Fractals Fractals2

GROUP: Silvia Battaglia, Giorgia Cenedese (Treviso, Italy); Andone Cristina, Bolinteanu Anca, Herea Nicoleta (Bucuresti, Romania)

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Just to start, what are fractals? Fractals are self-similar patterns, that means they are the same when you look them from near or from far. Sometimes they may be nearly the same at different scales. Here we have some examples.

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We can fnd fractals also in nature; the most famous example is a type of cabbage:
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And here an image to explain easily how to relize a fractal.
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In my opinion we can find a kind of fractal into our body too. I refer to the lungs. Their composition maybe considered as one of this geometrical equation. In fact they're a set of a ramification of bronchial tube, so they're a repetitive formulations of geometrical figure.

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Now we can deal with the history of this fascinating mathematic and maybe artistic elements. The history of fractals traces a path from chiefly theoretical studies to modern applications in computer graphics, with several notable people contributing canonical fractal forms along the way. Fractals were discovered in 1975 by Benoît Mandelbrot. He explained them as being geometric shapes that when divided into parts, each part would be a smaller replica of the whole shape. He came up with the term "Fractal" as the new scientific term for this mathematical expression. The word is actually an adaptation of the Latin word fractus. The Latin word fractus means "broken" or "fractured". The concepts behind fractals had been around for centuries but it was not until Mandelbrot had his realization that these great mathematical masterpieces were discovered. Fractals can also be found in nature, which is where Benoît's first research began. His investigational report, "How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension", was the first step in his eventual discovery of fractals.
Motive Designs' Fractals. Mandelbrot fractals are the most well-known fractals because they were discovered first.
It's better to notice that fractals were not discovered until the invention of computer. It was virtually impossible to discover fractals before the advent of computers because of their complexity and gargantuan output. Fractals existed only in theory before the computer and were published in a most basic form in 1918 by Gaston Julia. They were later published in an advanced form in 1925. It is form this advanced formula that Benoit Mandelbrot made his now famous and revolutionary discover.

Fractals have funny and important practical uses today. In fact they are a key element in computer graphics. Fractals have also been used to compress still and video images on computers. In 1987, English born mathematician Dr. Michael F. Barnesley discovered the fractal transformer which automatically detects fractal codes in real world images. The discovery spawned fractal image compression, used in a variety of multimedia and other image-based computer applications.

I want to show you some funny 3D fractal. I got these pictures from Alice Kelley's fractal gallery

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And then, here a great video about 3D fractals

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Fractal art developed from the 1980s; it is a genre of computer and digital art which are part of the new media art. Fractal art is not drawn or painted by hand but it is usually created with a fractal-generating software.
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We can find some artists that use fractal art; for example, William Latham, from England, has used fractal geometry in his works, Greg Sams created postcards, t-shirts and textiles.
A work of William Latham
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Some works of Greg Sams
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Because of their nice graphical aspect they're used also to do a kind of technologic art. In fact to realize that you must use an appropriate computer software which create some image superimposing math’s functions to the starting fractal. I can assure you that's difficult to explain, but that's really easy to understand seeing some process or some images. Here some of them!

''DayBreak''
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''Zorro''
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"Birth Of A Rose"
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"Sea Life"
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I've just said that fractals are math's function and that's the reason because it's also possible to realize some sound expression using them. In my opinion this kind of sounds are not really pleasant and it's a bit difficult to get right that they're fractals.
Listening carefully it could be noticed some regularity of music and repetitions of sound themes .
Here two links to listen some of these -—> http://www.miorelli.net/frattali/data/1.mid
http://www.miorelli.net/frattali/data/2.mid
[S.B.]

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