Talk:Non-halting Turing machine

BBS(2,2) and BBP(2,2)

Are BBS(2,2) = 9 and BBP(2,2) = 9 proven or are these just the current champions? Polygon (talk) 11:45, 17 August 2025 (UTC)

1RB0LC_1LA1RD_1RA1LD_0LA0RB

During each bounce, this machine grows 3 symbols on the left and 1 symbol on the right. I simulated the machine and stored the tape every time the head reaches -7-9*k (k >= 0) for the first time. Then I right-aligned the tapes. Here are the first 4 tapes:

                                    ^.11.11111
                        ^.11.111.1.111.1.1.1.1
            ^.11.111.1.111.1.111.1.111.1.1.111
^.11.111.1.111.1.111.1.111.1.111.1.111.11111.1

Every other column only contains 1. Here are the first 18 tapes after removing every other column:

               ^1.11
         ^1.1..1....
   ^1.1..1..1..1...1
1..1..1..1..1..1.11.
1..1..1..1..1..1.111
1..1..1..1..1..1.1..
1..1..1..1..1..1.1.1
1..1..1..1..111.1.1.
1..1..1..1..111.1.11
1..1..1..1..111.1...
1..1..1..1..111.1..1
1..1..1..1..111.111.
1..1..1..1..111.1111
1..1..1..1..111.11..
1..1..1..1..111.11.1
1..1..1..1..111...1.
1..1..1..1..111...11
1..1..1..1..111.....

The last column has a cycle of 2 (i.e. row i matches with row i+2). The 2nd last column has a cycle of 4. The 3rd last column has a cycle of 8. I looked at more columns and this pattern seems to continue. The right edge appears to be a binary counter, but it counts binary in a weird way. Int-y1 (talk)