In
1984, George Cowan organized a research group called the Santa Fe Institute,
assembled to study what could be one of the most fundamental theories about the
nature of our world’s complex systems, and the unifying principles that bind
them. Though following relatively simple basic principles, the structural
complexity of ant colonies is remarkable. World economies, with individual
agents acting in limited capacity, produce exclusively macro-level behavior.
The neuronal mess of the human brain produces concepts so liquid and elusive as
thought, and consciousness, with no apparent or conceivable physical, cognitive
correlate. The most core of these principles is this: that these seemingly
inexplicable complex systems manage to form from relatively simple rules and
initial, guiding principles. It is inconceivable, yet tempting, and subtle
despite ubiquity.
Related
to (but distinct from) complexity theory is chaos theory, which explains that
small change in initial conditions can bring about dramatic, seemingly
disordered effects. This is the theory that brought Edward Lorenz, in 1961, to
coin the term “the butterfly effect” (the situation of a butterfly flapping its
wings, and that slight effect it creates potentially generating a tornado that
otherwise would not have been). Basically, many phenomena are impossibly
unpredictable. They are completely chaotic, seemingly random. But, the very
fact that a change in initial conditions (sometimes as small a change as a 4th
decimal place for an initial value, or smaller) can bring about new results
does show a degree of causality.
Chaos
theory was developed in large part by Benoit Mandelbrot, who created the term
“fractal”. A fractal is a self-similar geometric phenomenon, irregular but with
a familiar and consistent pattern. Self-similarity refers to the property
whereby no matter how much you zoom into an image, the same fractal pattern is
represented. Or, rather, that the figure’s general theme/shape is composed of a
number of instances of that exact same theme/shape, and these individual
composing pieces are themselves composed of the same number and configuration
of parts as the level above. Fractals are generated mathematically, through the
use of specific types of self-referential equations. A small change in the
initial conditions of a fractal generation produces vastly different large-scale
results for the final picture.
Since
their discovery, fractals have since been found throughout nature, in swirling
seashells, electric bolts, types of broccoli, and are the most accurate
description of the trace of coastlines. Fractal mathematics have been used to
create complex and often beautiful works of art. The property of
self-similarity produces hypnotic swirls, maddening designs of infinite,
swallowing complexity.
References
/ Further Reading:
Chaos: Making a New Science, by James Gleick
Complexity: The Emerging Science at the Edge of Order and Chaos, by Mitchell M. Waldrop
Click here to see the self-similar nature of fractals by zooming in
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