Fractals

20 May 2014

Beauty lies in the eyes of the beholder.

I strongly believe that mathematics is nothing but intuition. One of the reasons that laid a foundation for such belief was when I encountered some qualitative knowledge of the fractal and how it came to be discovered.

Professor Benoit Mandelbrot, as Wikipedia says, was a Polish-born French and American mathematician. I heard only a part of it.

He was a mathematician.

Exaggerated, but not surprising that he used his mathematics genius to give a description of a piece of broken stone. His obsession with describing the shapes of broken pieces connected the world of complexity with simplicity (But it needs skill to see that connection, of course).

Talking about chaos in nature, messiness all around and his love for, on contrary, clear and regular-shaped objects like circles and ellipses, I read somewhere that he considered himself a mathematical scientist, not applied or any other scientist. Moreover, that was his designation at Yale University, deliberately chosen to be ambiguous. But to make it more sensible, he was a philosopher, a physicist, an economist and an artist.

Look at a tree dividing into branches, look at a branch dividing into sub-branches, look at the sub-branches dividing into smaller sub-branches, look at them dividing into tiny branches that carry the leaves, look at the leaves dividing inside into nerve-like pattern that resembled dividing branches again, so on and so forth. Nature is complex, it is messy.

But the messiness has pattern, complexity has order, a broken stone’s roughness could be well described. The bronchioli and the alveoli in lungs have this pattern. Price changes in financial markets have this pattern. Bones have patterns, microscopically viewed. Helical molecules inside cells have it. In our day-to-day philosophical contemplation too, (if anybody still does this anymore) has a pattern. Elementary particle paths after collisions have predictable shapes.

All matter has pattern. The landscapes on the earth, the galaxies in the universe have it. Maybe once photographed, blackholes might be seen having patterns. The earth as a whole has it. The waves on Jupiter have it. Music has it. Water waves have it. The surface of a broken stone has it. The broken stone is called fractus in Latin. Professor Mandelbrot picked it to name his mind-breaking universal concept of geometry. The so called fractal patterns!

I like to think that it is left to the mind that perceives things and life.

Why nobody else but a few aristocratic fellow humans could see things that not everybody could see? Therefore, can I call it intuition. Put things in perspective, put intuition in numbers and equations, and say,

Let there be mathematics!

Not everybody has such vision, such vigor. Especially in contemporary world full of 5 to 10 inch smart phones that don’t fit in pockets, we have no such leisure.