Reproducing the cyclic tag system developed by Matthew Cook with Rule 110 using the phases f1_1

Martinez, Genaro J.; McIntosh, Harold V.; Mora, Juan C.S.T; Vergara, Sergio V.C.

Abstract

This paper implements the cyclic tag system (CTS) in Rule 110 developed by Cook in [1, 2] using regular expressions denominated phases fi_1 [3]. The main problem in CTS is coding the initial condition based in a system of gliders. In this way, we develop a method to control the periodic phases of the strings representing all gliders until now known 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 with the results exposed in Wolfram's book [2], inclusively some mistakes which avoid to obtain an appropriated realization of CTS in Rule 110; fortunately, these irregularities were discussed and clarified by Cook.

• Journal Article Type: Article
• Publication Date: Jan 1, 2011
• Deposit Date: Jul 26, 2010
• Publicly Available Date: Jun 17, 2016
• Journal: Journal of Cellular Automata
• Print ISSN: 1557-5969
• Electronic ISSN: 1557-5977
• Publisher: Old City Publishing
• Peer Reviewed: Peer Reviewed
• Volume: 6
• Issue: 2-3
• Pages: 121-161
• Keywords: cyclic tag system, rule 110
• Public URL: https://uwe-repository.worktribe.com/output/970133
• Publisher URL: http://www.oldcitypublishing.com/JCA/JCAcontents/JCAv6n2-3contents.html
• Contract Date: Jun 17, 2016