کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4626898 | 1631799 | 2015 | 10 صفحه PDF | دانلود رایگان |
This paper proposes an application of the Infinite Unit Axiom and grossone, introduced by Yaroslav Sergeyev (see Sergeyev (2003, 2009, 2013, 2008, 2008) [15–19]), to classify one-dimensional cellular automata whereby each class corresponds to a different and distinct dynamical behavior. The forward dynamics of a cellular automaton map are studied via defined classes. Using these classes, along with the Infinite Unit Axiom and grossone, the number of configurations that equal those of a given configuration, in some finite central window, under an automaton map can now be computed. Hence a classification scheme for one-dimensional cellular automata is developed, whereby determination in a particular class is dependent on the number of elements in their respective forward iteration classes.
Journal: Applied Mathematics and Computation - Volume 255, 15 March 2015, Pages 15–24