  This paper is a numerical evaluation of some trajectories of the Collatz
function. Specifically, I assess the coalescence points of each integer
$n\equiv 0 (\bmod{2})$ and $n\equiv 2(\bmod{3})$ through a sophisticated
algorithm that has been developed to test on any different modulus classes. The
data discovered illustrate that the distribution of the first point of
coalescence is closely related to the solutions of some exponential diophantine
equation. Afterwards, I show that the first point of coalescence of the
integers $n$ and $3n+2$ appear to tend to an expected value of $4/5n$. When the
algorithm was pushed to its peak estimation it has been discovered that the
expected value begins to deviate from the initial estimation of $4/5n$. The
first point of coalescence of the integers $n$ and $3n+2$ appear eradicate from
a "step by step" point of view but from a topological point of view seem to be
localized around the diophantine solution of some particular functions.
