented descriptions, and future measurement-based datasets. The
framework is exploratory and comparative in nature, but it has been structured so that each parameter can be
refined using empirical measurements as more detailed architectural data become available.
1. Temple spaces may be abstracted as graphs where nodes represent architectural units and edges represent
pathways.
2. Recursive shikhara clustering is represented through a fractal-inspired geometric parameter intended to
capture hierarchical repetition and structural organization within the temple superstructure.
3. Radial wheel geometry at Konark Sun Temple may be analysed using circular symmetry and cyclic
partitioning.
4. The numerical values used in the present study represent normalized comparative indicators derived from
documented architectural characteristics and are intended to demonstrate the proposed methodology
rather than establish definitive archaeological measurements.
5. The proposed NTGI framework measures selected mathematical characteristics only and does not
evaluate artistic, religious, spiritual, or cultural value.
6. Certain numerical parameters are modelling assumptions requiring future validation through
architectural measurements and computational analysis.
Component
Interpretation
Future Validation
Recursive fractal parameter
Vertical hierarchical clustering
Image analysis, photogrammetry
Topological
connectivity
Spatial pathway organization
GIS and architectural plans
Radial geometry parameter
Cyclic wheel symmetry
Geometric measurement
NTGI framework
Comparative normalized index
Larger dataset validation
Table 4: Model Assumptions and Validation Scope
The assumptions adopted in the present framework are intended to provide a mathematically consistent basis for
comparative analysis rather than definitive architectural measurements. As additional datasets become available,
the parameters may be recalibrated and validated using direct geometric measurements, digital reconstruction
techniques, and computational heritage methodologies.
Mathematical Framework
Graph-Theoretic Representation
To represent temple layouts in a mathematically tractable form, the architectural organization of a temple may
be abstracted as a graph. In this representation, distinct architectural spaces are treated as nodes, while physical,
visual, or functional connections between these spaces are represented as edges. Such graph-based
representations enable the quantitative analysis of spatial connectivity and provide a foundation for comparative
architectural studies.
Page 3168
www.rsisinternational.org
INTERNATIONAL JOURNAL OF LATEST TECHNOLOGY IN ENGINEERING,
MANAGEMENT & APPLIED SCIENCE (IJLTEMAS)
ISSN 2278-2540 | DOI: 10.51583/IJLTEMAS | Volume XV, Issue V, May 2026
Definition 1. A temple graph is defined as
G = (V,E), (1)
where V represents temple components such as sanctum, mandapas, gateways, wheel structures, platforms, and
corridors, while E represents movement pathways or structural connectivity.
The connectivity degree of a node v is defined by
C(v) = deg(v). (2)
The adjacency matrix is represented as
A = [a
ij
], (3)
where
, if two spaces are connected,
(4)
otherwise.
The adjacency matrix provides a compact representation of temple connectivity and facilitates the
computation of graph-based measures such as connectivity density and spatial organization. Although
simplified, this abstraction captures the primary structural relationships between architectural
components.
S: Sanctum, M: Mandapa, G: Gateway, P: Platform
Figure 2: Simplified graph representation of Nagara temple spatial connectivity.
Topological Connectivity Parameter
The normalized topological connectivity parameter is defined as
(5)
This formulation corresponds to the standard graph density measure commonly used in network analysis and
provides a normalized indicator of spatial connectivity within the temple graph.
Since
S
M
M
G
P
G
Page 3169
www.rsisinternational.org
INTERNATIONAL JOURNAL OF LATEST TECHNOLOGY IN ENGINEERING,
MANAGEMENT & APPLIED SCIENCE (IJLTEMAS)
ISSN 2278-2540 | DOI: 10.51583/IJLTEMAS | Volume XV, Issue V, May 2026
(6)
it follows that
0 ≤ T ≤ 1. (7)
Higher values of T indicate stronger spatial connectivity within the selected graph abstraction.
Recursive Fractal Modelling
The clustered shikharas of Kandariya Mahadeva Temple suggest recursive geometric organization.
