Beautifully Complex..

 I consider myself lucky, to stay amidst this concrete jungle and still be blessed to
 have an unobstructed view of the skies from my home. I yearn for the days when the skies aren't cloudy so I can see the sun set in the horizon, painting the sky in hues and shades that one can only wonder at. The painting is never the same despite the canvas and artist remaining constant. With the same set of evening colors there are new intricate flowing streams on the sky.


Some patterns shock us. Some creep us out. But usually they do catch our attention. And the world is full of patterns. Take a look 
  

The first  is an image of Saturn's rings, the second an image of a leaf and the third the image of a human iris. Beautiful pictures? True but something more intrinsic binds them.

They are the examples objects that contain Fractals, amongst various other objects in the world.
Fractals are never ending patterns that exhibit "self-similarity" at different scales and will keep on repeating possibly infinite number of times. They originate due to simple processes  but yet look seemingly complex. Although there is no formal agreed mathematical definition of fractals,  Mandelbrot, the mathematician credited with advancements in fractal geometry summed it up as "Beautiful, damn hard, increasingly useful. That's fractals."The guy who made a huge contribution to the field said it is "damn hard". Then how can we still possibly appreciate the glory of it ? Well all of us may not be able to understand the math behind it but we might see glimpses of the vast beauty of the field.



As children growing up we rarely found examples in nature of what we studied exactly in math. When was the last time you saw a triangle floating around ? Probably never. I think nature exhibits a much deeper sense of math, a way more vibrant canvas than a painter's and a degree of complexity and simplicity that leaves us spellbound and will continue to do so. And as kids we are actually being taught the rudimentary math that in the future may or may not help us study these. But it would be so cool if atleast we were exposed to the beautiful patterns nature showers us with. And also if we started noticing the phenomena around us more carefully. For example this image of smoke from a candle. It shows the idea of turbulence which is still an unsolved problem in physics.

 

And remember fractals are a small glimpse, a tiny peek at the manifests of nature.
The truth is we still can't understand a lot of things that we see around us. It isn't a blot on our intellect, rather it shows how much of a cautious, ever-evolving and a complex entity nature is. And we as mammals walking the face of this planet shall continue being in awe of such exhibitions by mother nature. And hopefully our senses learn more and more with time...
 

"Nature uses only the longest threads to weave her patterns, so each small piece of her fabric reveals the organization of the entire tapestry."  :
Richard.P.Feynman 



 

http://paulbourke.net/fractals/googleearth/

Nature uses only the longest threads to weave her patterns, so that each small piece of her fabric reveals the organization of the entire tapestry.
Read more at: http://www.brainyquote.com/quotes/quotes/r/richardpf160463.html

We humans are enthralled by sheer size  and scale of things. Think about it , we always pore over the largest building, the biggest event, the biggest plane and the list goes on and on. As a society we seem to be tilting towards the idea of bigger a statue better it is ! I always feel over time people lost the ability to appreciate the subtleties of things. For example take a look at this picture  below. Called Madonna of the Stairs and sculpted by Michelangelo at the tender age of seventeen, it was one of his earliest works. Yes it is beautiful but is that all there is to it?  Devoid of any technology except his hammer, chisel and  the depth of his perception he carved beautiful sculptures. I shall quote a section from a biographical novel "The Agony and Ecstasy" on him by Irving Stone
to give you an idea of what went into this creation and why it symbolizes the excellence of execution, for years to come.

 

"There were so many things to think of at one time. His strokes had to hit towards the main mass,strike the marble toward the block it came out of, so that it could sustain the blow. He had designed his figures and stairs in a vertical position to lessen the possibility of cracking the block, but found that the marble would not yield to exterior force without accenting its own essence: stoniness. He had not realized to what extent marble had to be battled. His respect for  his material grew blow by blow."

Today to analyze any material we have a plethora of tools at our disposal. The man, from the moment he selected the marble block till the time he would finish the work would  be one with his marble.He would have to submit himself completely to it.  As the book quotes "Yet a marble contained a myriad of forms;had this not been so, all sculptors would carve identically." 

A custom  which Michelangelo used  to select the marble really fascinates me.

He would take the marble to a location which would receive the first morning light and observe how light falls on the marble. The seemingly transclucent marble and its veins and lines would be dissected  by his vision before making a choice. But why the morning light ? Why not the light due to any other source ?

I think it has to do something with the very nature of sunlight itself. It is composed of all seven colours which means there are seven distinct light waves which together give the perception of a single colour. Those days they didnt have any other light source which had  all the seven colours  in it. Or it would be that light coming from such great distance has planar wavefronts. For the layman, light which has planar wavefronts means the cross section to any light wave  is essentially a flat surface. Well something to figure out, right ? Interesting that he knew this in 1490, with no schooling or formal education to speak of...