The Hindu Temple as a Model of Fractal Cosmology – Forecasting Architecture with Recursive Instruction
Monday, 6 April 2015
Kandariya 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.
Kandariya 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
Yellamma Temple [Karnataka] – Paul Prudence
Architecton Series – Kazimir Malevich [1923]
Temple 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.
Shweta 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
Sri 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
No. 1 — April 7th, 2015 at 8:47 am
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
No. 2 — April 7th, 2015 at 10:11 am
@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.
No. 3 — April 7th, 2015 at 2:58 pm
Nice article.
No. 4 — April 8th, 2015 at 7:04 pm
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.
No. 5 — April 8th, 2015 at 7:38 pm
Hi Marta, the three images that were taken by me you are free to use. Feel free to email me for more images.
No. 6 — April 8th, 2015 at 11:57 pm
[…] vía de Data is Nature, encontramos este fascinante concepto de los tammatras, que parecen ser las unidades que componen […]
No. 7 — April 9th, 2015 at 11:56 am
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” ..
No. 8 — April 16th, 2015 at 6:07 pm
[…] No final de contas, este templo hindu reflete o modelo do Universo fractal, como explica o Dataisnature. […]
No. 9 — April 19th, 2015 at 3:30 am
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!
No. 10 — April 20th, 2015 at 3:59 pm
[…] Dataisnature: The Hindu Temple as a Model of Fractal Cosmology – Forecasting Architecture with Recursive Instruc… […]
No. 11 — April 30th, 2015 at 9:09 am
@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:
https://www.dataisnature.com/?p=596
No. 12 — April 30th, 2015 at 9:11 am
@Jasmine, thanks for the extra info on Kirti Trivedi’s paper and also the leads on Dr. Stahapati’s work.
No. 13 — August 15th, 2015 at 11:36 pm
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
No. 14 — May 7th, 2016 at 1:25 pm
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.
No. 15 — August 22nd, 2017 at 12:02 pm
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
No. 16 — August 22nd, 2017 at 9:29 pm
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.
No. 17 — August 27th, 2017 at 1:55 pm
Congratulations! This fine article has reached the front page of Hacker News!
No. 18 — August 27th, 2017 at 3:20 pm
nice article. i think you mean Karnataka, not Karatanka in the last line.
No. 19 — August 27th, 2017 at 10:24 pm
[…] The Hindu Temple as a Model of Fractal Cosmology – Forecasting Architecture with Recursive Instruc… […]
No. 20 — November 26th, 2017 at 8:22 am
@Dr. Jessie mercay , I have to disagree with your assessment since “Hinduism” itself predates all the other religions you mention. How can you tell that the Hindu architecture itself did not percolate down to Buddhism or Jainsim? Muslim architecture is nothing to be spoken about while clearly we know that Buddhism and Jainism have roots in India. your statement “Hence we must accept that the forms built per Vaastu and Silpa Shastras are beyond religion” sounds just like evangelists and leftists in India who appropriate everything from Yoga to Ayurveda and blames “brahmins” and caste for the mughal barbarism