Terminating Turmite

A Terminating Turmite or Relative Movement Turing Machine is a 1 dimentional Turing machine which uses relative directions instead of absolute ones. So instead of moving (L)eft or (R)ight, it (P)roceeds forward (for one step in the same direction as last move) or (T)urns-around (move one direction in the opposite direction). TT(n,k) is the maximum steps of all halting n-state, k-symbol Terminating Turmites when started on a blank tape.

History

2D Turmites, also called turNing machines, have been historically studied by Chris Langton in 1986 (Langton's ants), Allen Brady in 1988 (TurNing machines), and Greg Turk in 1989 (tur-mites). A collaborative effort led by Tim Hutton since 2011 has considered turmites on 2D square, triangular, and hexagonal grids. Until recently, it seems like much less investigation was put into 1D Turmites.

Values

Domain	Value	Champion
TT(2)	≥ 13	1TB---_1PA0PB
TT(3)	≥ 82	1PB0PA_1TA0PC_1PA---
TT(4)	≥ 48,186	1TB1PA_1PC0PA_1TA0PD_---1TA
TT(2,3)	≥ 223	1TB0PA2PA_2PA---1PA
TT(3,3)	≥ 45,153	1PB1PA1TA_2TB2PB2PC_---2PA1TC
TT(2,4)	> 3.467*1015	1TA2PB3TB---_3TA1PB1TA1PA

See Also

• Google Sheet recording known values: https://docs.google.com/spreadsheets/d/18EXcLXM4Xb_qpKenV4oRGQQpCd45MJ4uawNWgmVvKTY/edit?gid=0#gid=0