On Chaos and Order

The Fascinating Mandelbrot /Julia Sets:

Anyone who's been following my blog knows I have this unending fascination with the Mandelbrot Set...

Watch the video below, as one steps into the world of the Mandelbrot and Julia Sets. If Spock were around I'm sure you would hear him say, "Fascinating!"

WATCH THIS VIDEO FIRST: https://www.youtube.com/watch?v=vfteiiTfE0c&t=163s

The process by which the Mandelbrot evolves is sublime, magical, mathematical and above all mystical. Arresting. Mind Expanding. Mind Creating even. Truly Powerful. And exceptionally, exceptionally beautiful. And so , so simple. Who would have thought all it took was to plot an equation as basic as z= z^2 + c. Mandelbrot would have, of course!

And as he best put it himself in his inimitable french accented english and mischievous imp like smile, " I can see things that  nobody else suspects, until I point out to them, "Well, Of course! Of Course!" but they haven't seen before! "

DO WATCH THIS AMAZING PBS NOVA DOCUMENTARY  =>> : https://www.youtube.com/watch?v=ZbK92bRW2lQ&feature=youtu.be

On Order and Chaos:

The play between Order (Cosmos) and Randomness (Chaos) is ages and aeons old. Time and Space are thus but partitioners - partitioning infinitesimal segments of infinitesimal segments within this play. Wheels within wheels.Layers within Layers. Levels upon Levels. Like Warp and Woof. From the smallest point the mind posits to the largest Universe the Mind can conjure and all in between. Are they all connected ultimately?

The process where boundary fluctuation and turbulences give an illusion of interplay locally. But the interplay isn't local it's everywhere for every ordered system a boundary. At every boundary turbulence, at every turbulence , chance, randomness and Chaos.

Chaos or Cosmos? Randomness or Order? In effect the Mandelbrot is a very structured arrangement of geometric points (because as anyone who has played with Mandelbrot/Julia Animators will know, each and every point on the mandelbrot set corresponds exactly to corresponding points on any given Julia set), but, there are fascinating caveats to this order, like for instance, the unbelievably detailed and deep self symmetry, the profusion of details that proceeds when you zoom at any given point of the graph, or the fact that the boundary of the set is infinitely detailed / long / slipping into and out of the Mandelbrot set itself in a bizarre and unpredictable manner!

So What is it all about Ultimately?

And so, making leaps elsewhere from there, as Mandelbrot would I suspect, no doubt approve:

Does the Mandelbrot Set tell us something about the very nature and structure of the very fabric of our Space-Time Continuum? Is it a set that brilliantly illustrates the Transition from Chaos to Cosmos and its complicated transition from one to the other and vice versa? Is the set merely a tool to examine self similarity? Or does it say something about our Universe? Predict a Grander Order? Explain a Small Chaos?

This universe. Our grand mystery. Is really quite simple a story perhaps? And does the Mandelbrot have interesting multiple takes on this story?

This universe. Our grand mystery. Is really quite simple a story perhaps? And does the Mandelbrot have interesting multiple takes on this story?

I really don't know about late old Benoit..but I would really like to think so!

On The Awesome Land Of Tor'BleDnaM..

Benoit Mandelbrot

A Tribute:

Benoit Mandelbrot

Developer of fractal geometry dies at 85 in Mass.

The Associated Press

CAMBRIDGE, Mass. (AP) — Benoit Mandelbrot (ben-WAH' MAN'-dul-braht), a well-known mathematician who was largely responsible for developing the field of fractal geometry, has died. He was 85.

His wife, Aliette, says he died Thursday of pancreatic cancer. He had lived in Cambridge, Mass.

The Polish-born French mathematician founded the field of fractal geometry, the first broad attempt to quantitatively investigate the notion of roughness. He was interested in both the development and application of fractals, which he also showed could be used elsewhere in nature.

For years, he worked for IBM in New York. Later he became Sterling Professor Emeritus of Mathematical Sciences at Yale University.

Mandelbrot also received honorary doctorates and served on boards of scientific journals.

He is survived by his wife, two sons and three grandchildren.

>>>  Courtesy Associated Press

Benoit Mandelbrot..he of fractal curves and chaos theory, roughness and fat tailed distribution passed recently away of pancreatic cancer in Cambridge, Massachussets. One of my personal heroes, what suives is my personal fewliners on this giant brain and his impact on our lives.




A Brief History of the Man:

Benoît B. Mandelbrot (he added the middle initial himself, though it does not stand for a middle name) was born on Nov. 20, 1924, to a Lithuanian Jewish family in Warsaw. In 1936 his family fled the Nazis, first to Paris and then to the south of France, where he tended horses and fixed tools.

