The Hindu Temple as a Model of Fractal Cosmology – Forecasting Architecture with Recursive Instruction

Indian Temple FractalsKandariya Mahadev Temple [Madhya Pradesh] (source unknown)

The self-similar, cascading architectural forms found in Hindu temple architecture appear to have been pieced together by a hyper-industrious Minecrafter hooked on Hofstadter. Jagged waves of blocky ornamentation, rhythmically repeating, create diminishing echo’s of the temple’s form; tiny versions of itself repeating towards a proposed infinity. Baroque three-dimensional Cellular Automata. Cantor Set masonry. Malevich’s Architectons upscaled and iterated to the nth degree, often smothered with a teeming mass of deities and denizens, each one competing for your retina.

Indian Temple FractalsKandariya Mahadev Temple [Madhya Pradesh] – RM Nunes

It’s not just that these temples appear to be algorithmically generated, the ancient Vastu Sustra texts provide procedural rules or recipes for their design, layout and build (including the positions of ornaments). The texts transmit recursive programs, by verbal instruction, to masons so that according to Kirti Trivedi, the Hindu Temple becomes a model of a fractal Universe. A model which represents ‘views of the cosmos to be holonomic and self-similar in nature’. The idea of fractal cosmology is no stranger to western academia. In 1987 the Italian physicist Luciano Pietronero argued, in his paper, that the Universe shows ‘a definite fractal aspect over a fairly wide range of scale’ based on correlations of galaxies and clusters, their spatial distribution and average mass density.

‘According to Hindu philosophy the cosmos can be visualised to be contained in a microscopic capsule, with the help of the concept of subtle element called ‘tammatras’. The whole cosmic principle replicates itself again and again in ever smaller scales’ – Kirti Trivedi

Indian Temple FractalsYellamma Temple [Karnataka] – Paul Prudence

Indian Temple FractalsArchitecton Series – Kazimir Malevich [1923]

Indian Temple FractalsTemple Plan for Barwasagar Temple [Uttar Pradesh] from Geometry Measure in India Temple Plans

The initial temple plan is based on a grid form known as the Vastu-Purusha Mandala. Tellingly Trivedi remarks in his paper that the Vastu-Purusha Mandala is ‘not a blueprint for a temple, but a ‘forecast’, a marking of the potential within which a wide range of possibilities are implied’. The significance here, should not be underestimated. A ‘potential for possibilities’ within a predefined rule-set predisposes architecture to be governed by a degree of emergence. While emergence in parametric architecture arrived, recently, with computers and algorithms, India has been enacting emergent masonry for thousands of years thanks to the open rules of the Vastus Sustra.

Indian Temple FractalsShweta Varahaswamy Temple [Karnataka] – Paul Prudence

Using a system of measurement called the ‘Tala’, dimensional relationships of proportions rather than exact structural specifications are defined. Initial decisions (why not call them algorithmic seeds?) combined with rule sets are used to define the final outcome of the building. The ‘Tala’ system is scale invariant, just like fractal mathematics, so that a building of any size can be created, and decorated without compromising the model of self containment. The temple, as a whole, is built by interweaving fractalization processes with repetition and superimposition. An example of a typical recursive instruction, verbalised, is:

The layer of prahara (projection) will be above the chadya (eave of the roof). This is to be repeated again and again on the spire over the spire. A fraction of the prahara is to be constructed and again the spires are to be constructed. Each of the upper spires will be sprouted out with a measurement equal to half the size of the lower spire – Ksirarnava, 7.113

Indian Temple FractalsSri Meenakshi Amman Temple [Tamil Nadu] – Paul Prudence

The Kandariya Mahadev, in Madhya Pradesh, is one of the best examples of recursive temple architecture in India. The rising towers (Shikhara) of this structure are said to mimic the forms of mountains which are themselves self-similar. Shikhara literally translates to the word mountain.

Inspiration by way of a recent trip (one of many) to Karatanka, Tamil Nadu and Kerala.

Further Reading:

The Hindu Temple is a Model of a Fractal Universe – Kirti Trivedi [1993]
Infinite Sequences in The Constructive Geometry of 10th Century Hindu Temple Superstructures – Sambit Datta [2010]

Related Posts:

Stanley Tigerman & G. T. Crabtree – The Formal Generators of Structure
Breed – Driessens & Verstappen: Evolutional Diffusion Lattices
Yuri Avvakumov – Agitarch Structures: Reconfiguring Utopia

19 Responses to “The Hindu Temple as a Model of Fractal Cosmology – Forecasting Architecture with Recursive Instruction”

  1. Kevatha writes:

    Can I use this article for my talks and research ?
    I come from the lineage that built with the Vaastu parusha mandala our clan is called the vishwakarmans

  2. paul writes:

    @Kevetha, feel free to mention this post in your research/talks. A reference back to here would be appreciated, if possible. I’m going to look up on the ‘Vishwakarmans’, thanks.

  3. k p umapathy acharya writes:

    Nice article.

