Pass the 3-state INT Rule!

A forum for topics that don't fit elsewhere. Introduce yourselves to other members of the forums, discuss how your name evolves when written out in the Game of Life, or just tell us how you found it. Forum rules still apply.
Post Reply
User avatar
R2INT
Posts: 934
Joined: July 2nd, 2024, 7:42 pm

Pass the 3-state INT Rule!

Post by R2INT »

This is like Pass the Rule but with 3 states!

Code: Select all

x = 64, y = 54, rule = passthe3intrule
.A2.3AB.A2B2.2BA.B2.2B.A.B.2A.A4.B3.A2.2A.3A.BA2.B3.A.A2B$.B.BA2B2.B.
A.AB3ABAB2A2.B5.B2.3BA.3B.ABABA.2A2.B.BA2B.B2.B$.A.B.A2.AB3.3BA5.ABA.
A4.B4.3A2B3.2A2.B.B2.2A.B2A2.BA$.B.2B2A2B.A.A2BA2.A2.B.2BA.2ABABA5.B2A
.BAB2A.B3AB2.B.2B.ABA$A3.2A.2B4.B.B3.A2BA.2A.B4.2B.B.B3.B.AB3A2.2B2.A
B2.2B2AB$.AB2.AB4.A3.B2.A3.2B3.B2A2.A6.B.A5.ABA5.A2B.2BAB$3.A.B.2B.AB
.BA3.AB3.A.BA3.2A.2B2.2BA2.2AB2.2B.B.A.A2.A3.BA$.3B2.A.AB3.A.B2.3A.A.
B2A.3B.A2.A.B.A.A2.A.A.B3.A.A2.A3.3B$.A.2B2.2B3A.BA.BA.2B.A.A2.3B.BA.
B6.B3.3A.ABA.A.B4.2BA$2.A.B2.B.A.A2BAB.2A.B2A2.2AB4.2AB.3B3.B4.B2.2B2.
A2.AB.2A$4.2A.2B2.3A.A3.A4.A3B2A3.A.2AB.BAB.B.B.B2.A.A.A2B.B.AB$.2B.3B
A7.A2B.3A4.A2.2B.BA3.B.A4.2B.A.BAB2.A.2B2.B2.A$.2AB2A2.A.B2.A.ABA.2B.
B2A.BA4.AB2AB.A.A.B.ABAB.B3.3B3.AB$AB.2A2.A7.AB.2ABA.2BA2.A.2A4.B.AB3.
A4.BA4.B.ABA.A.B$2.B.BA.3A2.A2B2.BA.B3.2BA3.AB2A2.2A.3B6.3BA.A.A4.A.B
$A.ABA3.B.A.BA3.A2.A2.2AB.B.B.2ABA2.2B.B3.A.2BA3B2A2B.AB.BA.A$BAB.2BA
B3.BA.A3.2A2B3.A.2A2.B2A2.2A.2A2.3A.B2ABA.BAB.B4.B$3.A.B.B2.B2A.2A2.A
B.2BAB.BABAB.2A4.B.B.2B.4A.AB.BA.A2B.B.A$2.BA2.3B5.2B.A.B.3A4.ABA.2B.
A.A4.A2.A3.B4.A.A.B2.2AB$A2.2A2B.A3.B.2B2.A.2B2.A3.2A.AB.B2.B2A.A2.BA
.B2AB.A2.2A.B.BABA$2.2B3.3B.A5.3BA.AB2.A3.2A.B3A.2AB3.3B4.2A2.B2.2A3.
A$2.5A.BA.B.A3.AB.B.B2.2A2.A2B2.BA3.A.A2.2B2A.2BA.A8.AB$2AB.B6.3BA6.B
2.A2.2A.AB2A2B2.A2.BA5.2AB.B2AB.A.A2.BA$A.B.B2.AB.A.A.ABA.2B3.2B4.B.A
B2.A2.BA2.AB.A2.A.B.2BA2.ABA.A.B$2.A3.BA3.2BAB4.BA2B.2BA3.2A.BA3.2B4A
4.AB2.A2B2.2BABAB$.BA3.A.2BA.2A2.A.A.BA.A2.B3.BAB2.A.2BA.B.AB.2A.B.B4.
2A3.B$3.A.2B2.A.A3.B2.A4.2B4.2BAB.A.A.A.A.A3.A.2AB5.A2.2B$B.A2.B.B.2A
B.B.2B5.2A7.AB3.B3.A3.3B.2A3.2B3.3AB$3.A3.2A3.AB.2AB3.3A3.BA.B2.B.B.B
4.A3.A.2A2.A3.2BA.B.A$B2A.3A3.B4.B3A4.A.BAB.BA2B5.ABA4.B2.B.A3.A4.AB2.
B$.3B.B.B2.B.A.BA4.BA2.B.B3.A.2BA3.AB3A.B4.A.B2.A.B.B.3AB$2.BA.4A.2A.
A2B2.BA.A3.B3.B2.B.BA2.3A.BA.ABA3B.BA2.3AB3AB$.B.A.A.3AB.2A.B.2B2.B.2A
.BAB4A.B.B2.AB4.ABA3.2B2.2B2.3B$A2.AB.A2.ABA2.A3.3B2.B.B.A.A.B5.A2B3.
B3AB.B4.3A4.2B$A.A.B2.A.2ABA2B.B.B2.B3.A5.ABA2B.BA.BAB.B3.A.2A.A.2A.2B
.A$B2.B2A.AB.A2.2B2AB2.AB.BA2.AB2.B.BAB.B.BAB.BA2.2BA.A.B2.2A2.A2.A$2.
B2.2B2.AB.2B2.2ABA4.A2B.B3.A2.A5.B4.A3.A.B.A4B.B.BA$B2.B.B.2A2BA4.4BA
3.2AB.BABA.2A.2B4.B2.3A.B3.2B2.2A.A2.A$.A.B.2B.A4.A.2B2.B.B.A2.BA5BA2.
B.ABA5.AB2A2.BA2.B4A.BA$B.B.B3A5.B4.B.A.AB.2A2.B.A3B2.AB4.A.B.B3.A2.2B
3.AB2.A$.B2A3.AB2.B3.2A2.AB.BA.B2.2BABA3B.A2BA5.BAB2.ABAB2.AB.2B$2.2B
.B.B3.A.B.B.3A2.BA.B.B.A9.4B.AB3.3AB2.AB4.BA$A4.AB3.B2.2B.B.A.A4B.A2.
BA.AB.A.A3.A2B.A.B3AB3.2BA4.AB$A.A.3A.ABA8.AB.A.2AB.3B2.A.A.AB2.2B.B2.
A.2B.A2B.A.AB.AB$.2B2.3A3.B2A2B2.A2BA.B4.ABA.B.A2.A3.A2.A.BA.B.A.B2A.
B2.AB.A$B5.BA2.2B2A2.B.A3.B.AB2A.2B.A.AB.B3.A.B.2A.2AB2.A3B.3AB.A$.B.
2B4.B2.B.BA5.B2A3.BA.2A.2BA.B.BA4.B.B3.3B2.BA.AB2.B$B.A2BA.A2.A.A.B4.
B.B2AB.B5.2B2.A5.B4.2BAB4.2B3.B$B.B3.A.3B2A3.4A2.AB2.BA6.B.A.A.B4.B3.
2B.BA2.B2.B3.A$B.ABABAB7.B3.2A6.B5.BA2.2AB2AB2.A2.A2B.2B.A.AB.A$.B2.B
3A.A2.4A.B.B.AB.2B2.B4.B3.B3.A.AB3.A.B2.B2.B.A3.2B$.A.A6.A2.B4.BABA6.
BABA.B.2AB2.A.B.B4.BA3.B2.AB.A$2AB3.AB.BAB8.AB11.2A2.A.A3.A.3A2.A4.3A
.2A2B$.BA2B2.ABA3BA5.BA.B3.BAB3.B2.2A2.2A3B.B.A2B.B.B.A.BA2.3A!
@RULE passthe3intrule

