I can equate Collatz conjecture's function to:
If a string has an odd number of 1's append a 1
If a string has an even number of 1's :
a) copy the position of the 2's into a new 0 only string, and make them 1 then replace all the 2's in the original string with 0's
b) take all 1's and replace them with the string for one half. Noting these sum to 2 at every second 1's position so ex. 1010... becomes 120... then starting over with the 1's between placements of 1's and a 2 every second place a one resides and repeat.
c) add the resulting base 3 strings from a and b ...
This in some ways reminds me of busy beaver, so I was wondering: What is known about it ?