  4. Marta Leite Ferreira writes:

    Mr. Prudence,

    I’m writing about this issue in Observador, a portuguese online journal. Can you give me permission to use your photos with proper credits? Thank you.

  5. paul writes:

    Hi Marta, the three images that were taken by me you are free to use. Feel free to email me for more images.

  6. La fractalidad del universo se reitera en estos templos hindúes (y en estos fractales de templos hindúes) - La Tlayuda News writes:

    […] vía de Data is Nature, encontramos este fascinante concepto de los tammatras, que parecen ser las unidades que componen […]

  7. gregorylent writes:

    the third generation vastu shastri whose family constructed ramana ashram in tiruvannamalai would have recognized your ideas of recusiveness and fractals but his language and understanding derived from mysticism and sadhana .. spiritual practice .. important to remember that these things were created from the “inside out” ..

  8. Templos hindus, cosmologia fractal e uma arquitetura muito peculiar | Alameda 9 writes:

    […] No final de contas, este templo hindu reflete o modelo do Universo fractal, como explica o Dataisnature. […]

  9. Jasmine Shah writes:

    The article by Kirti Trivedi that is quoted here was presented at a Vastu Vedic Trust Conference organized by Dr. V Ganapathi Sthapati of Mamallapuram. It was Dr. V G Sthapati’s father who built the temple inside the Ramana Ashram. Dr. Stahapati has written prodigiously on this subject and worked tirelessly to preserve and present it to the modern world. It is truly thanks to him that today we are discussing this in this contemporary context!

  10. Whewell’s Gazette: Vol. #43 | Whewell's Ghost writes:

    […] Dataisnature: The Hindu Temple as a Model of Fractal Cosmology – Forecasting Architecture with Recursive Instruc… […]

  11. paul writes:

    @Gregory, I take your point here. This post could have expanded on the implicit vs explicit fractalization process in art and architecture. Quite often the explicit use of fractal processes can be quite worn, boring and generic. Fractal ’emergence’ a the result of philosophical ideas or physical constraints are much more interesting not only because of the resulting aesthetics, but also the trickle down effect of how certain ways of thinking can become externalised in form, as you say ‘ important to remember that these things were created from the inside out’

    Other great examples of philosophical or physical constraint based fractalization processes include those found in the Shipibo textiles and African tribal design:

    African Fractals: Modern Computing and Indigenous Design [PDF]:
    http://monoskop.org/images/f/fc/Eglash_Ron_African_Fractals_Modern_Computing_and_Indigenous_Design.pdf

    The Generative Song & Sound Pattern Matrixes of the Shipibo Indians:
    http://www.dataisnature.com/?p=596

  12. paul writes:

    @Jasmine, thanks for the extra info on Kirti Trivedi’s paper and also the leads on Dr. Stahapati’s work.

  13. Mayank_chatur writes:

    Please take a look at these papers….

    http://www.ijsr.net/archive/v3i12/U1VCMTQzMjI%3D.pdf

    http://www.researchgate.net/profile/Dongkuk_Chang/publication/222512493_Fractal_geometry_as_the_synthesis_of_Hindu_cosmology_in_Kandariya_Mahadev_temple_Khajuraho/links/0f31753b21e06bd624000000.pdf

    http://www.ijert.org/view-pdf/13155/role-of-fractal-geometry-in-indian-hindu-temple-architecture

    http://www.akashfoundation.com/Articals/Hindu_Temple_Models.pdf

  14. Dr. Jessie mercay writes:

    This lovely article is right on track with the cosmic understanding of temples per the Vishwakarma tradition. The late Dr. V. Ganapati Sthapati commented in depth about these ideas in his book Temples of Space science. We often think only of Hindu temples but this knowledge has been traditionally applied to Jain, Buddhist, and Islamic architecture as well as early Christain architecture. We like to think of it as “Hindu” but in fact, it is universal and not simply Hindu. Would a Buddhist, Jain or Muslim apply Hindu architecture? No. Hence we must accept that the forms built per Vaastu and Silpa Shastras are beyond religion – they are indeed universal forms that manifest fractals of consciousness for the well being of humanity.

  15. Seema Poudel writes:

    Hi,
    I am an IB student doing my extended essay in fractal geometry used in Hindu Architecture. I loved your article but I would like to know if you have the data about the measurements of the temple such as height of the each storey or the radius of the each part of the temple. That would be great help for my research. Thank you
    Sincerely,
    Seema Poudel

  16. paul writes:

    hi @Seema Unfortunately I don’t have access to the data you require. My info was gleaned from visiting many temples in India and reading some of the articles mentioned in this post. Good luck.

  17. Criação writes:

    Congratulations! This fine article has reached the front page of Hacker News!

  18. allan writes:

    nice article. i think you mean Karnataka, not Karatanka in the last line.

  19. Dataisnature: The Hindu Temple as a Model of Fractal Cosmology – Forecasting Architecture with Recursive Instruction – The Known Worlds: writes:

    […] The Hindu Temple as a Model of Fractal Cosmology – Forecasting Architecture with Recursive Instruc… […]

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