Cyclic Behaviour of 3-State 3-Neighborhood Cellular Automata

Cyclic Behaviour of 3-State 3-Neighborhood Cellular Automata | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Cyclic Behaviour of 3-State 3-Neighborhood Cellular Automata Sukanya Mukherjee, Jakkula Sidhuja This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6570417/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This work studies the problem of cycle structures of 3-state 3-neighborhood uniform cellular automata under both the null and periodic boundary conditions. Here, the target rules are studied on the aspect of non self replicating RMTs and we classify these rules broadly in two categories: rules with one non self replicat- ing RMT and rules with more than one non self replicating RMTs. The former category ensures the generation of strictly single length cycle cellular automata. An effcient scheme of evaluating the cycle structures of these CAs is also reported. Also, the property of isomorphism is found in the CAs designed by the rules of this category. The latter category brings the notion of multi-length cycles in CA and the minimum count of non-self-replicating RMTs is figured out for multi-length cycle generation. Besides, the cycle structures are estimated for the CAs with at least two non self replicating RMTs. Single length cycle 3-state CA non self-replicating RMT cycle structure Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6570417","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":525903555,"identity":"2d298f7d-5b56-4650-bf01-f5d29d10e5b2","order_by":0,"name":"Sukanya Mukherjee","email":"data:image/png;base64,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","orcid":"","institution":"Institute of Engineering and Management Kolkata, University of Engineering and Management, Kolkata, West Bengal- 700091, India","correspondingAuthor":true,"prefix":"","firstName":"Sukanya","middleName":"","lastName":"Mukherjee","suffix":""},{"id":525903557,"identity":"20ed29ae-6237-4f06-8336-60edff5a76d8","order_by":1,"name":"Jakkula Sidhuja","email":"","orcid":"","institution":"Schlumberger Technology Services India (STS-I), Building-6, Commerzone IT Park Inter nal Rd, Commerzone IT Park, Yerawada, Pune, Maharashtra 411006, India","correspondingAuthor":false,"prefix":"","firstName":"Jakkula","middleName":"","lastName":"Sidhuja","suffix":""}],"badges":[],"createdAt":"2025-05-01 08:38:07","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6570417/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6570417/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":102295469,"identity":"0b91fbde-2b16-44af-a1bc-7e38b2c00fab","added_by":"auto","created_at":"2026-02-10 10:11:29","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":308012,"visible":true,"origin":"","legend":"","description":"","filename":"NaturalComputingJournal2025.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6570417/v1_covered_ca7c5313-46e1-43d2-a0b4-70a57cb61938.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"\u003cp\u003eCyclic Behaviour of 3-State 3-Neighborhood Cellular Automata\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Single length cycle, 3-state CA, non self-replicating RMT, cycle structure","lastPublishedDoi":"10.21203/rs.3.rs-6570417/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6570417/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis work studies the problem of cycle structures of 3-state 3-neighborhood uniform cellular automata under both the null and periodic boundary conditions. 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