| An Artificial Life View of the Collatz Problem. | |
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MedLine Citation:
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PMID: 21370956 Owner: NLM Status: Publisher |
Abstract/OtherAbstract:
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Abstract This letter presents a new, artificial-life-based view of the Collatz problem, a well-known mathematical problem about the behavior of a series of positive integers generated by a simple arithmetical rule. The Collatz conjecture asserts that this series always falls into a 4 ? 2 ? 1 cycle regardless of its initial values. No formal proof has been given yet. In this letter, the behavior of the series is considered an ecological process of artificial organisms (1's in bit strings). The Collatz conjecture is then reinterpreted as the competition between population growth and extinction. This new interpretation has made it possible to analytically calculate the growth and extinction speeds of bit strings. The results indicate that the extinction is always faster than the growth, providing an ecological explanation for the conjecture. Future research directions are also suggested. |
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Authors:
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Hiroki Sayama |
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Publication Detail:
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Type: JOURNAL ARTICLE Date: 2011-3-3 |
Journal Detail:
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Title: Artificial life Volume: - ISSN: 1064-5462 ISO Abbreviation: - Publication Date: 2011 Mar |
Date Detail:
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Created Date: 2011-3-4 Completed Date: - Revised Date: - |
Medline Journal Info:
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Nlm Unique ID: 9433814 Medline TA: Artif Life Country: - |
Other Details:
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Languages: ENG Pagination: - Citation Subset: - |
Affiliation:
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Collective Dynamics of Complex Systems Research Group, Binghamton University. |
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From MEDLINE®/PubMed®, a database of the U.S. National Library of Medicine
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