A Decomposition of the Collatz Tree

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.