# Life on the union of states 1 and 2.
# Pure-state subspaces 0/1 and 0/2 are closed.
# Mixed-state outputs are reproducibly pseudorandom per D4 orbit.

@COLORS
0 0 0 0
1 255 255 255
2 0 255 255

@TABLE
n_states:3
neighborhood:Moore
symmetries:rotate4reflect

0 0,0,0,0,0,1,1,1 1
0 0,0,0,0,0,1,1,2 2
0 0,0,0,0,0,1,2,1 1
0 0,0,0,0,0,1,2,2 2
0 0,0,0,0,0,2,1,2 1
0 0,0,0,0,0,2,2,2 2
0 0,0,0,0,1,0,1,1 1
0 0,0,0,0,1,0,1,2 1
0 0,0,0,0,1,0,2,1 1
0 0,0,0,0,1,0,2,2 2
0 0,0,0,0,1,1,0,1 1
0 0,0,0,0,1,1,0,2 2
0 0,0,0,0,1,1,1,0 1
0 0,0,0,0,1,1,2,0 2
0 0,0,0,0,1,2,0,1 2
0 0,0,0,0,1,2,0,2 1
0 0,0,0,0,1,2,1,0 1
0 0,0,0,0,1,2,2,0 1
0 0,0,0,0,2,0,1,1 1
0 0,0,0,0,2,0,1,2 2
0 0,0,0,0,2,0,2,1 2
0 0,0,0,0,2,0,2,2 2
0 0,0,0,0,2,1,0,1 2
0 0,0,0,0,2,1,0,2 2
0 0,0,0,0,2,1,2,0 2
0 0,0,0,0,2,2,0,1 1
0 0,0,0,0,2,2,0,2 2
0 0,0,0,0,2,2,2,0 2
0 0,0,0,1,0,0,1,1 1
0 0,0,0,1,0,0,1,2 1
0 0,0,0,1,0,0,2,1 2
0 0,0,0,1,0,0,2,2 1
0 0,0,0,1,0,1,0,1 1
0 0,0,0,1,0,1,0,2 2
0 0,0,0,1,0,2,0,1 1
0 0,0,0,1,0,2,0,2 2
0 0,0,0,1,1,0,0,2 1
0 0,0,0,1,2,0,0,2 1
0 0,0,0,2,0,0,1,2 1
0 0,0,0,2,0,0,2,2 2
0 0,0,0,2,0,1,0,2 2
0 0,0,0,2,0,2,0,2 2
0 0,0,1,0,0,0,1,1 1
0 0,0,1,0,0,0,1,2 2
0 0,0,1,0,0,0,2,1 2
0 0,0,1,0,0,0,2,2 2
0 0,0,1,0,0,1,0,1 1
0 0,0,1,0,0,1,0,2 1
0 0,0,1,0,0,2,0,2 1
0 0,0,1,0,1,0,0,1 1
0 0,0,1,0,1,0,0,2 2
0 0,0,1,0,1,0,1,0 1
0 0,0,1,0,1,0,2,0 2
0 0,0,1,0,2,0,0,1 2
0 0,0,1,0,2,0,0,2 1
0 0,0,1,0,2,0,1,0 1
0 0,0,1,0,2,0,2,0 1
0 0,0,1,1,0,0,2,0 1
0 0,0,1,2,0,0,2,0 1
0 0,0,2,0,0,0,2,1 2
0 0,0,2,0,0,0,2,2 2
0 0,0,2,0,0,1,0,1 1
0 0,0,2,0,0,1,0,2 1
0 0,0,2,0,0,2,0,2 2
0 0,0,2,0,1,0,2,0 1
0 0,0,2,0,2,0,0,1 1
0 0,0,2,0,2,0,0,2 2
0 0,0,2,0,2,0,2,0 2
1 0,0,0,0,0,0,1,1 1
1 0,0,0,0,0,0,1,2 2
1 0,0,0,0,0,0,2,1 2
1 0,0,0,0,0,0,2,2 2
1 0,0,0,0,0,1,0,1 1
1 0,0,0,0,0,1,0,2 1
1 0,0,0,0,0,1,1,1 1
1 0,0,0,0,0,1,1,2 2
1 0,0,0,0,0,1,2,1 1
1 0,0,0,0,0,1,2,2 2
1 0,0,0,0,0,2,0,2 2
1 0,0,0,0,0,2,1,2 1
1 0,0,0,0,0,2,2,2 2
1 0,0,0,0,1,0,0,1 1
1 0,0,0,0,1,0,0,2 2
1 0,0,0,0,1,0,1,0 1
1 0,0,0,0,1,0,1,1 1
1 0,0,0,0,1,0,1,2 1
1 0,0,0,0,1,0,2,0 2
1 0,0,0,0,1,0,2,1 1
1 0,0,0,0,1,0,2,2 2
1 0,0,0,0,1,1,0,1 1
1 0,0,0,0,1,1,0,2 2
1 0,0,0,0,1,1,1,0 1
1 0,0,0,0,1,1,2,0 2
1 0,0,0,0,1,2,0,1 2
1 0,0,0,0,1,2,0,2 1
1 0,0,0,0,1,2,1,0 1
1 0,0,0,0,1,2,2,0 1
1 0,0,0,0,2,0,0,1 2
1 0,0,0,0,2,0,0,2 2
1 0,0,0,0,2,0,1,1 1
1 0,0,0,0,2,0,1,2 2
1 0,0,0,0,2,0,2,0 2
1 0,0,0,0,2,0,2,1 2
1 0,0,0,0,2,0,2,2 2
1 0,0,0,0,2,1,0,1 2
1 0,0,0,0,2,1,0,2 2
1 0,0,0,0,2,1,2,0 2
1 0,0,0,0,2,2,0,1 1
1 0,0,0,0,2,2,0,2 2
1 0,0,0,0,2,2,2,0 2
1 0,0,0,1,0,0,0,1 1
1 0,0,0,1,0,0,0,2 2
1 0,0,0,1,0,0,1,1 1
1 0,0,0,1,0,0,1,2 1
1 0,0,0,1,0,0,2,1 2
1 0,0,0,1,0,0,2,2 1
