Sunday, May 29, 2011

A Font-astic quote on Fractals..!

Fractal Universe! :)

Hi pa..!!

Please click on the below image, download it if you please,  observe it...after reading it..!

Would you believe that it took almost 45 minutes to carefully "type" out the above paragraph..?? :) You may find the book mentioned above, but you will never find it in a way presented above.

Just notice the minute details, like for example, the way the words "cold" & "dry"  (the quotes around them rather !) have been 'rendered', as also the fact that "i" is/am wearing a "hat" too...!!! ;-) :)

This is in fact, the opening paragraph of the magnum-opus of Benoit Mandelbrot (notice the right way to spell his name)--"The Fractal Geometry of Nature", which took the world by storm, & almost single-handedly elevated Fractals into the realm of the believable, rather than being mocked upon as 'silly program artefacts' that have no practical applications or implications what-so-ever...! It now turns out that Fractals & Chaos are at the 'heart' of almost every Physical phenomenon or manifestations of the Universe...!!

I am really shocked to find people who routinely ask me --"WHAT use is OLL this mathematics of?? It does not have any practical use..." That is the farthest from the TruTh anyone could ever get! :-)

Anyway, I just wanted to share this fantastic piece of quote by 'dressing it up' with an amount of care perhaps never given to it before..! Hope you liked it, & it makes you (p/w)onder pa...?

I should soon make some FRESH starts...of discoveries, & this has really inspired me indeed...! :-)

I wonder if...if...
"our universe is itself, a fractal...?!??" :)

Love & Best Wishes,

The boy in 'rags'
Planet Earth
'Begin at the beginning,' the King said gravely, 'and go on till you come to the end: then stop.'
:- Lewis Carroll (Alice in Wonderland)

Sunday, May 8, 2011

Shear Magic...! <3 :)

Hi pa!!

Well, one of my friends Shreyas, had shared a link on the topic of matrices in general, & there they had shown a very interesting "shear" transformation of the image of the famous MonaLisa of Leonardo Da Vinci.

Here is that image...courtesy Wikipedia ( Click this link )

And I had promised that I too would try n somehow do that on my own...!!
Because, I felt, with my Wishful Thinking, that OLL it needs, is a matrix representation of the image in question, & then, apply a 2X2 or 3X3X3 "transformation" matrix on it...! :)

And I shut myself up, trying this way & that...checking if there's a very simple representation I could work with...but all my efforts had either gone astray or in vain...into the drain...!! :-(

But all of a sudden, teday, (on the eve of Mothers' Day..!?!?) I was able to JUST Do it..!! :)

And hence, without much ado, let me SHARE this sheer miracle..!!
[Note: SHEAR & SHARE are anagrams of each other! Howzzthat..?? :P]

Fer this experiment, I decided to use the snap of the beautiful Maria Sharapova--guess she's lucky enough to be chosen by Me fer some image make-over(s)..!!? ;) 

BEFORE the SHEAR: (As-is, in fact the "shearing" parameter is all zeroed out..!) 

AFTER a +ve SHEAR in the horizontal (x-axis) direction

AFTER a -ve SHEAR in the horizontal (x-axis) direction

Hope u liked it pa..!??! :)

As fer me, i jusst LOVE--D it...(including the snap of Maria too..! ;) Sorry Maria...but thanks fer your b'ful snap & fer bearing with this...!! :) )

Thus, with some stubborn determination & image-ination, we can always manage to do some "transformations"...!! :P

Keep Smiling....AL(L)-ways...! :-* :)

Love & cheers,

the moron in "rags"
Note: As a follow-up to this, I was able to extend it, & achieve a 3-D shear setting up a nice, 3-dimensional [3X3X3] matrix.
But I feel the 2-D shear illustrates it just fine enough... :) 

Here's one of my favourite oxy-moronic quotes in this context... :) 
I close my eyes, in order to "see"...
- Paul Gauguin