FORMA
Back
Forma, Vol. 36 (No. 1), pp. 31-34, 2021
doi:10.5047/forma.2021.004

Forum

A Decomposition of the Collatz Tree

Syuji Miyazaki

Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan
E-mail address: miyazaki.syuji.8m@kyoto-u.ac.jp

(Received May 27, 2021; Accepted October 16, 2021)

Abstract. The Collatz tree, or the directed graph of the 3x + 1 problem, was demonstrated to be decomposed into three different subgraphs. An arbitrary positive integer is assigned uniquely to a specific position of the nodes of either of the three subgraphs. The manner of connecting a specific subgraph to its neighboring subgraphs is explicitly given. A comparison with complete chaos synchronization was made.

Keywords: Collatz Conjecture, Collatz Tree, Directed Graph


[Full text] (PDF 61 KB)