Rule:Codd2

@RULE Codd2

2. Codd, E.F., _Cellular_Automata_, Academic Press 1968 (ACM Monograph #3).
4. Originally distributed with XLife as codd.r
6. Several corrections have been made from the XLife version, to match Codd's
7. printed transition table. Stasis transitions have been taken out. More
8. importantly, some extra transitions have been added, to deal with sheathing-
9. signal collision cases that Codd hadn't considered. These additions are at the
10. bottom of the file and clearly marked. Hopefully these changes can be
11. considered to be the intent of Codd's work, if not his exact specification.
12. Just to be clear, these changes change nothing about the way the examples in
13. Codd's book work, and only affect rarely-encountered situations.
14. Contact: Tim Hutton <tim.hutton@gmail.com>

@TABLE n_states:8 neighborhood:vonNeumann symmetries:rotate4

var a={4,5} var b={2,3} var c={2,3} var d={4,5,6,7} var e={4,5,6} var f={0,1} var g={1,2} var h={0,1,2} var i={1,2,6} var j={1,6} var k={4,5} var l={4,6,7} var m={1,2,3} var n={6,7} var o={1,2,7} var p={0,2,3}

1. Almost all configurations with neighborhoods in [0-3] are stable
2. These are the exceptions (Codd's `short table', page 66)

0,1,2,1,2,1 # Path self-repair 3,0,0,0,2,2 # Path self-repair 3,0,1,0,2,2 # Gate control 3,0,1,0,3,0 # Gate control 2,1,2,3,2,3 # Gate control 3,1,2,3,2,2 # Gate control 0,0,2,1,3,1 # Path end self-repair 0,1,2,3,2,6 # Echo generation 0,1,2,2,2,7 # Echo generation

1. The long table

0,0,2,7,2,1 # j 0,0,3,6,3,1 # i 0,1,1,2,d,1 # fi = fan-in 0,1,1,e,2,1 # fi 0,1,2,1,d,1 # fi 0,1,2,2,d,1 # p = signal propagation 0,1,2,3,5,1 # p 0,1,2,4,2,1 # p 0,1,2,4,4,1 # fo = fan-out 0,1,2,5,b,1 # p (was fi) 0,1,2,5,5,1 # fo 0,1,2,6,2,1 # p 0,1,2,6,6,1 # fo 0,1,2,7,b,1 # p 0,1,2,7,7,1 # fo 0,1,3,2,4,1 # p 0,1,3,d,2,1 # pg - propagation at gate (subordinate path) 0,1,3,7,3,1 # t7 = transforming to 07 0,1,4,2,2,1 # p 0,1,4,2,4,1 # fo 0,1,4,3,2,1 # p 0,1,4,4,2,1 # fo 0,1,5,2,b,1 # p 0,1,5,2,5,1 # fo 0,1,5,3,2,1 # p 0,1,5,5,2,1 # fo 0,1,6,2,2,1 # p 0,1,6,2,6,1 # fo 0,1,6,6,2,1 # fo 0,1,7,2,2,1 # p 0,1,7,2,7,1 # fo 0,1,7,7,2,1 # fo 0,0,0,f,6,2 # k 0,0,0,2,5,2 # xl = extend left 0,0,0,2,6,2 # sh = sheathing 0,0,0,4,2,2 # xr = extend right 0,0,0,6,1,2 # k 0,0,0,6,2,2 # sh 0,0,0,6,6,2 # sh 0,0,1,0,6,2 # sh 0,0,1,1,6,2 # k 0,0,1,2,6,2 # sh 0,0,1,6,1,2 # k 0,0,1,6,2,2 # sh 0,0,1,6,6,2 # sh 0,0,2,0,6,2 # g = gate control 0,0,2,2,6,2 # sh 0,0,2,6,g,2 # sh 0,0,6,1,1,2 # k 0,0,6,2,1,2 # sh 0,0,6,2,2,2 # sh 0,0,6,2,6,2 # sh 0,0,6,6,1,2 # sh 0,1,1,1,6,2 # k 0,1,1,6,6,2 # sh 0,2,2,2,6,2 # sh 0,2,2,6,6,2 # sh 0,0,0,0,7,3 # k 0,0,0,1,5,3 # i 0,0,0,5,1,3 # i 0,0,1,0,7,3 # e 0,0,2,0,7,3 # g 1,0,0,0,4,0 # e 1,0,0,1,4,0 # e 1,0,0,4,1,0 # e 1,0,1,0,4,0 # e 1,0,1,1,4,0 # e 1,0,1,4,1,0 # e 1,0,4,1,1,0 # e 1,1,1,1,4,0 # e 1,0,0,3,6,2 # i 1,0,0,6,3,2 # i

