An artificial life view of the collatz problem

Research output: Contribution to journalArticle

3 Citations (Scopus)

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 (1s 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.

Original languageEnglish
Pages (from-to)137-140
Number of pages4
JournalArtificial Life
Volume17
Issue number2
DOIs
Publication statusPublished - 2011 Mar
Externally publishedYes

Fingerprint

Population Growth
Growth
Direction compound

Keywords

  • Bit strings
  • Collatz problem
  • Ecological interpretation
  • Spatiotemporal patterns

ASJC Scopus subject areas

  • Artificial Intelligence
  • Biochemistry, Genetics and Molecular Biology(all)

Cite this

An artificial life view of the collatz problem. / Sayama, Hiroki.

In: Artificial Life, Vol. 17, No. 2, 03.2011, p. 137-140.

Research output: Contribution to journalArticle

@article{77770bc7471948cb90f76841f0d34299,
title = "An artificial life view of the collatz problem",
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 (1s 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.",
keywords = "Bit strings, Collatz problem, Ecological interpretation, Spatiotemporal patterns",
author = "Hiroki Sayama",
year = "2011",
month = "3",
doi = "10.1162/artl_c_00024",
language = "English",
volume = "17",
pages = "137--140",
journal = "Artificial Life",
issn = "1064-5462",
publisher = "MIT Press Journals",
number = "2",

}

TY - JOUR

T1 - An artificial life view of the collatz problem

AU - Sayama, Hiroki

PY - 2011/3

Y1 - 2011/3

N2 - 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 (1s 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.

AB - 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 (1s 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.

KW - Bit strings

KW - Collatz problem

KW - Ecological interpretation

KW - Spatiotemporal patterns

UR - http://www.scopus.com/inward/record.url?scp=79955698092&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79955698092&partnerID=8YFLogxK

U2 - 10.1162/artl_c_00024

DO - 10.1162/artl_c_00024

M3 - Article

VL - 17

SP - 137

EP - 140

JO - Artificial Life

JF - Artificial Life

SN - 1064-5462

IS - 2

ER -