1 0,0,0,1,0,1,0,1 1
1 0,0,0,1,0,1,0,2 2
1 0,0,0,1,0,2,0,1 1
1 0,0,0,1,0,2,0,2 2
1 0,0,0,1,1,0,0,2 1
1 0,0,0,1,2,0,0,2 1
1 0,0,0,2,0,0,0,2 2
1 0,0,0,2,0,0,1,2 1
1 0,0,0,2,0,0,2,2 2
1 0,0,0,2,0,1,0,2 2
1 0,0,0,2,0,2,0,2 2
1 0,0,1,0,0,0,1,0 1
1 0,0,1,0,0,0,1,1 1
1 0,0,1,0,0,0,1,2 2
1 0,0,1,0,0,0,2,0 1
1 0,0,1,0,0,0,2,1 2
1 0,0,1,0,0,0,2,2 2
1 0,0,1,0,0,1,0,1 1
1 0,0,1,0,0,1,0,2 1
1 0,0,1,0,0,2,0,2 1
1 0,0,1,0,1,0,0,1 1
1 0,0,1,0,1,0,0,2 2
1 0,0,1,0,1,0,1,0 1
1 0,0,1,0,1,0,2,0 2
1 0,0,1,0,2,0,0,1 2
1 0,0,1,0,2,0,0,2 1
1 0,0,1,0,2,0,1,0 1
1 0,0,1,0,2,0,2,0 1
1 0,0,1,1,0,0,2,0 1
1 0,0,1,2,0,0,2,0 1
1 0,0,2,0,0,0,2,0 2
1 0,0,2,0,0,0,2,1 2
1 0,0,2,0,0,0,2,2 2
1 0,0,2,0,0,1,0,1 1
1 0,0,2,0,0,1,0,2 1
1 0,0,2,0,0,2,0,2 2
1 0,0,2,0,1,0,2,0 1
1 0,0,2,0,2,0,0,1 1
1 0,0,2,0,2,0,0,2 2
1 0,0,2,0,2,0,2,0 2
2 0,0,0,0,0,0,1,1 1
2 0,0,0,0,0,0,1,2 2
2 0,0,0,0,0,0,2,1 2
2 0,0,0,0,0,0,2,2 2
2 0,0,0,0,0,1,0,1 1
2 0,0,0,0,0,1,0,2 1
2 0,0,0,0,0,1,1,1 1
2 0,0,0,0,0,1,1,2 2
2 0,0,0,0,0,1,2,1 1
2 0,0,0,0,0,1,2,2 2
2 0,0,0,0,0,2,0,2 2
2 0,0,0,0,0,2,1,2 1
2 0,0,0,0,0,2,2,2 2
2 0,0,0,0,1,0,0,1 1
2 0,0,0,0,1,0,0,2 2
2 0,0,0,0,1,0,1,0 1
2 0,0,0,0,1,0,1,1 1
2 0,0,0,0,1,0,1,2 1
2 0,0,0,0,1,0,2,0 2
2 0,0,0,0,1,0,2,1 1
2 0,0,0,0,1,0,2,2 2
2 0,0,0,0,1,1,0,1 1
2 0,0,0,0,1,1,0,2 2
2 0,0,0,0,1,1,1,0 1
2 0,0,0,0,1,1,2,0 2
2 0,0,0,0,1,2,0,1 2
2 0,0,0,0,1,2,0,2 1
2 0,0,0,0,1,2,1,0 1
2 0,0,0,0,1,2,2,0 1
2 0,0,0,0,2,0,0,1 2
2 0,0,0,0,2,0,0,2 2
2 0,0,0,0,2,0,1,1 1
2 0,0,0,0,2,0,1,2 2
2 0,0,0,0,2,0,2,0 2
2 0,0,0,0,2,0,2,1 2
2 0,0,0,0,2,0,2,2 2
2 0,0,0,0,2,1,0,1 2
2 0,0,0,0,2,1,0,2 2
2 0,0,0,0,2,1,2,0 2
2 0,0,0,0,2,2,0,1 1
2 0,0,0,0,2,2,0,2 2
2 0,0,0,0,2,2,2,0 2
2 0,0,0,1,0,0,0,1 1
2 0,0,0,1,0,0,0,2 2
2 0,0,0,1,0,0,1,1 1
2 0,0,0,1,0,0,1,2 1
2 0,0,0,1,0,0,2,1 2
2 0,0,0,1,0,0,2,2 1
2 0,0,0,1,0,1,0,1 1
2 0,0,0,1,0,1,0,2 2
2 0,0,0,1,0,2,0,1 1
2 0,0,0,1,0,2,0,2 2
2 0,0,0,1,1,0,0,2 1
2 0,0,0,1,2,0,0,2 1
2 0,0,0,2,0,0,0,2 2
2 0,0,0,2,0,0,1,2 1
2 0,0,0,2,0,0,2,2 2
2 0,0,0,2,0,1,0,2 2
2 0,0,0,2,0,2,0,2 2
2 0,0,1,0,0,0,1,0 1
2 0,0,1,0,0,0,1,1 1
2 0,0,1,0,0,0,1,2 2
2 0,0,1,0,0,0,2,0 1
2 0,0,1,0,0,0,2,1 2
2 0,0,1,0,0,0,2,2 2
2 0,0,1,0,0,1,0,1 1
2 0,0,1,0,0,1,0,2 1
2 0,0,1,0,0,2,0,2 1
2 0,0,1,0,1,0,0,1 1
2 0,0,1,0,1,0,0,2 2
2 0,0,1,0,1,0,1,0 1
2 0,0,1,0,1,0,2,0 2
2 0,0,1,0,2,0,0,1 2
2 0,0,1,0,2,0,0,2 1
2 0,0,1,0,2,0,1,0 1
2 0,0,1,0,2,0,2,0 1
2 0,0,1,1,0,0,2,0 1
2 0,0,1,2,0,0,2,0 1
2 0,0,2,0,0,0,2,0 2
2 0,0,2,0,0,0,2,1 2
2 0,0,2,0,0,0,2,2 2
2 0,0,2,0,0,1,0,1 1
2 0,0,2,0,0,1,0,2 1
2 0,0,2,0,0,2,0,2 2
2 0,0,2,0,1,0,2,0 1
2 0,0,2,0,2,0,0,1 1
2 0,0,2,0,2,0,0,2 2
2 0,0,2,0,2,0,2,0 2

