Sierpinski carpet and Chaos in the periodic table of the elements

Fractals are self-similar geometric pattern which can be found in nature. They have applications in mathematic, electronic, architecture. Fractal sets also can be used to create chaotic systems. This work is about applying Sierpinski carpet order on the periodic table of theelements to create a new pattern for the chemical elements. With using Fibonacci numbers, Mathlab and the golden spiral in this new pattern, it can be concluded that the created system is no longer a linear system and has spiral properties. The new pattern which is consisted of layers shows that the flows among chemical elements are based on Archimedes spiral equation .The purpose of this study is to show there is a hidden chaos even in a orderly system like the periodic table of the chemical elements.

Keywords:

Sierpinski carpet , Fibonacci numbers , golden spiral , the periodic table of the elements , Archimedes spiral equation , Chaos.