An Immersive Experience In The Realm Of Fractals and Fractality of Genome: Ancient Indian Mathematical Prowess in Fractal Geometry Revisited!!.


Author and Thought Leader Ram Ramanujam with Fractal Mandalas in Sun Temple, Konark, Odisha.

In Bangalore, India, I read the works of giants in Fractals upon completion of ENCODE International Consortium Project. The research papers revealed a repetitive self-similar structure of fractal globules and loops in Genome architecture. Fractal rendering is reminiscent of the fact that humans are multifractals. Lungs, heart and brain are fractal structures, and the cancer genome has fractal defects. Cancer is a genome misregulation disease.

The immediate resonance probably happened as in India, our ancient culture, art, and science are rather deep-rooted in self-similar repetitions and mathematics. The Indian temples are standing examples of “fractal architecture” since ancient times. Therefore, we naturally and immediately embraced these pioneers. With all that talk about “everything is fractal in India”, we are not ignorant of Western cultures. Indeed, European mathematicians are much appreciated. Archimedes, Pythagoras, Euclid, etc. were admittedly of great influence on the mind of French philosopher and natural scientist Rene Descartes even in 1629. Newton’s Euclidean geometry and Einstein’s groundbreaking theories and observations were on par with philosopher Immanuel Kant. We know very little about Euclid and way too little about Pythagoras. Along these lines, some keen insights into biology were shaped by mathematicians, namely Euler, Gauss, Jacobi, and David Hilbert, followed by physics giants Niels Bohr, Erwin Schrodinger and John von Neumann. Alan Turing projected Thinking machines. Physicists, with an interest in biology and genomics, were common. We can see this in “What is Life” by Erwin Schrodinger.

At this point emerged Benoit Mandelbrot, who embraced the Fractals and Fractal theory but stayed away from life sciences as he speculated that biologists were not ready, even after the insistence of John von Neumann to apply mathematics to biology. 

A Rendering Fractal Structure of Gopuram, Tamil Nadu Meenakshi Amman Temple in Madurai, India.

Mathematics is the mother of all sciences. Norbert Weiner developed a distinct discipline named Cybernetics which centred on feedback. In the Indian Vedic period, speculated to be started by 5000 BC, Indian mathematics and astronomy were embedded in Vedic inscriptions. The principal scientist of his times was Dirgatamas Mamateya 4000 BC, a priest of King Bharata, who ruled ancient India and was a great scholar, a saint. While the term “fractal” was coined by Dr Mandelbrot in the late seventies, the concept goes back to SALBUSUTRA (Sutra means “Formula”). Arguably, the Sri Yantra diagram involves the application of two irrational numbers, the Pi and the Golden Ratio. Fibonacci numbers seem to have originated in India by several mathematical observers.

Fractal Temples in India

What is depicted above is a raising fractal-like structure of spires of Kandariya temple in Khajuraho. The Temple structure is reminiscent of features in the Mandelbrot set.

The Indian prowess in Fractal dates back to our forefathers, who pioneered Fractal Geometry. I can cite several examples across the country where the Fractal nature of temples including one in Hampi Karnataka.

The temple figures have been acknowledged exclusively to a website called Fractal Enlightenment, which richly depicts temple structures and Fractal delight the way of life for our eminent math forefathers.

Central Dome in Fractal Temple
Sun Temple Modhera, Gujarat. Fractal Temple.

Srinivasa Ramanujan compared with the likes of giants, also laid solid foundations for fractals in 1916. His partition theorems were recently explored as foundations of fractals by Emory University researchers in the USA.

Recognition of the Late Benoit Mandelbrot came very delayed.

“The future pharma will be IT-led” and smartphones will revolutionize genomic medicine as embraced by Dr Eric Topol, in his famous book Creative Destruction of Medicine.

The mathematization of Genomics and Genome Editing will pave the way for the Agricultural Revolution, Production, and Food security. In addition to treating the debilitating single-cell mutative Mendelian disorders, to extend diagnosis and therapy for autism to cancer. 

A Fractal Art:

Examples of biological and mathematical fractal patterns. Biological fractals may be statistically self-similar over a limited range of scales, known as a scaling window. a | Rat pulmonary arterial vasculature, imaged via contrast-enhanced CT angiography, which is an example of a biological fractal. b | Normal lung tissue specimen stained with haematoxylin and eosin, which also has fractal properties, and thus is amenable to fractal-dimension analysis. In comparison with biological fractals, mathematical fractals can be infinitely self-similar, examples are fractal trees and the Hilbert curve. c | A fractal tree, showing the first 10 iterations of symmetrical branching. d | The Hilbert curve, is a continuous space-filling fractal curve with a fractal dimension of 2—a non-fractal curve has a dimension of 1. The first 5 iterations of the Hilbert curve are shown here.

Nat Rev Clin Oncol. 2015 Nov; 12(11): 664–675. Reference.

Discovery Epitome of 20th century the Indian Maize fame Barbara McClintock. For the History of Science, it may not matter much. For doing away with cancer it will be a life-or-death issue for mankind. In the name of curing cancer, an enemy of the Planet and there cannot be a Plan B in this aspiration, but his unrelenting march towards the fight against cancer, a minute-by-minute killer, a natural enemy, and can cause havoc in destabilizing the stability and wellness of the nations.

