Here is an unfinished rule for a spaceship with speed on the order of 2^(2^(7 million)):
Code: Select all
@RULE 1C3SShip (incomplete)
@TABLE
n_states:3
neighborhood:Moore
symmetries:none
#delay
0,0,0,0,0,2,1,2,0,2
2,0,0,0,0,0,1,0,0,1
1,0,0,0,0,0,1,0,0,0
2,0,0,0,0,0,2,0,0,1
1,0,0,0,0,0,2,0,0,0
#leftward expansion
0,0,0,1,0,0,0,0,0,2
0,0,0,0,0,1,2,0,0,2
0,0,0,2,1,2,0,0,0,1
2,0,0,0,2,1,2,0,0,0
2,1,0,1,2,0,0,0,0,1
1,0,0,0,1,1,0,0,0,0
1,1,0,1,2,0,0,0,0,2
0,0,1,1,0,0,0,0,0,2
0,0,0,1,1,0,0,0,0,1
2,1,0,2,0,0,0,0,0,1
2,0,0,0,0,1,2,0,0,0
1,1,0,2,0,0,0,0,0,2
1,0,0,0,2,1,0,0,0,0
#downward expansion
0,1,0,0,0,0,0,0,0,2
0,0,0,0,0,0,2,1,0,2
0,2,0,0,0,0,0,2,1,1
2,0,0,0,0,0,2,1,2,0
2,1,2,1,0,0,0,0,2,1
2,0,0,0,0,1,2,1,0,0
1,0,0,0,0,0,0,1,1,0
2,1,0,1,0,0,0,0,1,1
1,1,0,1,0,0,0,0,2,2
0,1,1,0,0,0,0,0,0,2
0,1,0,0,0,0,0,0,1,1
2,2,0,1,0,0,0,0,0,1
1,2,0,1,0,0,0,0,0,2
1,0,0,0,0,0,0,1,2,0
0,0,0,0,0,2,1,0,0,2
2,0,0,0,0,2,1,0,0,0
#downward stop
0,1,0,0,0,0,2,1,0,1
1,0,0,0,0,0,2,1,0,2
2,0,0,0,0,0,2,1,0,0
0,2,0,0,0,1,1,2,2,2
2,1,0,2,0,2,0,0,1,1
2,0,0,0,0,0,2,2,1,0
0,2,0,0,0,1,2,2,2,2
2,0,0,0,0,1,1,2,1,0
2,1,0,2,1,1,0,0,0,1
1,2,2,1,0,0,0,0,0,2
1,2,0,0,0,0,0,1,2,2
2,1,0,2,1,2,0,0,0,1
2,0,0,0,0,1,2,2,1,0
1,2,0,0,0,0,0,2,2,0
2,2,1,1,0,0,0,0,0,0
1,1,0,0,0,0,0,2,2,0
0,0,0,2,2,1,2,1,1,1
1,0,0,0,2,1,2,1,1,2
2,1,2,1,0,0,0,0,0,0
1,2,0,2,0,0,0,2,1,0
0,0,0,0,0,2,1,1,0,2
1,1,0,2,1,2,0,0,1,0
2,0,0,0,2,1,2,1,1,0
2,0,1,0,0,0,0,1,2,0
#downward counting
0,1,0,0,0,0,1,1,0,2
1,1,1,0,0,2,2,0,0,2
1,1,0,0,0,0,2,1,1,0
0,0,2,0,0,0,1,2,2,1
0,0,0,0,0,1,1,1,1,1
0,0,2,0,0,0,2,1,1,1
0,2,0,0,0,1,2,2,1,1
0,0,2,0,0,0,2,2,2,1
1,1,0,1,0,1,0,0,1,2
1,1,0,0,0,0,2,2,2,0
1,1,0,0,0,0,1,2,2,0
1,0,0,0,0,0,2,2,1,0
1,0,0,0,0,0,1,2,1,0
1,1,0,0,0,0,1,1,1,0
0,0,2,0,0,0,1,1,1,1
0,0,0,0,0,0,2,0,2,1
1,0,0,0,0,2,0,0,1,0
2,0,0,0,0,0,1,1,0,0
1,1,2,0,0,1,0,0,1,2
0,2,0,0,0,0,1,2,1,2
2,0,0,0,0,0,1,2,1,0
2,1,0,2,0,1,0,0,2,1
1,2,2,0,0,1,0,0,0,2
1,1,2,0,0,2,0,0,1,2
0,2,0,0,0,0,2,2,1,2
0,2,0,0,0,0,1,2,2,2
2,1,0,2,0,1,0,0,0,1
1,2,2,0,0,2,0,0,0,2
0,2,0,0,0,0,2,2,2,2
2,1,0,2,0,2,0,0,0,1
0,2,0,0,0,0,0,2,2,2
2,0,0,0,0,0,0,1,1,0
2,0,1,2,0,0,0,0,0,0
2,1,0,0,0,0,0,2,0,1
2,1,1,1,0,0,0,0,2,0
1,1,0,0,0,0,0,2,1,0
1,0,0,0,0,0,0,2,0,2
0,0,2,0,0,0,1,1,2,1
#upward signal
0,0,1,1,2,2,0,0,0,2
0,0,1,1,1,2,0,0,0,2
0,0,2,1,1,2,0,0,0,2
0,0,2,2,1,2,0,0,0,2
0,0,2,2,2,2,0,0,0,2
0,0,2,1,2,2,0,0,0,2
0,0,1,2,1,2,0,0,0,2
0,0,1,2,2,2,0,0,0,2
2,0,1,1,1,0,0,0,0,0
2,0,1,1,2,0,0,0,0,0
2,0,1,2,1,0,0,0,0,0
2,0,1,2,2,0,0,0,0,0
2,0,2,1,1,0,0,0,0,0
