3X+1问题中扩展Collatz模型的环结构研究

Research of Ring Structure on Extended Collatz Model in 3X+1 Problem

本文从3x+1问题的原始Collatz函数出发,放宽对原Collatz函数的限制条件,将确定的Collatz程序推广到非确定程序,得到扩展的Collatz模型。从一个特殊的角度描述3x+1问题,引入互逆操作的概念,建立自然数之间同等类型数的联系,发现扩展Collatz模型的存在环结构。通过选取大范围的自然数深度搜索遍历,得出扩展模型下存在一定的规律的环结构。

This article starts from the original Collatz function in 3x + 1 problem to ease the constraints on the original Collatz function, and generalized the determined Collatz program to the non-deterministic program and get the expanded Collatz model. From the perspective of a special to describe 3x + 1 problem, introduce the concept of mutual inverse operation and establish the relationship between the number of the same type of natural numbers and found that the ring structure in the extended Collatz model. This paper through selecting a wide range of natural numbers completed depth search and traversal, and achieved the certain law of the ring structure under extended model.