2005/01/02

The exponential rise in scientific imaging. (4) FRACTALS

On December 30, 2004, I indicated the 3 paths followed by the imaging revolution:
- towards the microscopic
- towards the macroscopic
- towards mathematical abstractions
Today I'll concentrate on the path toward the mathematical formulas.
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"Mandelbrot became convinced that a common theme of self-similar structures ran through all of the real-world problems. In 1975 Mandelbrot coined the term fractal to describe these structures, and published his ideas in "Les objets fractals, forme, hasard et dimension" (translated into English as Fractals: form, chance and dimension in 1977).
He emphasized the use of fractals as realistic and useful models of many natural phenomena, including the shape of coastlines and river basins; the structure of plants, blood vessels and lungs; the clustering of galaxies; Brownian motion; and stock market prices. Far from being unnatural, Mandelbrot held the view that fractals were, in many ways, more intuitive and natural than the artificially smooth objects of traditional Euclidean geometry.
As he says in the Introduction to The Fractal Geometry of Nature:
Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.
Mandelbrot's informal and passionate style of writing and his emphasis on visual and geometric intuition (supported by the inclusion of numerous illustrations) made The Fractal Geometry of Nature accessible to non-specialists. It sparked a widespread popular interest in fractals as well as contributing to new fields of science such as chaos theory."(1)


Artists sized with enthusiasm on Mendelbrot's approach and they are churning images out of their programs at the speed of breads baked in industrial baking factories. The profusion of fractal images available on the net is simply astounding.

Notwithstanding the popularity of fractals and other pixel manipulation programs, artists digital works are still not generally recognized as being art works by the managers and the bureaucracy of the arts. It makes no doubt in my mind that digital techniques are nothing more than the brush and pencil of the Middle-Age painter so I do not see how digital techniques could be held at the margins of art for much longer.


(1) About Mandelbrot in Wikipedia.

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