Many in security and Intelligence circles believe that genome editing is a cause for worry as it can inflict not only destruction at a mass level but genome-engineered designed soldiers are possible. Intelligence circles cannot disregard the caveats and potential remote possibility of a mildly potent genome-engineered version of the arsenal. While it is certainly not a garage-style DIY science, it should be no secret that scientists are already working on it. If the so-called skilled in the art hardly can decipher the fact of what to edit first, then the perils of misuse are at least far from reality at present. When designer babies are not welcome, and germline editing is a contentious issue subject to regulation, one can assume genome editing for diseases is the real potential for the next decade and Genetic Engineering of the 21st Century.

Fractal genomics would make sense, making a home run for India since fractals are deeply embedded into ancient cultures and architecture and math. It is a rare opportunity for India to claim a space in the world of genomics enterprise. The symbolism of L-Systems or Lindenmeyer fractals has been absorbed by myself the author of this piece and India has to enter its metal in the world Genomics enterprise to carve out a niche place.

Before I conclude, I find it intriguing to quote Dr Rumana Sinha Singhal and her Fractal arts. Her illustrious work is cited here with a few of her recent works.


Prof Dr Andras Jeno Pellionisz, President, HolGenTech Inc, Sunnyvale CA USA

Prof Dr Jean Claude Perez, IBM Professor, Paris, France.

Prof Dr Sergey Petoukhov, Laureate of Science, Russian Academy of Science, Moscow.

Prof Dr Ethirajan Govindarajan, President, Pentagram Technologies, Hyderabad India

Prof. Dr Kangs, Ex NUS and Nanyang Univ, Pondy, India, Editor in Chief, Bioinformation.

Dr Jana Krishnamoorthy, Prof. Jimma Univ, Biomedical Engg Dept., Addis Ababa Ethiopia

Dr Rumana Singh Sehgal, Karma Veer Chakra awardee, President Serendipity HYD India

Dr Gargi Roy Goswami, Editor in Chief, Genomeden & Managing Director, Dr KamleshRoy Research and Diagnostics

Author: Ram Ramanujam.

Ram is currently the Founder &CEO of Propinquity Therapeutics, Bangalore, India. Ram has 32 years of experience and is a seasoned biotech professional. He is a functional biologist having worked on Enzymology, Protein Chemistry, Microbial physiology, Nucleic acid enzymology and Genomics. Ram also has worked on Biologics, RNA Biology, and Genome informatics. Ram has work experience with global leaders spanning four countries US, FRG, Japan and India. Ram discovered a procaryotic TGase from B. subtilis cells and is widely cited for this work in the late 80s. His name is listed in Icons Webster sporulating timeline history 2007. Ram also invented a technique for Rz diagnostics, in which he used FRET to monitor Rz reactions in real-time. He also is an RNA specialist who worked on Rz kinetics. He worked in the 90s with Regeneron, USA and Biocon, India. He was also at the University of Kiel FRG and NAIR Univ of Tsukuba Japan. He was a first generation Bioinformatician at DSQ and Satyam India and later continued as an intrapreneur at many start-ups including V Clin Bio labs India and currently a stakeholder, and Strategic advisor in Clevergene Pvt Ltd. India. Ram was guided by Dr James H Hageman and Dr Glenn D Kuehn of NMSU USA who hail from Dr Daniel Atkinson’s lab in UCLA and mentored by Dr Paul D Boyer. Ram’s Nucleic acids Enzymology advisor Dr Peter A Gegenheimer comes from the world’s leading labs of Dr Sid Altman, Dr David Apirion and John Abelson. Ram’s Genomics mentor and advisor is Dr Andras J Pellionisz, a triple PhD in Genomics, Biology and computer science from the USA, and an informatic coach is Dr E G Rajan PhD, a World leader in Signal Processing and Image Processing. Ram is also commercializing his discovery of Transglutaminase from Bacillus subtilis cells for various Food and Industrial applications. Ram is also looking at Commercial ventures involving Genomics and Genome Informatics, concentrating on Fractal Genomics and Cancer Genomics with Internationally Renowned Figure Dr Andras J Pellionisz, his collaborator from Silicon Valley, USA. Ram has current responsibilities as global business development, Strategic planning and development, organizational development, Techno commercial activities, and fundraising activities. Clevergene is poised to become a world leader in Novel Genomics and Genome Analytics Technologies, and Ram is currently deeply involved in its development into a global leader. Ram has taught and lectured in various Universities like NMSU, USA and KU USA, and offered Genomics lectures as Visiting Faculty in many Universities and Private Colleges in India. Ram is committed, with a perfect combination of Biology and IT and has worked in various organizations, e.g., product and service sectors. He has an eye for detail, timely execution of projects and succinct performance. He organized the 2012 ICSCI conference Life Sciences track as a convener and ICETT 2012 Life Sciences conference in India. He is the Chief Coordinator & convener for the Genomics, Genome Analytics and Precision Medicine track of the ICSCI conference held in Hyderabad in 2017. He is the Founder and CEO of Propinquity Genomics Inc., Bangalore.


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