When looking at 2D Turing machines, many of them eventually become predictable. For example, Langton's Ant, the champion 2-color 1-state turmite, develops a highway after 10,000 steps. Predictable behavior includes Traps (as in Worm Trails), Highways, Spirals, Wedges and Sequences (like the binary counter). Examples at 2D Turing Machines, within Golly, and at wikipedia's Turmite entry.
For 2-color, 2-state Turmites, {{{1,1,1},{0,8,1}},{{1,8,1},{0,1,0}}} found by Georgi Gochev runs for 240 million steps before becoming predictable.
EDIT: Beating that is {{{1,8,1},{0,2,0}},{{1,8,0},{0,1,0}}}, with 7.735 billion timesteps before making a wedge: (Georgi Gochev)
EDIT: Beating that is {{{0,1,1},{0,4,0}},{{1,4,0},{1,2,1}}}, with 9.533 trillion timesteps before making a highway (found by Mark Jeronimus).
Is that the longest unpredictable run for a 2-color, 2-state termite?
Non-halting Busy Beaver is a repository for known results.
