I've been working on Turmites, or 2-D Turing machines. What Turmite runs longest before becoming predictable? Various people have been building up the following page:  https://code.google.com/p/ruletablerepository/wiki/EdPeggsBusyBeaverTurmiteC... For RULS (Right, U-turn, Left, Straight), the Langton's Ant series can considered as RL    --           9,977 steps until highway RUL   --       2,669,000 steps until highway RUUL  --   1,589,104,000 steps until highway RUUUL -- 217,782,000,000 steps until highway  I haven't yet figured out how order emerges out of chaos in this series. I could probably run RUUUUL in a month on my current machine, but I'm hoping someone will figure out something more clever.  I have no idea how to approach making bounds for the number of distinct, unpredictable-for-awhile machines of type 2c3s, 3c2s, or other combinations. If anyone has insights, anecdotes, asides, ideas, or new records, feel free to make comments on the pages. --Ed Pegg Jr