Open AccessOn the Construction of Chaotic Dynamical Systems on the Box Fractal
Author(s) -
Nisa Aslan,
Mustafa Saltan
Publication year - 2021
Publication title -
researches in mathematics
Language(s) - English
Resource type - Journals
eISSN - 2664-5009
pISSN - 2664-4991
DOI - 10.15421/242105
Subject(s) - fractal , dynamical systems theory , chaotic , mathematics , representation (politics) , metric (unit) , code (set theory) , dynamical system (definition) , square (algebra) , statistical physics , computer science , mathematical analysis , physics , geometry , artificial intelligence , operations management , set (abstract data type) , quantum mechanics , politics , political science , law , economics , programming language
In this paper, our main aim is to obtain two different discrete chaotic dynamical systems on the Box fractal ($B$). For this goal, we first give two composition functions (which generate Box fractal and filled-square respectively via escape time algorithm) of expanding, folding and translation mappings. In order to examine the properties of these dynamical systems more easily, we use the intrinsic metric which is defined by the code representation of the points on $B$ and express these dynamical systems on the code sets of this fractal. We then obtain that they are chaotic in the sense of Devaney and give an algorithm to compute periodic points.