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SVET FRAKTALA
WORLD OF FRACTALS
AUTOR: LUKA ŢIVKOVIĆ ,III5 , “ XIII Beogradska gimnazija“ Beograd
PROFESOR: JADRANKA JANKOVIĆ , “ XIII Beogradska gimnazija“ Beograd
MENTOR: VIOLETA KOMNENOVIĆ,dipl.matematiĉar,“ETŠ Nikola Tesla“Beograd

REZIME

Ĉoveĉanstvo je hiljadama godina razvijajući geometriju stvaralo sebi mesto za ţivot. To mesto
su ĉinile ravne povrsine i pravilni lukovi. Na prirodu se gledalo kao na jedan nasumiĉan poredak
koji se nije mogao povezati sa matematikom. Tek u drugoj polovini XX veka, matematiĉar
Benoa Mandel-brot ( Benoit Mandelbrot 1924.-2010.) je uoĉio zakonitosti koje taj haos, naizgled
nasumiĉan raspo-red, ĉini krajnje urednim i jednostavnim. Mandelbrot je ovu reĉ fraktali skovao
1975. godine od latinske recifractusšto znaĉi razlomljen, slomljen.Fraktali se sastoje od delića
koji su sliĉni ĉitavoj celini. Fraktalne slike nastaju iteracijom, tj uzastopnim ponavljanjem nekog
raĉunskog ili geometrij-skog postupka, ili rekurzijom ,odnosno ponavljanjem nekih
funkcija.Fraktali su, dakle, slike nastale ponovljenim matematiĉkim raĉunom ili geometrijskom
konstrukcijom.

Ključne reči:fraktal, fraktalnadimenzija, topološka dimenzija, iteracija, rekurzija.

SUMMARY

For thousands of years, mankind has been developing geometry, and in that way
createdthemselves a place to live. That place consisted of smoothen out surfaces and regular arcs.
The nature was seen as a random order that cannot be related to mathematics. Only in the second
half of the XX century, the mathematician Benoit Mandelbrot (1924.-2010), observed
regularities in that chaos, seemingly it was random disorder, but to him it looked extremely neat
and simple. Mandelbrot coined the word fractal in 1975. from the Latin wordfractus meaning
fractured, broken. Fractals are made up of particles that are similar to the entire whole. Fractal
image created by iteration, in other words, by constantly repeating a calculation or a geometric
procedure, or recursion, which means repetition of certain functions. Fractals are, therefore,
repeated images made of mathematical calculations or geometrical construction.

Key words: fractal, fractal dimension, topological dimension, iteration, recursion.