An artificial life view of the collatz problem

Hiroki Sayama*

*この研究の対応する著者

研究成果: Article査読

3 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)137-140
ページ数4
ジャーナルArtificial Life
17
2
DOI
出版ステータスPublished - 2011
外部発表はい

ASJC Scopus subject areas

  • 生化学、遺伝学、分子生物学(全般)
  • 人工知能

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