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.
Fractal geometry is not just a chapter of mathematics, but one that helps Everyman to see the same world differently.
Benoit Mandelbrot
At any given moment, life is completely senseless. But viewed over a period, it seems to reveal itself as an organism existing in time, having a purpose, trending in a certain direction.
Aldous Huxley
Does the flap of a butterfly’s wings in Brazil set off a tornado in Texas?
Edward Lorenz
“When I judge art, I take my painting and put it next to a God-made object like a tree or flower.If it clashes, it is not art
Paul Cézanne
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]]>In 29 December 1979 , Lorenz at the annual meeting of American Society of Science Progress
made his speech about the “predictability” ,which described the chaos and the speech would be
known as the Butterfly Effect. When a butterfly flaps its wing in Brazil , does it cause a tornado in
Texas?
On the other hand, a scientist who had a vast knowladge about geometry also working at IBM
was looking for a word to describe one of the principles established order of a geometric nature
intended-barbed ,tangled ,separated into small pieces, twisted, broken, scattered-some. Cigarette
smoke rises into the air return in the form of some irregular spirals. A flag in the wind, waves
splashing it from side to side. Tap dripping water falling at regular intervals before the order is
broken later. Air behavior, the behavior of oil flowing in pipes underground, there will be chaos .. "²
In the Euclidien geometry descrbing any object by the simpliest words in the geometry such as
circle, triangle, cone like was sufficent but in the nature we see clouds, waves, sea shores, the folds
of the leaf margin, the branches of a tree, the irregular nature, such as different types of vibrations
on the surface of the water, this was not easy to define simple forms.The word “Fractal” was used in
scientific article which is published in the magazine American Scientific written by Mandelbroth. The
article was about a question , “What is the length of the coast of Great Britain?”
According to Mandelbroth , the clouds were not spheres , mountains were not cone-likes and the
lightning does not spread in a straight line ,those things could not be defined by Euclidien geometry
and needed a name to identify it. When he was looking into the Latin dictionary belonging to his son
who just came back from the school , he noticed the word “fractus”. It was derived from the verb
frangere and the adjectives fracture and fraction just sounded similar ergo Mandelbroth called it
“fractal”.
Chaos
When Chaos was examined in itself the result was the concept of “self-similarity”. Thus ,Fractal
meant self-similar. Self-similarity at all levels means that scale symmetry. All in all ,it means
returning to the starting point
5, finding patterns in the patterns.
Mandelbrot, using technology in IBM with the latest technology of those years , he was able to
transform a massive amount of data into the computer graphics which is known as "Mandelbrot
set”. It shows the forms of so-called first glance, had created an endless complexity. When he
entered the interesting event that took place throughout the history at similar times such as the Nile
river water rise, prices of cotton, etc. The computer created the similar shapes. When you zoomed
to those complex images, its complexity and diversity continued as same.Was complexity moving
according to a pattern in itself?
Throughout the history , the chaos is the very center of the creation in legends of the ancient
times. In Chinese creation legend , the light rushes out from the chaos ; in Egyptian mythology , the
god of Sun-Ra- was risen from chaotic floods called Nun. According to Hesiod , first of all there was
chaos.
The classical science stops when chaos starts. As long as physics has existed , the laws of nature
was questioned however physicians weren’t different than uneducated people when it came down
to the atmosphere, turbulent seas, the populations of wild fluctuations, the irregularity of the heart
and brain vibrations says says James Gleick, " Chaos-A New Theory of Science "² in the preface of his
book.
Fractal Images
Chaos is an art that is created by chaos philosophy ,theory and visuals, computer work-however
not all of the work is done by it- working on complex mathematical without needing the know the
mathematics ; worked as a photo but not taken whereas the color, light and shadow have huge
importance; beginning the work with an empty screen such as starting with an empty canvas and
filled with creativity by the artist, in 24-bit true color.
As a brief scientific background information on chaos and its expositions –fractals- are used
everywhere , from design of bridges, anatomy, design parameters for spacecraft began to be used in
fields ranging from animations in Holywood movies, created by the visual beauty, and then after
1995 it was used as a software package by many digital artists. Expressed in complex patterns of
non-linear formulas, fractal image at a later stage, starting with "self" to resemble "the visual beauty
of symmetry and chaos that is within.
A fractal image begins with progress of selecting a formula in the program. The selected formula
sometimes is a simple thing just like a dot on the screen ,sometimes a blank screen or a draft.
However, each point represents the very secrets of chaos and is produced by a mathmetical formula
which can be complex or simple. Afterwards,anywhere in the image is selected then another
formula is added to the selected area (iteration) thus a new image appears in front of your eyes.
Moreover the image that is produced is transformed to another image who has been made in the
same way(twisting,breaking). If the image is completed , the layer is fixed and the other layer will be
the one that you are working on until you’re satisfied. Fractal images have limited predictability and
infinite amount of coincidences within itself. Fractal images are not started to become a portrait of a
human nor a tree. However , in any phase of a fractal image , many unforeseen things can come up ,
such as in the image below the Spanish Dancer , you can have the classical art whereas in the Green
Planet , you can find a simple stylized planet in symmetry.
Appendix
1: Kaos John Bridggs & F. David Peat Çeviren Sezer Soner, Ege meta yayınları
2: Chaos James Gleick, Çeviren Fikret ÜçcanTUBİTAK
3: The Fractal Geomety of Nature,Benoit B.Mandelbrot, Freeman and Company 1977
4: Sema Onurlu (ODTÜ)
5: Change and Chaos David Ruelle.Ceviren Deniz Yurtören TUBİTAK
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