Definition 2. The recursive fractal parameter is defined as
, (8)
where N
r
denotes recursively repeating structural units and N
t
denotes total structural units considered.
The parameter (F) provides a normalized measure of recursive architectural repetition. In Nagara temple
architecture, subsidiary shikharas frequently occur in clustered arrangements surrounding a dominant central
tower. The ratio therefore estimates the relative contribution of repeating structural elements within the observed
tower hierarchy. Although simplified, the parameter permits comparison across temple systems of different
scales by reducing the measure to a normalized interval between 0 and 1.
Radial Geometry and Cyclic Symmetry
Konark Sun Temple demonstrates strong radial organization through wheel structures and cyclic partitioning.
Recursive clustered shikhara abstraction
Figure 3: Recursive vertical clustering inspired by Kandariya Mahadeva Temple.
Definition 3. The radial symmetry parameter is defined as
, (9)
where n
s
denotes symmetric radial sectors and n
t
denotes total sectors.
The parameter (R) quantifies the degree of radial organization present within a selected architectural feature. For
Konark Sun Temple, the monumental wheel structures provide a natural basis for radial partitioning. A larger
Page 3170
www.rsisinternational.org
INTERNATIONAL JOURNAL OF LATEST TECHNOLOGY IN ENGINEERING,
MANAGEMENT & APPLIED SCIENCE (IJLTEMAS)
ISSN 2278-2540 | DOI: 10.51583/IJLTEMAS | Volume XV, Issue V, May 2026
proportion of symmetric sectors produces a higher value of (R), indicating stronger geometric regularity and
radial order.
Radial wheel abstraction inspired by Konark Sun Temple
Figure 4: Radial geometry inspired by Konark Sun Temple wheel structures.
Nagara Temple Geometric Index
The proposed composite mathematical parameter is defined as
NTGI = αF + βT + γR, (10)
where:
• F = recursive fractal component,
• T = topological connectivity component,
• R = radial symmetry component.
The NTGI is formulated as a weighted linear combination of three normalized architectural characteristics:
recursive geometry, topological connectivity, and radial symmetry. The use of normalized parameters ensures
that each component contributes on a common scale, thereby allowing meaningful aggregation within a single
comparative index.
The weighting coefficients and represent the relative importance assigned to the three architectural
characteristics.
The weights satisfy
α + β + γ = 1, (11)
with
α,β,γ ≥ 0. (12)
The non-negativity condition ensures that each component contributes positively to the composite index and
prevents cancellation effects between different architectural characteristics.
For the baseline model,
(13)
Page 3171
www.rsisinternational.org
INTERNATIONAL JOURNAL OF LATEST TECHNOLOGY IN ENGINEERING,
MANAGEMENT & APPLIED SCIENCE (IJLTEMAS)
ISSN 2278-2540 | DOI: 10.51583/IJLTEMAS | Volume XV, Issue V, May 2026
In the absence of empirical calibration data, equal weighting is adopted in the baseline model so that no individual
geometric characteristic is preferentially emphasized.
Thus,
(14)
Under the equal-weight assumption, the NTGI represents the arithmetic mean of the three normalized
components. Consequently, higher NTGI values indicate a greater combined presence of recursive hierarchy,
spatial connectivity, and radial organization within the selected architectural framework.
The NTGI should be interpreted as a comparative indicator rather than an absolute measure of architectural
quality, cultural significance, or aesthetic value.
Figure 5: Triangular representation of the three mathematical components contributing to NTGI.
Numerical Modelling
Parameter Estimation Framework
The numerical values used in the present study were obtained as normalized indicators derived from the
architectural characteristics identified in Sections 4 and 5. Since comprehensive measurement datasets are not
presently available for the selected temples, the values should be interpreted as comparative modelling estimates
intended to demonstrate the proposed framework rather than definitive archaeological measurements.
The estimation process considered three principal characteristics: recursive shikhara clustering, spatial
connectivity represented through graph abstraction, and radial organization represented through geometric
symmetry. All parameter values were normalized to the interval [0,1] to facilitate comparison between temple
systems.
