Building on my last post of the #Collatz visualization one can see that the **highest bits in binary representation of the Collatz sequence are highly predictable**. Here is how: Look at the reverse odd Collatz sequence in binary representation. Once a number starts with 100 (which is guaranteed to happen within the first 4 odd numbers) the pattern starts: Starting from the next number all other second highest bits of the odd numbers will reproduce exactly one of the two subsequence blocks: * `10 01010` * `01010` The start of every next sequence block is determined simply from the next second highest bit. Try it out! Or use my demo app: https://py.cafe/Gerenuk/collatz-automaton In fact I can probably prove such sequences for any number of highest bits! Unfortunately, it turns out it is not yet directly useful to decide about the Collatz conjecture. #math #cellular_automata