Sierpinski Carpet and Chaos in the Periodic Table of the Elements
Leila Hojatkashani *
Department of Chemistry, College of Basic Sciences, Yadegar-e-Imam Khomeini (RAH) Branch, Islamic Azad University, Tehran, Iran.
*Author to whom correspondence should be addressed.
Abstract
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 the elements to create a new pattern for the chemical elements. Fibonacci numbers and Math lab software are used to transform a linear system to three spiral systems. This new pattern which is consisted of three layers shows that the flows among chemical elements are based on Archimedes spiral equation The purpose of this study is to show Sierpinski carpet order in the periodic table of the chemical elements and also there can be a chaos even in chemical elements.
Keywords: Sierpinski carpet, Fibonacci numbers, golden spiral, the periodic table of the elements, Archimedes spiral equation, Chaos