Temple
Recursive Geometry
(F)
Topological Connectivity
(T)
Radial Symmetry
(R)
Kandariya Mahadeva
Temple
0.78
0.52
0.88
Konark Sun Temple
0.62
0.66
0.95
Table 5: Normalized parameter values used in the NTGI framework.
F
T
R
NTGI
RecursiveGeometry
Topology
RadialSymmetry
Page 3172
www.rsisinternational.org
INTERNATIONAL JOURNAL OF LATEST TECHNOLOGY IN ENGINEERING,
MANAGEMENT & APPLIED SCIENCE (IJLTEMAS)
ISSN 2278-2540 | DOI: 10.51583/IJLTEMAS | Volume XV, Issue V, May 2026
Kandariya Mahadeva Temple
For Kandariya Mahadeva Temple, the recursive geometry component was estimated within the proposed
normalized framework as
F
K
= 0.78.
This value reflects the pronounced clustering of subsidiary shikharas around the dominant central tower.
The topological connectivity component was estimated as:
(15)
T
K
= 0.52.
while the radial symmetry component was estimated as:
(16)
R
K
= 0.88.
(17)
Therefore, these values indicate a temple system characterized by strong recursive hierarchy and substantial
geometric regularity.
Hence,
NTGI
K
≈ 0.727. (19)
The resulting value reflects the strong recursive hierarchy and geometric regularity exhibited by the clustered
shikhara system of Kandariya Mahadeva Temple.
Konark Sun Temple
For Konark Sun Temple, the recursive geometry component was estimated as:
F
C
= 0.62, (20)
reflecting a comparatively lower emphasis on recursive tower clustering. The topological connectivity
component was estimated as
T
C
= 0.66, (21)
while the radial symmetry component was estimated as
R
C
= 0.95. (22)
The high radial symmetry value reflects the prominence of wheel-based geometry and cyclic spatial organization
within the temple complex.
Thus,
(23)
Page 3173
www.rsisinternational.org
INTERNATIONAL JOURNAL OF LATEST TECHNOLOGY IN ENGINEERING,
MANAGEMENT & APPLIED SCIENCE (IJLTEMAS)
ISSN 2278-2540 | DOI: 10.51583/IJLTEMAS | Volume XV, Issue V, May 2026
Hence,
NTGI
C
≈ 0.743.
(24)
The slightly higher NTGI value reflects the strong contribution of radial symmetry and spatial organization
associated with the wheel-based geometry of the Konark Sun Temple.
The comparison suggests that Kandariya Mahadeva Temple exhibits stronger recursive vertical clustering,
whereas Konark Sun Temple demonstrates stronger radial geometry and cyclic ordering.
Sensitivity Analysis
Alternative weighting schemes may also be considered.
If recursive geometry is prioritized:
α = 0.50,
If radial geometry is prioritized:
β = 0.25,
γ = 0.25.
(25)
α = 0.25,
If topology is prioritized:
β = 0.25,
γ = 0.50.
(26)
α = 0.25,
β = 0.50,
γ = 0.25.
(27)
Thus, the NTGI model provides flexibility for different architectural interpretations.
To evaluate the influence of weighting choices, the sensitivity of the index may be expressed as
where
and
denote index values obtained under different weighting schemes.
Mathematical Justification and Proofs
Proposition 1. The NTGI framework is bounded between 0 and 1.
Proof. Since
0 ≤ F,T,R ≤ 1, (28)
and
α + β + γ = 1, (29)
with nonnegative weights,
0 ≤ NTGI ≤ 1. (30)
Hence the index is normalized.
Proposition 2. Recursive tower clustering increases the fractal-inspired parameter F.
Proof.
Page 3174
www.rsisinternational.org
INTERNATIONAL JOURNAL OF LATEST TECHNOLOGY IN ENGINEERING,
MANAGEMENT & APPLIED SCIENCE (IJLTEMAS)
ISSN 2278-2540 | DOI: 10.51583/IJLTEMAS | Volume XV, Issue V, May 2026
Since
with
, increasing the number of recursively repeating shikhara units while keeping the total number of
structural units fixed increases the value of F.