var a1={0,1,2}
var a2=a1
var a3=a1
var a4=a1
var a5=a1
var a6=a1
var a7=a1
var a8=a1
var a9=a1
a1 a2,a3,a4,a5,a6,a7,a8,a9 0
I set the rule to emulate Life for both states 1 and 2, and mixtures of states 1 and 2 emulate Life with randomly initialized outputs. This is so that you can have interesting rules earlier, have multiple 2-state rules compete, and start wandering into 3-state dynamics without having to destroy Life's dynamics.

Rules:
  • Only modify one transition at a time. You can suggest transitions for others to modify.
  • No variables are allowed, except for the catch-all at the end. Variables would modify multiple transitions at a time and break the rule above.
  • Do not doublepost, unless someone has not posted for 7 days.
  • Do not restart the game. The game is playable indefinitely.
  • Do not change the transition the previous player modified.
  • Clearly state the transition that you modified when posting.
  • If you find anything interesting in your rule, please post it.
Range-2 INT
R2INT's Rule Collection

3-state rules are the final frontier.
Top
User avatar
R2INT
Posts: 934
Joined: July 2nd, 2024, 7:42 pm

Re: Pass the 3-state INT Rule!

Post by R2INT »

I'll start. State 2 S3j becomes state 1, so we can start having more of a mix of states which allows more pattern types.

State 1 emulation is still intact.

