Thursday, June 9, 2016

Fractal Hunting

The human search for pattern


It took a mathematician to tell us why we love the art of Jackson Pollock.

That the subject is under discussion is evidence, we suppose, that not everyone is as enamored as we with the work of the great mid-century action-painter, expressionist. Where we see a hypnotic and original style of painting, others see disordered dribbles and splashes of pigment, more suggestive of a studio mishap than deliberate art. Why, one philistine of our acquaintance even threatened to haul his oft-used, crusty drop cloth out of the basement, forge Pollock’s signature to it, and try his luck selling it to MoMA.

Cretins like that aside, Pollock’s body of work is celebrated world wide by lovers of modern art. And art being art, it almost seems antithetical to examine the reasons why.

But there’s a hidden logic to aesthetic rules or at least guidelines that govern what we find pleasing to the eye or ear, even though we’re often quite unaware of it.

In the case of Pollock, there’s no overt symmetry or pattern we can cling to which would seem to explain the allure. Or is there?

Fractals are a relatively new (or newly recognized) family of geometrical designs, defined as patterns that repeat themselves at any scale. The most familiar ones, such as the Mandelbrot set, are purely imaginary, existing as computer models and born from complicated mathematical formulae.

But then fractal hunters noticed something amazing: Fractals do exist in the real world, and they’re far from rare.

Look at that tree outside. The trunk sprouts limbs, from which sprout branches, then twigs. Zoom in on any of those twigs, and see how it mimics, in its abbreviated way, the propagation of the greater tree.

Or pick up a rock, one no bigger than your fist. Bring it in close and get a good look. Then try to imagine what would distinguish it from a multi-ton boulder sitting a few yards away.

The scales change. The patterns do not.

Which brings us back to Pollock. The man shuffled off his mortal coil back in 1956 so we can’t be sure if he was aware of it, but turns out, he was making fractals too.

Dr. Richard Taylor from the University of Oregon’s Department of Physics was the first to demonstrate this back in 2011. Lacking the ability to mimic Pollock’s technique by hand, he built a paint-spattering rig (he calls it the “Pollockizer”) that fairly accurately reproduces this signature style. And he found that what makes a Pollock a Pollock is the depth of saturation. And the randomness? It’s illusory. Patterns assert themselves. Perhaps most importantly, like fractals, they do so at scale. Slice out one square inch of a Pollock canvas (actually, please, don’t)...enlarge it, and compare it the original. You’ll find they’re twins.

There is indeed a point here, and it’s as relevant to business and human nature as it is to art. We are pattern-seeking creatures. Unlike most mammalians our olfactory prowess is pretty feeble. Our hearing likewise leaves a lot to be desired. We rely instead on sight. We depend upon our eyes to provide timely input on whether that face down the block is a familiar one, and whether it belongs to a friend or foe. We need to know if a vague shape in the leaves where we’re walking is a stick, or a deadly viper.



This has evolved into an amazingly versatile faculty. We’re not just able to see shapes and faces floating in the clouds, we can find revelation and courses of action hidden in reams of raw data. We can wade through noise, through chaos, and find that no, it’s actually information.

Savants like Jackson Pollock need not understand the theory behind the pattern-making. Neither do we. This is our natural element. And just as easily as he dipped his hands and splashed the paint, we too can dip into the seeming tumult, and make sense of it.

The C4:
1. Chaos Theory (a close cousin of fractal theory) tells us that chaos itself is a rare bird indeed. Nature abhors randomness. Order asserts itself, even when, on the surface, disorder seems to abound.

2. Just knowing this offers an advantage—in the business realm, certainly, but just as certainly in every other realm of human endeavor.

3. Finding signals in the noise takes a bit of a knack, perhaps, but no special training or aptitude. All it really requires is the willingness to try, and the conviction that doing so will be worth it.

4. Jackson Pollock (Jan. 28, 1912 - Aug. 11, 1956) was an American painter and one of the most influential artists of the twentieth century. He may or may not have consciously pioneered the aesthetic use of fractal design. Does it matter? You can lose yourself in his Full Fathom Five without ever needing to know exactly how he created it.