As for the randomness, I have wondered if Collatz sequences are somehow related to the properties of a common prng with multiplier 3/2, infinite length state vector, and mod 2 on the output with this formula: https://en.m.wikipedia.org/wiki/Linear_congruential_generato.... I assume this could be part of what makes the conjecture both interesting and difficult and beautiful.

Very cool to see there is some patterns hiding in the randomness too!