Code: Select all

x = 64, y = 54, rule = passthe3intrule
.A2.3AB.A2B2.2BA.B2.2B.A.B.2A.A4.B3.A2.2A.3A.BA2.B3.A.A2B$.B.BA2B2.B.
A.AB3ABAB2A2.B5.B2.3BA.3B.ABABA.2A2.B.BA2B.B2.B$.A.B.A2.AB3.3BA5.ABA.
A4.B4.3A2B3.2A2.B.B2.2A.B2A2.BA$.B.2B2A2B.A.A2BA2.A2.B.2BA.2ABABA5.B2A
.BAB2A.B3AB2.B.2B.ABA$A3.2A.2B4.B.B3.A2BA.2A.B4.2B.B.B3.B.AB3A2.2B2.A
B2.2B2AB$.AB2.AB4.A3.B2.A3.2B3.B2A2.A6.B.A5.ABA5.A2B.2BAB$3.A.B.2B.AB
.BA3.AB3.A.BA3.2A.2B2.2BA2.2AB2.2B.B.A.A2.A3.BA$.3B2.A.AB3.A.B2.3A.A.
B2A.3B.A2.A.B.A.A2.A.A.B3.A.A2.A3.3B$.A.2B2.2B3A.BA.BA.2B.A.A2.3B.BA.
B6.B3.3A.ABA.A.B4.2BA$2.A.B2.B.A.A2BAB.2A.B2A2.2AB4.2AB.3B3.B4.B2.2B2.
A2.AB.2A$4.2A.2B2.3A.A3.A4.A3B2A3.A.2AB.BAB.B.B.B2.A.A.A2B.B.AB$.2B.3B
A7.A2B.3A4.A2.2B.BA3.B.A4.2B.A.BAB2.A.2B2.B2.A$.2AB2A2.A.B2.A.ABA.2B.
B2A.BA4.AB2AB.A.A.B.ABAB.B3.3B3.AB$AB.2A2.A7.AB.2ABA.2BA2.A.2A4.B.AB3.
A4.BA4.B.ABA.A.B$2.B.BA.3A2.A2B2.BA.B3.2BA3.AB2A2.2A.3B6.3BA.A.A4.A.B
$A.ABA3.B.A.BA3.A2.A2.2AB.B.B.2ABA2.2B.B3.A.2BA3B2A2B.AB.BA.A$BAB.2BA
B3.BA.A3.2A2B3.A.2A2.B2A2.2A.2A2.3A.B2ABA.BAB.B4.B$3.A.B.B2.B2A.2A2.A
B.2BAB.BABAB.2A4.B.B.2B.4A.AB.BA.A2B.B.A$2.BA2.3B5.2B.A.B.3A4.ABA.2B.
A.A4.A2.A3.B4.A.A.B2.2AB$A2.2A2B.A3.B.2B2.A.2B2.A3.2A.AB.B2.B2A.A2.BA
.B2AB.A2.2A.B.BABA$2.2B3.3B.A5.3BA.AB2.A3.2A.B3A.2AB3.3B4.2A2.B2.2A3.
A$2.5A.BA.B.A3.AB.B.B2.2A2.A2B2.BA3.A.A2.2B2A.2BA.A8.AB$2AB.B6.3BA6.B
2.A2.2A.AB2A2B2.A2.BA5.2AB.B2AB.A.A2.BA$A.B.B2.AB.A.A.ABA.2B3.2B4.B.A
B2.A2.BA2.AB.A2.A.B.2BA2.ABA.A.B$2.A3.BA3.2BAB4.BA2B.2BA3.2A.BA3.2B4A
4.AB2.A2B2.2BABAB$.BA3.A.2BA.2A2.A.A.BA.A2.B3.BAB2.A.2BA.B.AB.2A.B.B4.
2A3.B$3.A.2B2.A.A3.B2.A4.2B4.2BAB.A.A.A.A.A3.A.2AB5.A2.2B$B.A2.B.B.2A
B.B.2B5.2A7.AB3.B3.A3.3B.2A3.2B3.3AB$3.A3.2A3.AB.2AB3.3A3.BA.B2.B.B.B
4.A3.A.2A2.A3.2BA.B.A$B2A.3A3.B4.B3A4.A.BAB.BA2B5.ABA4.B2.B.A3.A4.AB2.
B$.3B.B.B2.B.A.BA4.BA2.B.B3.A.2BA3.AB3A.B4.A.B2.A.B.B.3AB$2.BA.4A.2A.
A2B2.BA.A3.B3.B2.B.BA2.3A.BA.ABA3B.BA2.3AB3AB$.B.A.A.3AB.2A.B.2B2.B.2A
.BAB4A.B.B2.AB4.ABA3.2B2.2B2.3B$A2.AB.A2.ABA2.A3.3B2.B.B.A.A.B5.A2B3.
B3AB.B4.3A4.2B$A.A.B2.A.2ABA2B.B.B2.B3.A5.ABA2B.BA.BAB.B3.A.2A.A.2A.2B
.A$B2.B2A.AB.A2.2B2AB2.AB.BA2.AB2.B.BAB.B.BAB.BA2.2BA.A.B2.2A2.A2.A$2.
B2.2B2.AB.2B2.2ABA4.A2B.B3.A2.A5.B4.A3.A.B.A4B.B.BA$B2.B.B.2A2BA4.4BA
3.2AB.BABA.2A.2B4.B2.3A.B3.2B2.2A.A2.A$.A.B.2B.A4.A.2B2.B.B.A2.BA5BA2.
B.ABA5.AB2A2.BA2.B4A.BA$B.B.B3A5.B4.B.A.AB.2A2.B.A3B2.AB4.A.B.B3.A2.2B
3.AB2.A$.B2A3.AB2.B3.2A2.AB.BA.B2.2BABA3B.A2BA5.BAB2.ABAB2.AB.2B$2.2B
.B.B3.A.B.B.3A2.BA.B.B.A9.4B.AB3.3AB2.AB4.BA$A4.AB3.B2.2B.B.A.A4B.A2.
BA.AB.A.A3.A2B.A.B3AB3.2BA4.AB$A.A.3A.ABA8.AB.A.2AB.3B2.A.A.AB2.2B.B2.
A.2B.A2B.A.AB.AB$.2B2.3A3.B2A2B2.A2BA.B4.ABA.B.A2.A3.A2.A.BA.B.A.B2A.
B2.AB.A$B5.BA2.2B2A2.B.A3.B.AB2A.2B.A.AB.B3.A.B.2A.2AB2.A3B.3AB.A$.B.
2B4.B2.B.BA5.B2A3.BA.2A.2BA.B.BA4.B.B3.3B2.BA.AB2.B$B.A2BA.A2.A.A.B4.
B.B2AB.B5.2B2.A5.B4.2BAB4.2B3.B$B.B3.A.3B2A3.4A2.AB2.BA6.B.A.A.B4.B3.
2B.BA2.B2.B3.A$B.ABABAB7.B3.2A6.B5.BA2.2AB2AB2.A2.A2B.2B.A.AB.A$.B2.B
3A.A2.4A.B.B.AB.2B2.B4.B3.B3.A.AB3.A.B2.B2.B.A3.2B$.A.A6.A2.B4.BABA6.
BABA.B.2AB2.A.B.B4.BA3.B2.AB.A$2AB3.AB.BAB8.AB11.2A2.A.A3.A.3A2.A4.3A
.2A2B$.BA2B2.ABA3BA5.BA.B3.BAB3.B2.2A2.2A3B.B.A2B.B.B.A.BA2.3A!
@RULE passthe3intrule