2,2,2,1,2,0,0,0,0,0
2,0,2,2,1,0,0,0,0,0
2,0,2,2,2,0,0,0,0,0
2,1,0,0,0,1,0,2,0,1
2,2,0,0,0,1,0,2,0,1
0,1,1,2,1,2,0,0,2,1
0,1,1,1,2,2,0,0,1,1
1,1,1,2,2,0,0,0,2,2
0,2,1,2,0,0,0,0,1,2
2,1,0,2,0,2,2,0,1,1
2,1,0,2,0,1,0,2,0,1
2,1,1,0,1,1,0,1,1,1
1,1,2,0,0,2,0,1,1,2
1,1,0,0,0,2,0,1,1,2
1,0,1,2,1,0,1,0,0,2
2,2,2,0,0,1,0,0,2,1
1,0,0,1,2,1,0,1,0,2
2,0,0,1,1,2,0,1,0,1
1,1,1,2,2,0,0,0,1,2
2,1,0,0,0,2,0,1,1,1
2,2,1,1,2,0,0,0,1,0
1,0,0,2,2,0,0,1,0,2
1,0,0,2,2,0,0,2,0,2
2,0,0,1,0,2,0,1,0,1
#leftward stop
0,0,0,0,0,2,2,0,0,2
2,0,0,0,0,2,2,0,0,0
0,0,0,0,0,0,2,2,0,2
0,0,0,2,2,2,2,0,0,2
2,0,0,0,2,2,2,0,0,0
2,2,0,2,0,0,0,2,0,1
2,0,0,0,1,2,2,0,0,0
2,2,0,1,0,0,0,2,0,1
0,0,0,2,2,2,1,1,0,2
0,0,0,2,2,2,2,1,0,2
1,0,0,2,2,1,0,0,0,2
2,0,0,0,1,2,1,1,0,0
2,2,0,1,0,0,0,1,1,1
1,0,0,2,1,2,0,0,0,0
2,0,2,0,1,1,2,1,0,1
1,0,1,0,1,1,2,0,0,0
2,1,1,0,0,0,0,0,2,0
1,0,0,1,1,2,0,0,0,0
1,0,0,0,1,1,1,0,0,0
2,0,0,1,2,0,0,1,1,1
2,0,0,2,0,2,0,1,1,1
0,0,0,0,1,1,2,1,0,1
1,0,0,1,1,2,0,0,0,0
1,0,0,0,1,1,2,0,0,0
2,0,1,1,0,0,0,0,0,1
2,2,1,0,0,0,0,0,1,0
2,0,0,1,0,2,0,1,1,1
#leftward counting
0,2,1,2,0,0,0,0,2,2
2,2,1,0,0,0,0,0,2,0
0,2,2,2,0,0,0,0,1,2
0,2,2,2,0,0,0,0,2,2
2,0,0,1,0,2,0,2,0,1
2,1,1,2,2,0,0,0,2,0
2,1,1,0,0,0,0,0,1,0
0,2,2,2,0,0,0,0,0,2
2,0,0,2,2,0,0,0,0,0
2,0,1,0,0,0,0,0,0,0
1,0,0,1,0,0,2,0,0,2
#ending
2,2,0,2,0,0,0,0,0,0
2,0,0,0,2,0,0,0,0,0
2,0,0,0,0,0,0,0,0,1
#diagonal mode
#2,0,0,0,2,0,0,0,0,0
#2,0,1,0,0,0,0,0,2,0
#0,0,0,1,0,2,0,2,0,1
#extra length
2,0,2,1,2,0,0,1,1,1
2,1,0,0,1,1,0,0,1,1
2,0,0,0,0,0,1,1,2,0
1,1,0,0,0,0,0,0,0,0
2,0,1,0,2,0,0,0,0,0
0,1,0,0,0,2,0,2,0,1
#back up
0,2,1,1,0,0,0,0,0,2
2,1,1,0,1,1,0,2,1,1
0,2,1,1,1,0,0,0,2,2
2,2,1,2,2,0,0,0,0,0
2,1,1,1,1,2,0,2,2,0
2,0,1,1,1,2,0,2,0,0
#TODO: convert binary counter push into binary counter pull
#TODO: collapse back into a single cell
The basic idea involves turning the bottom counter from a timer into a proper counter, and every 27 overflows the left counter (still a normal shrinking counter) will count twice. Once the horizontal counter shrinks all the way, it will send a signal down, which is supposed to but doesn't currently convert it from a growing to a shrinking counter, which should but doesn't collapse into a single cell once it shrinks all the way. I'm not going to complete it, but I'm posting it here in case someone else wants to.
An idea for making it way slower involves turning the bottom counter head back into a c/2 wickstretcher, causing it to achieve tetrational growth.