Saturday, 31 December 2011

Chaos and Cap'aphony

Feature Column on Chaos Theory 
by Aisoorya Vijayakumar

More chaos, and even more clutter

The persistent Kawphi girl and her hapless faculties are at their game, trying mighty hard to unravel the puzzling complex mysteries of the chaos theory. They are in the midst of fathoming the deep definitions of fractals, and her left brain tries, mostly in vain, to enlighten her right brain on the wondrous possibilities of fractals.

Thud thud thud! Kawphi girl bangs the table with her weary fists in one of her feeble attempts at ensuring that all the information pouring in from the left-brain doesn’t drain out through her ears. One recollection of the memories of the frog-faced exam supervisor sends her faculties – the left-brain, the mind, and the right brain, scurrying off to assemble all their learnings together.

The mind (ever the strict commander): ‘Alrighty fellas! Let’s learn about the fractals. We have four more hours to go before the exam!

Right brain: Woohoo! I’m all set. Left brain, pal, have you learnt to speak human, or do you still resort to speaking incomprehensible gibberish?

Left brain: Right-brain, let’s be serious! This calls for some united defense.

Right brain: Goodness left-brain, pal, can’t you take a joke?! Fine, what’s on our cards?

Mind: What we need to do is stay focused on the subject.

Left-brain: …And not indulge in some mass delusional yapping about substantiating our individual contentions on our apparent preeminence in cognitive capabilities!

Right brain (with a muddled expression): Err… Not indulge in what?

Left brain: It’s tough to be me! Having to deal with retarded other-halves!

Right brain (Advancing menacingly towards the left brain): You speak with an outlandish resolute conviction of a lunatic intent upon using all possible words in your sentences, irrespective of whether they make sense or not, and you have the audacity to call ME a retard?!

Mind: Aww, cut that out you two! I told you! FOCUS!

Left brain: Right! So, fractals, as we were discussing, are, in simple terms, fragmented patterns of similarity. What I have read so far on this is that, Mandelbrot is credited with having brought some illumination and clarity into what most people believed to be amorphous – the mathematical patterns of predictable and unpredictable occurrences in the world.

Mind: Hmmm, and was there any specific science that at least tried to comprehend this before Mandelbrot’s days?

Left brain: Maybe not comprehend per se, but the field of Euclidian geometry encompassed the study of realizing perfections in abstract forms that was nearly non-existent back then. And what Mandelbrot theoretically did was envisage and foster a method for observing and mathematically defining many nebulous natural phenomena.

Right brain: Such as?

Left brain: Such as, for instance, cloud shapes, coastline patterns, and so many more.

Mind: When did all this start?

Left brain: You see, this was one of those serendipity breakthroughs. I read in the Telegraph that Mandelbrot, a research fellow with IBM, started a series of analyses in the 1960s, of electronic "noise." His experiments began because this noise seemingly meddled with IBM’s other electronic transmissions. He and his team noted that the glitches and interferences occurred in clusters, and that these clusters also formed a pattern. Each period of interferences and the periods of smooth transmissions, when enlarged, mimed the overall pattern of the large scale graph as well. They called this a “self-similarity.” Mandelbrot further demonstrated the occurrence of such patterns in other areas such price curves, coastlines , and so on.
In a viewpoint-turning pivotal essay that he called How Long Is the Coast of Britain? (1967), Mandelbrot stated his points and observations on fractals in coastlines.

Right brain: Yaay! The left brain gets this year’s award for non-stop rattling nonsense. Really! Left-brain, did you mug that up all by yourself or did you take a drug?

Mind: You, again!!!

Right brain: Well what the heck am I supposed to gather from that load of lines?

Left brain: Well, let me show you some classic examples of what I mean. I found these in the pages of University of Wisonsin, Madison.

Look at how each of these patterns in nature are self-similar, each smaller fragment being a replica of the overall figure.

The Cantor Set

The Koch Curve

The Sierpinski Gasket

A Dragon

The Cantor Maze

A Twig

A Crystal

A Snowflake

A Tree

The Barnsley Fern

Right brain and Mind (in unision): Wow!!!!

Left brain: That’s not all. You can still see instances of these fractals in the rich offerings of nature everyday. Look what I found in the archives of the WebEcoist Site – Nature's Examples for Fractals.

Mind: This is mind-blowing. What does it mean? The word – “fractal?”

Left brain: Mandelbrot is said to have coined this term from the Latin word frangere which means “to break.”

…. The Kawphi girl faculties would continue to study the chaos theory tirelessly amidst all the din and pandemonium, and all you need to do is visit this column in the next issue to get to know about the progress the team makes…

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