# Life on the union of states 1 and 2.
# Pure-state subspaces 0/1 and 0/2 are closed.
# Mixed-state outputs are reproducibly pseudorandom per D4 orbit.

@COLORS
0 0 0 0
1 255 255 255
2 0 255 255

@TABLE
n_states:3
neighborhood:Moore
symmetries:rotate4reflect

2 0,0,0,0,2,2,0,2 1 # R2INT, turn 1
# base rule
0 0,0,0,0,0,1,1,1 1
0 0,0,0,0,0,1,1,2 2
0 0,0,0,0,0,1,2,1 1
0 0,0,0,0,0,1,2,2 2
0 0,0,0,0,0,2,1,2 1
0 0,0,0,0,0,2,2,2 2
0 0,0,0,0,1,0,1,1 1
0 0,0,0,0,1,0,1,2 1
0 0,0,0,0,1,0,2,1 1
0 0,0,0,0,1,0,2,2 2
0 0,0,0,0,1,1,0,1 1
0 0,0,0,0,1,1,0,2 2
0 0,0,0,0,1,1,1,0 1
0 0,0,0,0,1,1,2,0 2
0 0,0,0,0,1,2,0,1 2
0 0,0,0,0,1,2,0,2 1
0 0,0,0,0,1,2,1,0 1
0 0,0,0,0,1,2,2,0 1
0 0,0,0,0,2,0,1,1 1
0 0,0,0,0,2,0,1,2 2
0 0,0,0,0,2,0,2,1 2
0 0,0,0,0,2,0,2,2 2
0 0,0,0,0,2,1,0,1 2
0 0,0,0,0,2,1,0,2 2
0 0,0,0,0,2,1,2,0 2
0 0,0,0,0,2,2,0,1 1
0 0,0,0,0,2,2,0,2 2
0 0,0,0,0,2,2,2,0 2
0 0,0,0,1,0,0,1,1 1
0 0,0,0,1,0,0,1,2 1
0 0,0,0,1,0,0,2,1 2
0 0,0,0,1,0,0,2,2 1
0 0,0,0,1,0,1,0,1 1
0 0,0,0,1,0,1,0,2 2
0 0,0,0,1,0,2,0,1 1
0 0,0,0,1,0,2,0,2 2
0 0,0,0,1,1,0,0,2 1
0 0,0,0,1,2,0,0,2 1
0 0,0,0,2,0,0,1,2 1
0 0,0,0,2,0,0,2,2 2
0 0,0,0,2,0,1,0,2 2
0 0,0,0,2,0,2,0,2 2
0 0,0,1,0,0,0,1,1 1
0 0,0,1,0,0,0,1,2 2
0 0,0,1,0,0,0,2,1 2
0 0,0,1,0,0,0,2,2 2
0 0,0,1,0,0,1,0,1 1
0 0,0,1,0,0,1,0,2 1
0 0,0,1,0,0,2,0,2 1
0 0,0,1,0,1,0,0,1 1
0 0,0,1,0,1,0,0,2 2
0 0,0,1,0,1,0,1,0 1
0 0,0,1,0,1,0,2,0 2
0 0,0,1,0,2,0,0,1 2
0 0,0,1,0,2,0,0,2 1
0 0,0,1,0,2,0,1,0 1
0 0,0,1,0,2,0,2,0 1
0 0,0,1,1,0,0,2,0 1
0 0,0,1,2,0,0,2,0 1
0 0,0,2,0,0,0,2,1 2
0 0,0,2,0,0,0,2,2 2
0 0,0,2,0,0,1,0,1 1
0 0,0,2,0,0,1,0,2 1
0 0,0,2,0,0,2,0,2 2
0 0,0,2,0,1,0,2,0 1
0 0,0,2,0,2,0,0,1 1
0 0,0,2,0,2,0,0,2 2
0 0,0,2,0,2,0,2,0 2
1 0,0,0,0,0,0,1,1 1
1 0,0,0,0,0,0,1,2 2
1 0,0,0,0,0,0,2,1 2
1 0,0,0,0,0,0,2,2 2
1 0,0,0,0,0,1,0,1 1
1 0,0,0,0,0,1,0,2 1
1 0,0,0,0,0,1,1,1 1
1 0,0,0,0,0,1,1,2 2
1 0,0,0,0,0,1,2,1 1
1 0,0,0,0,0,1,2,2 2
1 0,0,0,0,0,2,0,2 2
1 0,0,0,0,0,2,1,2 1
1 0,0,0,0,0,2,2,2 2
1 0,0,0,0,1,0,0,1 1
1 0,0,0,0,1,0,0,2 2
1 0,0,0,0,1,0,1,0 1
1 0,0,0,0,1,0,1,1 1
1 0,0,0,0,1,0,1,2 1
1 0,0,0,0,1,0,2,0 2
1 0,0,0,0,1,0,2,1 1
1 0,0,0,0,1,0,2,2 2
1 0,0,0,0,1,1,0,1 1
1 0,0,0,0,1,1,0,2 2
1 0,0,0,0,1,1,1,0 1
1 0,0,0,0,1,1,2,0 2
1 0,0,0,0,1,2,0,1 2
1 0,0,0,0,1,2,0,2 1
1 0,0,0,0,1,2,1,0 1
1 0,0,0,0,1,2,2,0 1
1 0,0,0,0,2,0,0,1 2
1 0,0,0,0,2,0,0,2 2
1 0,0,0,0,2,0,1,1 1
1 0,0,0,0,2,0,1,2 2
1 0,0,0,0,2,0,2,0 2
1 0,0,0,0,2,0,2,1 2
1 0,0,0,0,2,0,2,2 2
1 0,0,0,0,2,1,0,1 2
1 0,0,0,0,2,1,0,2 2
1 0,0,0,0,2,1,2,0 2
1 0,0,0,0,2,2,0,1 1
1 0,0,0,0,2,2,0,2 2
1 0,0,0,0,2,2,2,0 2
1 0,0,0,1,0,0,0,1 1
1 0,0,0,1,0,0,0,2 2
1 0,0,0,1,0,0,1,1 1
1 0,0,0,1,0,0,1,2 1
