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What is a fractal?

by Sally Morem

Created on: May 10, 2009

Process rules our universe. The Big Bang brings forth energy, matter, space and time. Quarks form subatomic particles, which in turn form atoms. Atoms bind themselves together into molecules. Molecules assemble themselves into crystals and living matter, which form complex relationships with one another.

French mathematician and astronomer Laplace believed that our jangling, booming, buzzing confusion of a universe was, at least in theory, fully comprehensible. If we could imagine a consciousness great enough to know the exact locations and velocities of all the objects existing in the universe at the present instant, as well as the exact nature of the basic forces of nature, then there could be, in principle, no secrets from that consciousness. It could calculate anything about the past or the future according to strict laws of cause and effect.

Laplace was profoundly wrong. In order to carry out those calculations, that consciousness would have to know the exact state of the entire universe at that instant. But, given the immense size of the universe and the inherent fuzziness of the subatomic realm implied by quantum physics, that is precisely what no one will ever be able to do.

A powerful intelligence could only specify approximations of approximations. But, in a universe where so many systems are poised on the edge of chaos, approximations just won't do. The error rate would multiply quickly as events follow events after the predictions were made. As a result, the universe would quickly veer off its predicted path. No matter how many errors were accounted for, new ones would pop up and stymie any accurate prognostication.

The universe does follow strict cause-effect rules. It is deterministic. But it is also inherently unpredictable.

Stuart Kauffman, a leading researcher in complexity theory, explained one aspect of the universe's self-organized criticality with a simple illustration: The central image here is of a sand pile on a table to which grains of sand are added at a slow, constant rate. Eventually, as the sand piles up, avalanches begin. What one finds are lots of small avalanches and few large ones.

Kauffman emphasized the central fact of this system by pointing out what happens at criticality. One additional grain of sand can tip the system in one of three directions: toward a small avalanche, a large avalanche, or no avalanche. Additionally, an observer can never tell before the instant the grain of sand is dropped

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