Birth of Fractals
 

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