Therefore, recursive tower clustering contributes positively to the fractal-inspired parameter .
Proposition 3. Radial partitioning contributes positively to cyclic symmetry.
Proof. As the number of symmetric radial sectors increases, the parameter
(32)
approaches 1. Hence, highly ordered wheel geometry contributes positively to radial symmetry.
RESULTS AND DISCUSSION
The proposed framework offers a mathematical perspective on selected geometric characteristics of Nagara
temple architecture. Although the two temples considered in this study belong to the same broad architectural
tradition, the analysis suggests that they achieve architectural complexity through different geometric strategies.
Kandariya Mahadeva Temple is characterized by its prominent clustered shikhara arrangement, where numerous
subsidiary towers rise around the central superstructure. This hierarchical arrangement contributes to a strong
recursive geometry component and creates a visually unified upward movement. From a mathematical
viewpoint, the temple demonstrates how repetition and hierarchical organization can be represented through
normalized geometric measures.
In contrast, Konark Sun Temple derives much of its geometric character from radial organization. The wheel
structures, circular forms, and ordered spatial arrangement contribute significantly to its radial symmetry
component. Rather than emphasizing vertical clustering, the temple expresses geometric order through cyclic
patterns and spatial regularity.
The NTGI values obtained for the two temples are relatively close, indicating that both structures exhibit
substantial geometric organization despite their contrasting architectural forms. Kandariya Mahadeva Temple
achieves this through recursive hierarchy, whereas Konark Sun Temple achieves it through radial symmetry and
spatial connectivity. This observation highlights the diversity of geometric expression within the Nagara
architectural tradition.
The results should be interpreted as comparative mathematical observations rather than definitive assessments
of architectural value. The framework is intended to provide a structured approach for analysing selected
geometric characteristics and may be refined further through measurement-based studies and computational
validation.
Page 3175
www.rsisinternational.org
INTERNATIONAL JOURNAL OF LATEST TECHNOLOGY IN ENGINEERING,
MANAGEMENT & APPLIED SCIENCE (IJLTEMAS)
ISSN 2278-2540 | DOI: 10.51583/IJLTEMAS | Volume XV, Issue V, May 2026
Figure 6: Comparison of NTGI values for Kandariya Mahadeva Temple and Konark Sun Temple under
the equal-weight baseline model.
As shown in Figure 6, the NTGI values of Kandariya Mahadeva Temple (0.727) and Konark Sun Temple (0.743)
are relatively close, suggesting that both temple systems exhibit substantial geometric organization despite
emphasizing different architectural characteristics.
Applications of the Study
The proposed framework may be useful in:
Computational heritage studies
Digital reconstruction of monuments
AI-assisted architectural interpretation
Mathematical modelling of sacred architecture
Spatial network analysis
Heritage-based STEM education
Comparative studies of Indian temple systems
Novelty of the Study
The novelty of the study lies in:
Integrating fractal-inspired geometry with Nagara architecture.
Introducing radial geometry analysis for temple wheel symbolism.
Developing the Nagara Temple Geometric Index.
Applying graph-theoretic abstraction to temple connectivity.
Providing a normalized mathematical interpretation of North Indian temple systems.
Connecting mathematical modelling with Indian Knowledge Systems and computational heritage.
Establishing a reproducible framework linking architectural observations with normalized mathematical
descriptors.
Providing a foundation for future validation through computational heritage techniques including
photogrammetry, GIS analysis, and image-based feature extraction.
0.727
0.743
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Kandariya Mahadeva Temple Konark Sun Temple
NTGI Value
Page 3176
www.rsisinternational.org
INTERNATIONAL JOURNAL OF LATEST TECHNOLOGY IN ENGINEERING,
MANAGEMENT & APPLIED SCIENCE (IJLTEMAS)
ISSN 2278-2540 | DOI: 10.51583/IJLTEMAS | Volume XV, Issue V, May 2026
Limitations of the Study
The study develops a conceptual normalized framework rather than a field-measured archaeological model.
