  This work represents an in-depth study of the structural behavior of the
Collatz sequences. We consider a finite arithmetic progression with a common
difference is 2 and the number of terms in the sequence is equal to 2^n .
After, we consider a 2^n x(n+1) matrix ((n+1) columns and 2^n rows) such as the
first column contains the terms of arithmetic progression and each row of the
matrix represent a finite Collatz sequence. Then, each element of the matrix
will be replaced by 0 or 1 according to the following rule: the even integer is
replaced by 0 and the odd integer is replaced by 1. We obtained a table
contains all binary permutation with repetition this property is called the
property of structural complementarily. Based on these tables, we can determine
any other fundamentals properties characterizing the behavior of Collatz
sequences. Thus, we can distinguish two other important properties such as the
property of structural cyclical behavior characterized by a structural
periodicity and the structural sliding property that can be called also the
property of structural divergence.
