Sacred Geometry of Hindu Temples

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Fractals exhibit similar patterns at increasingly small scales called self-similarity, also known as expanding symmetry or unfolding symmetry; if this replication is the same at every scale, it is called affine self-similar
-Dr Ujwala Chakradeo

a_1  H x W: 0 x 
Scale and proportions have prime importance in temple architecture. Square is considered to be the basic form. Vaastu Purusha Mandal is also square in shape and has square sub-components. Temple plan and elevation and overall form mostly evolve from square shape. Fractions and small parts of the temple form have been carefully designed to keep in mind the nature and laws of nature and simple and complex fractions of the square.
In Hindu philosophy, Parabramha is supreme, complete and infinite–Anantha, yet every jivatma, every living being has a small part of this Parmatma as his/her atma. Each atma is also complete in itself.
“Om purna mada purna midam
Purnaat purna mudachyate
Purnasya purnam madaaya
Purna meva vasishyate
Om shanti shanti shantih”
This translates into: "That is the whole, this is the Whole; from the Whole, the Whole arises; taking away the Whole from the Whole, the Whole remains."
Sloka from Ishavasya Upanishad explains this concept of being complete as a whole and yet also being reflected in every component or a part of that whole.
This can be explained with the example of a mirror. The mirror always showcases the image of the object in front of it. When a mirror is broken into multiple pieces, the image then multiplies into as many smaller images, yet each image in the smaller components is also complete.
According to Hindu Sankhya Shastra Darshan, the entire Cosmos is holonomic, as explained with a mirror example.
यत् पिंडी तत् ब्रम्हांडी. Temple form is considered to be the icon or a symbol of this Hindu philosophy. Therefore the proportions/fractions adopted in the temple plan and elevation are very carefully crafted.
Fractal geometry is comparatively a new terminology which Benoit Mandelbrat coined in the mid-60s. The western world has been using fractal geometry in art and architecture since then. However, in India, this geometry has been in use for more than 1500 years.
Fractal geometry lies within the mathematical branch of measure theory—the miniature of the whole in precisely the same proportions.
There can be many examples quoted from temple architecture to explain the use of fractal geometry. Shikhar design of Kandariya Mahadev temple of Khajuraho is one of the best examples which displays miniature Shikhar form all around its main Shikhar. Miniatures of the main Shikhar form are placed all around this main Shikhar in geometrical order. Each miniature Shikhar is called a urushringa.
Another example is that of Kunda at the Sun temple of Modhera. Steps leading to the bottom of the kund are examples of fractal geometry showcasing self-replicating shapes.
(The columnist is Principal of SMM College of Architecture, Nagpur and specialises in Bharatiya Architectural Heritage)