Statistical study of Collatz function suggests that the function picks its iterates at random.

A Collatz system can be represented by a physical system as it behaves similar to a system operating under a feedback design using sliding control mode. Such dynamic systems may present a statistical space that can be studied rigorously. In a previous study, the author, Barghout, presented Collatz space in a unique dynamic numerical mode by tabulating a sequential correlation pattern of division by 2 of Collatz function's even numbers until the numbers became odd with consecutive occurrence, following an attribute of a 50:50 probability of division by 2 once as opposed to division by 2 more than once until the number became odd. The tabulated data indicated that division by 2 once process increased the starting odd number of the function while division by 2 more than once decreased it, allowing a quantification process of the direction the Collatz function's process takes. The tabulated data also indicated that any row of data seems to extend indefinitely holding the same numerical value while any column of data repeats the same numerical subspace. This unique representation of such dynamical systems may aid in numerical analysis in mathematics and computer science. In this paper, the authors conducted a statistical study of the path of the Collatz function by studying its probabilistic contracting behaviour for all positive starting odd numbers up to 1002097149, until the function leads to the first odd number that is less than the starting odd number. We present a strong indication that the function's dynamic behaviour maybe probabilistic in nature. [ABSTRACT FROM AUTHOR]