Basics of Cyclical Sequences Theory

This paper introduces two types recursive impulse algorithms that create a new subject of numerical sequences which are called cyclical pulsatory sequences and the Collatz sequence is classified in them. They also divide integers into tree partitions. This theory studies the structure of cyclical pulsatory sequences. One of the obstacles to proving Collatz's conjecture has been the lack of sufficient knowledge about the Collatz sequence. This article provides a new and complete understanding of Collatz's conjecture, in which, we have also redefined the collatz sequence with a parameter.