I've been wondering about the statistics of the length of Collatz sequences so I wrote a program to print a chart of the distribution. (It's a Python program that produces a pbm file. You'll need netpbm to get something useful out of it.) Since the length of the Collatz sequence for \(2^n\) is \(n\), it makes sense to scale the lengths by dividing them by \(\log_2 n\). The results are as follows:
I didn't expect to see an interference pattern.