Certain numerical values are modelling assumptions requiring future validation through architectural drawings,
LiDAR mapping, image analysis, and computational extraction methods.
The proposed NTGI framework measures selected mathematical characteristics only and should not be
interpreted as a measure of artistic, religious, cultural, or spiritual value. Since only two temple systems are
considered, broader generalization requires a larger dataset of Nagara temples.
A further limitation of the study is that the parameter values are based on normalized modelling estimates derived
from documented architectural characteristics rather than direct field measurements. Future investigations
incorporating architectural surveys, digital reconstruction, and computational feature extraction may provide
more precise parameter estimation and broader validation of the proposed framework.
Future Scope
Future studies may include:
LiDAR-based geometric validation
GIS mapping of temple plans
Computational extraction of fractal dimensions
AI-based classification of temple styles
Comparative studies between Nagara and Dravidian systems
Astronomical alignment modelling
Image-processing-based measurement of shikhara clustering
Development of automated NTGI computation using computer vision and image-processing techniques
Construction of a larger temple geometry dataset for comparative analysis across multiple Nagara temple
systems
CONCLUSION
Nagara temple architecture demonstrates remarkable mathematical richness through recursive vertical hierarchy,
radial geometry, symbolic ordering, and spatial topology. The present study proposes a normalized mathematical
framework for interpreting selected features of Kandariya Mahadeva Temple and Konark Sun Temple using
graph theory, topology, fractal-inspired modelling, and symmetry analysis.
The analysis suggests that Kandariya Mahadeva Temple exhibits stronger recursive clustering, whereas Konark
Sun Temple demonstrates stronger radial geometry and cyclic organization. The proposed NTGI framework
contributes to interdisciplinary research connecting mathematics, architecture, computational heritage studies,
and Indian Knowledge Systems.
The present work should be viewed as an initial step toward the development of quantitative approaches for
analysing Indian temple architecture. Future studies incorporating direct architectural measurements, digital
heritage documentation, and computational geometry techniques may further refine the proposed framework and
extend its applicability to a broader range of temple systems. Such approaches may contribute to a deeper
quantitative understanding of the geometric principles embedded within India's architectural heritage.
REFERENCES
1. Kramrisch, S. (1946). The Hindu Temple. University of Calcutta, Calcutta.
2. Hardy, A. (1995). Indian Temple Architecture: Form and Transformation. Wiley Academy, London.
3. Michell, G. (1988). The Hindu Temple: An Introduction to Its Meaning and Forms. University of Chicago
Press, Chicago.
4. Mandelbrot, B. B. (1982). The Fractal Geometry of Nature. W. H. Freeman, New York.
Page 3177
www.rsisinternational.org
INTERNATIONAL JOURNAL OF LATEST TECHNOLOGY IN ENGINEERING,
MANAGEMENT & APPLIED SCIENCE (IJLTEMAS)
ISSN 2278-2540 | DOI: 10.51583/IJLTEMAS | Volume XV, Issue V, May 2026
5. Bovill, C. (1996). Fractal Geometry in Architecture and Design. Birkhäuser, Boston.
6. Diestel, R. (2017). Graph Theory. 5th ed., Springer, Berlin.
7. Batty, M. (2013). The New Science of Cities. MIT Press, Cambridge.
8. UNESCO World Heritage Centre. Khajuraho Group of Monuments. World Heritage List Documentation.
9. UNESCO World Heritage Centre. Sun Temple, Konark. World Heritage List Documentation.
10. Remondino, F. (2011). Heritage Recording and 3D Modeling with Photogrammetry and 3D Scanning.
Remote Sensing, 3(6), 1104–1138.
11. Stylianidis, E., & Remondino, F. (2016). 3D Recording, Documentation and Management of Cultural
Heritage. Whittles Publishing.