1 0,0,0,1,0,0,2,1 2
1 0,0,0,1,0,0,2,2 1
1 0,0,0,1,0,1,0,1 1
1 0,0,0,1,0,1,0,2 2
1 0,0,0,1,0,2,0,1 1
1 0,0,0,1,0,2,0,2 2
1 0,0,0,1,1,0,0,2 1
1 0,0,0,1,2,0,0,2 1
1 0,0,0,2,0,0,0,2 2
1 0,0,0,2,0,0,1,2 1
1 0,0,0,2,0,0,2,2 2
1 0,0,0,2,0,1,0,2 2
1 0,0,0,2,0,2,0,2 2
1 0,0,1,0,0,0,1,0 1
1 0,0,1,0,0,0,1,1 1
1 0,0,1,0,0,0,1,2 2
1 0,0,1,0,0,0,2,0 1
1 0,0,1,0,0,0,2,1 2
1 0,0,1,0,0,0,2,2 2
1 0,0,1,0,0,1,0,1 1
1 0,0,1,0,0,1,0,2 1
1 0,0,1,0,0,2,0,2 1
1 0,0,1,0,1,0,0,1 1
1 0,0,1,0,1,0,0,2 2
1 0,0,1,0,1,0,1,0 1
1 0,0,1,0,1,0,2,0 2
1 0,0,1,0,2,0,0,1 2
1 0,0,1,0,2,0,0,2 1
1 0,0,1,0,2,0,1,0 1
1 0,0,1,0,2,0,2,0 1
1 0,0,1,1,0,0,2,0 1
1 0,0,1,2,0,0,2,0 1
1 0,0,2,0,0,0,2,0 2
1 0,0,2,0,0,0,2,1 2
1 0,0,2,0,0,0,2,2 2
1 0,0,2,0,0,1,0,1 1
1 0,0,2,0,0,1,0,2 1
1 0,0,2,0,0,2,0,2 2
1 0,0,2,0,1,0,2,0 1
1 0,0,2,0,2,0,0,1 1
1 0,0,2,0,2,0,0,2 2
1 0,0,2,0,2,0,2,0 2
2 0,0,0,0,0,0,1,1 1
2 0,0,0,0,0,0,1,2 2
2 0,0,0,0,0,0,2,1 2
2 0,0,0,0,0,0,2,2 2
2 0,0,0,0,0,1,0,1 1
2 0,0,0,0,0,1,0,2 1
2 0,0,0,0,0,1,1,1 1
2 0,0,0,0,0,1,1,2 2
2 0,0,0,0,0,1,2,1 1
2 0,0,0,0,0,1,2,2 2
2 0,0,0,0,0,2,0,2 2
2 0,0,0,0,0,2,1,2 1
2 0,0,0,0,0,2,2,2 2
2 0,0,0,0,1,0,0,1 1
2 0,0,0,0,1,0,0,2 2
2 0,0,0,0,1,0,1,0 1
2 0,0,0,0,1,0,1,1 1
2 0,0,0,0,1,0,1,2 1
2 0,0,0,0,1,0,2,0 2
2 0,0,0,0,1,0,2,1 1
2 0,0,0,0,1,0,2,2 2
2 0,0,0,0,1,1,0,1 1
2 0,0,0,0,1,1,0,2 2
2 0,0,0,0,1,1,1,0 1
2 0,0,0,0,1,1,2,0 2
2 0,0,0,0,1,2,0,1 2
2 0,0,0,0,1,2,0,2 1
2 0,0,0,0,1,2,1,0 1
2 0,0,0,0,1,2,2,0 1
2 0,0,0,0,2,0,0,1 2
2 0,0,0,0,2,0,0,2 2
2 0,0,0,0,2,0,1,1 1
2 0,0,0,0,2,0,1,2 2
2 0,0,0,0,2,0,2,0 2
2 0,0,0,0,2,0,2,1 2
2 0,0,0,0,2,0,2,2 2
2 0,0,0,0,2,1,0,1 2
2 0,0,0,0,2,1,0,2 2
2 0,0,0,0,2,1,2,0 2
2 0,0,0,0,2,2,0,1 1
2 0,0,0,0,2,2,2,0 2
2 0,0,0,1,0,0,0,1 1
2 0,0,0,1,0,0,0,2 2
2 0,0,0,1,0,0,1,1 1
2 0,0,0,1,0,0,1,2 1
2 0,0,0,1,0,0,2,1 2
2 0,0,0,1,0,0,2,2 1
2 0,0,0,1,0,1,0,1 1
2 0,0,0,1,0,1,0,2 2
2 0,0,0,1,0,2,0,1 1
2 0,0,0,1,0,2,0,2 2
2 0,0,0,1,1,0,0,2 1
2 0,0,0,1,2,0,0,2 1
2 0,0,0,2,0,0,0,2 2
2 0,0,0,2,0,0,1,2 1
2 0,0,0,2,0,0,2,2 2
2 0,0,0,2,0,1,0,2 2
2 0,0,0,2,0,2,0,2 2
2 0,0,1,0,0,0,1,0 1
2 0,0,1,0,0,0,1,1 1
2 0,0,1,0,0,0,1,2 2
2 0,0,1,0,0,0,2,0 1
2 0,0,1,0,0,0,2,1 2
2 0,0,1,0,0,0,2,2 2
2 0,0,1,0,0,1,0,1 1
2 0,0,1,0,0,1,0,2 1
2 0,0,1,0,0,2,0,2 1
2 0,0,1,0,1,0,0,1 1
2 0,0,1,0,1,0,0,2 2
2 0,0,1,0,1,0,1,0 1
2 0,0,1,0,1,0,2,0 2
2 0,0,1,0,2,0,0,1 2
2 0,0,1,0,2,0,0,2 1
2 0,0,1,0,2,0,1,0 1
2 0,0,1,0,2,0,2,0 1
2 0,0,1,1,0,0,2,0 1
2 0,0,1,2,0,0,2,0 1
2 0,0,2,0,0,0,2,0 2
2 0,0,2,0,0,0,2,1 2
2 0,0,2,0,0,0,2,2 2
2 0,0,2,0,0,1,0,1 1
2 0,0,2,0,0,1,0,2 1
2 0,0,2,0,0,2,0,2 2
2 0,0,2,0,1,0,2,0 1
2 0,0,2,0,2,0,0,1 1
2 0,0,2,0,2,0,0,2 2
2 0,0,2,0,2,0,2,0 2