After the war he enrolled in the École Polytechnique in Paris, where his sharp eye compensated for a lack of conventional education. His career soon spanned the Atlantic. He earned a master’s degree in aeronautics at the California Institute of Technology, returned to Paris for his doctorate in mathematics in 1952, then went on to the Institute for Advanced Study in Princeton, N.J., for a postdoctoral degree under the mathematician John von Neumann.

After several years spent largely at the Centre National de la Recherche Scientifique in Paris, Dr. Mandelbrot was hired by I.B.M. in 1958 to work at the Thomas J. Watson Research Center in Yorktown Heights, N.Y. Although he worked frequently with academic researchers and served as a visiting professor at Harvard and the Massachusetts Institute of Technology, it was not until 1987 that he began to teach at Yale, where he earned tenure in 1999.

Dr. Mandelbrot received more than 15 honorary doctorates and served on the board of many scientific journals, as well as the Mandelbrot Foundation for Fractals. Instead of rigorously proving his insights in each field, he said he preferred to “stimulate the field by making bold and crazy conjectures” — and then move on before his claims had been verified. This habit earned him some skepticism in mathematical circles.

>>>  Courtesy : www.nytimes.com

A brief history of his work & legacy :

Dr. Mandelbrot coined the term “fractal” to refer to a new class of mathematical shapes whose uneven contours could mimic the irregularities found in nature.

“Applied mathematics had been concentrating for a century on phenomena which were smooth, but many things were not like that: the more you blew them up with a microscope the more complexity you found,” said David Mumford, a professor of mathematics at Brown University. “He was one of the primary people who realized these were legitimate objects of study.”

In a seminal book, “The Fractal Geometry of Nature,”published in 1982, Dr. Mandelbrot defended mathematical objects that he said others had dismissed as “monstrous” and “pathological.” Using fractal geometry, he argued, the complex outlines of clouds and coastlines, once considered unmeasurable, could now “be approached in rigorous and vigorous quantitative fashion.”

For most of his career, Dr. Mandelbrot had a reputation as an outsider to the mathematical establishment. From his perch as a researcher for I.B.M. in New York, where he worked for decades before accepting a position at Yale University, he noticed patterns that other researchers may have overlooked in their own data, then often swooped in to collaborate.

“He knew everybody, with interests going off in every possible direction,” Professor Mumford said. “Every time he gave a talk, it was about something different.”

Dr. Mandelbrot traced his work on fractals to a question he first encountered as a young researcher: how long is the coast of Britain? The answer, he was surprised to discover, depends on how closely one looks. On a map an island may appear smooth, but zooming in will reveal jagged edges that add up to a longer coast. Zooming in further will reveal even more coastline.

“Here is a question, a staple of grade-school geometry that, if you think about it, is impossible,” Dr. Mandelbrot told The New York Times earlier this year in an interview. “The length of the coastline, in a sense, is infinite.”

In the 1950s, Dr. Mandelbrot proposed a simple but radical way to quantify the crookedness of such an object by assigning it a “fractal dimension,” an insight that has proved useful well beyond the field of cartography.

Over nearly seven decades, working with dozens of scientists, Dr. Mandelbrot contributed to the fields of geology, medicine, cosmology and engineering. He used the geometry of fractals to explain how galaxies cluster, how wheat prices change over time and how mammalian brains fold as they grow, among other phenomena.

His influence has also been felt within the field of geometry, where he was one of the first to use computer graphics to study mathematical objects like the Mandelbrot set, which was named in his honor.

“I decided to go into fields where mathematicians would never go because the problems were badly stated,” Dr. Mandelbrot said. “I have played a strange role that none of my students dare to take.”

>>>  Courtesy : www.nytimes.com

My respects to the man and his genius..RIP Benoit Madelbrot !!


The Awesome Land Of Tor'BleDnaM :


Plots and zooms essentially of the graph known as the Mandelbrot plot (And referred to  often as the land of ..you guessed it..)

On Why Architects Refraining from Ganja is a good idea...

Well, one of my favourite artists of all times is Maurits C. Escher. Now he was known for capturing finer points of Riemannian, Lobachevskian and other more mathematically complex topologies through his art. His works span some of the more subtle concepts of relativity, dimensional bending,etc. apart from other stuff. The picture above is a print by him called "Relativity" (c.1953)

So what does this print have to do with architects ?
Just this: take a look at our hostel (the pic on top)...this maze of ladders and corridors leaves us feeling like snakes in one big game of "snakes and ladders" in the new hostel that we at IIFT call our home for now. Either the architect of this crazy maze was a fan of Escher like me, or he overdid his daily dose of ganja prior to designing our hostel, which brings me full circle back to the title of this blog as my parting thought....

Alright so you're a hot shot architect and the only way you can prove it to the world is by designing something that's way out of the ordinariness sweepstakes, but is it essential that you source your inspirations from dreams inspired by particularly potent variants of cannabis smoked by you and your buddies??



P.S. On second thoughts the Escher-esque topography of our hostel does seem to grow on one as the academic year progresses...but till then..:(