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Reproducing the cyclic tag system developed by Matthew Cook with Rule 110 using the phases $f_{i_-}1$. (English)
J. Cell. Autom. 6, No. 2-3, 121-161 (2011).
Summary: This paper implements the cyclic tag system (CTS) in Rule 110 developed by Cook using regular expressions called phases $f_{i_-}1$. The main problem in CTS is coding the initial condition based on a system of gliders. We develop a method to control the periodic phases of the strings representing all gliders known until now in Rule 110, including glider guns. These strings form a subset of regular expressions implemented in a computational system to facilitate the construction of CTS. Thus, these phases are useful to establish distances and positions for every glider and then to delineate more sophisticated components or packages of gliders. In this manuscript, it is possible to find differences to the results exposed in {\it S. Wolfram}’s book [A new kind of science. Champaign, IL: Wolfram Media (2002; Zbl 1022.68084)], including some mistakes which avoid obtaining an appropriate realization of CTS in Rule 110; fortunately, these irregularities were discussed and clarified by Cook.