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Mandelbrot’sconcept of fractal geometry is a powerful approach in order to precisely
characterize natural structures, structures that follow geometric laws not in
common with the classic Euclidean rules. The term “fractal” is
related to highly irregular shapes, with non-integer, or fractional,
dimensions, and a property known as self-similarity. Unlike a smooth Euclidean
line, a fractal line is irregular or wrinkly, it owns a non-integer dimension:
values placed between 1 and 2 observing a 2D image. If we imagine observing
this fractal line with the lens of a microscope with increasing power of
magnification we look smaller wrinkles that resemble the wrinkles of the larger
ones. Further magnification shows yet smaller wrinkles and so on.
Ina theoretical (mathematical) fractal that behavior is repeated toward the
infinite, in a natural fractal this is only true for few scales, at least for
two order of magnitude: the object presents subunits that resembles the larger
scale structure, maintaining the same, shape, at least statistically, if
observed at various magnification: a property named self-similarity, that give
us an index called fractal dimension. Fractal dimension may be explained as a
statistical index of complexity, able to characterize the space-filling
capacity of a pattern. Fractal analysis has become in recent years very
powerful to study many phenomena in astrophysics, economics, agriculture as
well in biology and medicine.
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