What Is a Fractal?
And who is Mandelbrot?
The word "fractal" was coined less than twenty years ago by one of
history's most creative mathematicians, Benoit Mandelbrot, whose seminal
work, The Fractal Geometry of Nature, first introduced and
explained concepts underlying this new vision. Although prior
mathematical thinkers had attained
isolated insights of fractal understanding, such ideas were largely
ignored until Mandelbrot's genius forged them at a single blow into a
gorgeously coherent and fruitful discipline.
Mandelbrot derived the term "fractal" from the Latin verb frangere,
meaning to break or fragment. Basically, a fractal is any pattern that
reveals greater complexity as it is enlarged. Thus, fractals
graphically portray the notion of "worlds within worlds" which has
obsessed Western culture from its tenth-century beginnings.
Traditional Euclidean patterns appear simpler as they are magnified; as
you home in on one area, the shape looks more and more like a straight
line. In the language of calculus such curves are differentiable. The
trajectory of an artillery shell is a classic example. But fractals,
like dendritic branches of lightning or bumps of broccoli, are not
differentiable: the closer you
come, the more detail you see. Infinity is implicit and invisible in
the computations of calculus but explicit and graphically manifest in
fractals.
Whether generated by computers or natural processes, all fractals
are spun from what scientists call a "positive feedback loop."
Something--data or matter--goes in one "end," undergoes a given, often
very slight, modification and comes out the
other. Fractals are produced when the output is fed back into the
system as input again and again.
Fractals show us that the simplest engines of change often produce
exquisitely elaborate patterns. Such systems are at work all around us,
from the stock market to the stars. And to the fractal artist,
Mandelbrot's insights echo Kandinsky`s assertion that "the process of creation is the same in art and nature
Simply: "A fractal is a rough or fragmented
geometric shape that can be subdivided in parts, each of which is (at least
approximately) a reduced-size copy of the whole. Fractals are generally
self-similar and independent of scale."