var a1={0,1,2}
var a2=a1
var a3=a1
var a4=a1
var a5=a1
var a6=a1
var a7=a1
var a8=a1
var a9=a1
a1 a2,a3,a4,a5,a6,a7,a8,a9 0
We should probably get going on adding births or removing survivals, so we can start having interesting patterns.
Range-2 INT
R2INT's Rule Collection

3-state rules are the final frontier.
Top
User avatar
unname4798
Posts: 2591
Joined: July 15th, 2023, 10:27 am
Location: Near ConwayLife servers

Re: Pass the 3-state INT Rule!

Post by unname4798 »

This game can't be played indefinitely, because the space of 3-state INT rules is finite.
Top
User avatar
R2INT
Posts: 934
Joined: July 2nd, 2024, 7:42 pm

Re: Pass the 3-state INT Rule!

Post by R2INT »

unname4798 wrote: November 2nd, 2026, 5:03 am This game can't be played indefinitely, because the space of 3-state INT rules is finite.
The rule states "do not change the transition the previous player modified." It is perfectly reasonable to change a transition a player modified two or more turns ago.

About the finiteness concern: the space of 3-state rules is about 10¹⁰⁰⁰, which is so large that you can play once every microsecond and not revisit the same rule until the end of the universe. The same also applies for 2-state rules.

Additionally, "do not revisit a rule previously encountered" is not in the rules, so it is, in fact, possible to play this indefinitely.
Range-2 INT
R2INT's Rule Collection

3-state rules are the final frontier.
Top
User avatar
LuveelVoom
Posts: 961
Joined: April 27th, 2022, 7:59 pm
Location: The 102 dimensional INT hypercube

Re: Pass the 3-state INT Rule!

Post by LuveelVoom »

R2INT wrote: November 2nd, 2026, 11:26 am About the finiteness concern: the space of 3-state rules is about 10¹⁰⁰⁰, which is so large that you can play once every microsecond and not revisit the same rule until the end of the universe. The same also applies for 2-state rules.
Microsecond? You can only reach 10^270 total computations (referring to one logical operation) in the lifespan of the universe...
Top
Post Reply

Return to “The Sandbox”