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1.
FRACTALS - SACRED GEOMETRY

ANDREA MAKSOVIC
BELGRADE
INTRODUCTION

In the first part of the work, we are going to be introduced Pascal's triangle and that with "Chaos Game" we can also
with the term of fractals, their basic properties and fractal create Sierpinski triangle.
dimension itself. We will see different examples of fractal
shapes and count their dimension in several ways. By using
mathematical analysis, there will be made some interesting
conclusions. Furthermore, we will look at the great
application of fractals in all science disciplines and Picture no.2. Some numbers that belong to Mandelbrot’s
appearance of their motives in nature, Universe and Set
ourselves. The aim of the research i is the construction of CONCLUSION
some of the most famous fractal shapes [1], theoretical
analysis and conclusion with the purpose of applying The more we deal with fractal issues, the more of their
knowledge of fractals in contemporary researches, as well incredible properties and characteristics we witness. Just
as the overview of the application of fractal geometry. when we think we have solved a problem, some other
questions confuse us, I have come up with the following
questions: Can we make that rope of certain length reduce
so much that it is no longer visible to the naked eye, by
applying Koch’s technique, the same way the Cohen
significantly reduced the area of satellite antenna? Opposite
to that, can we "untangle" a tiny molecule’s fractal structure
and make it visible? Considering that the human's lungs are
fractal, human's blood vessels, brain, and heart beat are
fractal, can we conclude that the human himself is the most
complex, the most perfect fractal and describe one
mathematically?

LITERATURE
Picture no.1. The iterated Sierpinski triangle
1. http://en.wikipedia.org/wiki/Fractal
METHOD OF WORK 2. http://classes.yale.edu/fractals/
The research methods used during this research are analysis 3. http://www.fractal.org/Bewustzijns-Besturings-
of data collected from the literature on this topic, analysis Model/Fractals-Useful-Beauty.htm
of previous research in this area with the processing of data 4. http://matematikapn.blogspot.com/2015/01/kohov
obtained from previous analysis and arrangement of data, a-pahulja.html
making parallels between different, previously researched
data, conclusion method based on previously researched 5. http://fractalfoundation.org/OFC/OFC-12-4.html
facts in this area. 6. http://e.math.hr/fraknum/index.html
7. http://www-
03.ibm.com/ibm/history/ibm100/us/en/icons/fracta
RESULTS OF RESEARCH l/
Results of research show that this is an, truly, ubiquitous 8. http://www.ted.com/talks/benoit_mandelbrot_fract
mathematical area. Although we have intensively started to als_the_art_of_roughness
deal with this discipline only recently, since it has only
recently been discovered, we have realized that it was, 9. http://www.viva-fizika.org/fraktali-i-deo/
actually, always around us. http://fractalfoundation.org/OFC/OFC-12-1.html
Using the line, square and cube I came up with a general 10. http://www.youthedesigner.com/inspiration/interes
formula for calculating the fractal dimensions which I then ting-patterns-and-fractals-from-nature/
applied to various fractal shapes: Koch’s curve, Sierpinski
triangle, Cantor set ... and then I applied the Box Counting
method for calculating the fractal dimension, where I came
to the same results.
Next, I proved for certain numbers that they do belong to
Mandelbrot’s set [2], and, as far as the data given in
Appendix is concerned, I proved that Cantor set is
uncountable set, that Sierpinski triangle is present in