1. error in codd.r: 10107[23] # s = sense

1,0,1,0,7,2 # s = sense 1,0,0,0,7,3 # s

1,0,0,2,4,4 # xr 1,0,b,4,c,4 # pe = path end 1,1,1,2,4,4 # fo 1,1,g,4,2,4 # fo,p 1,1,2,g,4,4 # fo,p 1,1,2,4,3,4 # pg 1,1,2,7,7,4 # fi 1,1,4,2,2,4 # p 1,1,7,2,7,4 # fi 1,1,7,7,2,4 # fi

1,2,b,2,4,4 # pe 1,2,b,4,3,4 # pe 1,2,2,4,4,4 # c = collision 1,2,3,2,4,4 # pe 1,b,3,3,4,4 # pe 1,2,4,2,2,4 # c 1,2,4,3,3,4 # pe

1,0,0,5,2,5 # xl 1,0,1,0,5,5 # i 1,0,b,5,c,5 # pe 1,1,1,2,5,5 # fo 1,1,g,5,2,5 # fo,p 1,1,2,g,5,5 # fo,p 1,1,2,4,4,5 # fi 1,1,2,5,3,5 # pg 1,1,4,2,4,5 # fi 1,1,4,4,2,5 # fi 1,1,5,2,2,5 # p 1,2,2,b,5,5 # pe 1,2,2,5,3,5 # pe 1,2,2,5,5,5 # c 1,2,3,b,5,5 # pe 1,2,3,5,3,5 # pe 1,2,5,2,5,5 # c 1,2,5,3,3,5 # pe 1,3,3,3,5,5 # pe 1,0,0,h,6,6 # sh 1,0,0,6,i,6 # sh 1,0,1,h,6,6 # sh 1,0,1,6,i,6 # sh 1,0,2,2,6,6 # pe 1,0,2,6,1,6 # sh 1,0,b,6,c,6 # pe 1,0,6,0,6,6 # sh 1,0,6,1,j,6 # sh 1,0,6,2,g,6 # sh,pe 1,0,6,2,6,6 # c 1,0,6,0,6,6 # sh 1,0,6,1,j,6 # sh 1,0,6,2,i,6 # sh,pe,c 1,0,6,6,1,6 # sh 1,1,1,1,5,6 # i 1,1,1,2,6,6 # fo 1,1,1,6,2,6 # fo 1,1,2,1,6,6 # fo 1,1,2,2,6,6 # p 1,1,2,5,5,6 # fi 1,1,2,6,2,6 # p 1,1,2,6,3,6 # pg 1,1,2,6,6,6 # fi 1,1,5,2,5,6 # fi 1,1,5,5,2,6 # fi 1,1,6,2,2,6 # p 1,1,6,2,6,6 # fi 1,1,6,6,2,6 # fi 1,2,2,b,6,6 # pe 1,2,2,6,3,6 # pe 1,2,2,6,6,6 # c 1,2,3,b,6,6 # pe 1,2,3,6,3,6 # pe 1,2,6,2,6,6 # c 1,2,6,3,3,6 # pe 1,3,3,3,6,6 # pe 1,0,2,7,b,7 # pe 1,0,3,7,b,7 # pe 1,1,1,2,7,7 # fo 1,1,1,7,2,7 # fo 1,1,2,g,7,7 # fo,p 1,1,2,7,b,7 # p,pg 1,1,3,e,3,7 # t7 1,1,3,7,3,7 # t7 1,1,7,2,2,7 # p 1,2,2,b,7,7 # pe 1,2,2,7,3,7 # pe 1,2,2,7,7,7 # c 1,2,3,b,7,7 # pe 1,2,3,7,3,7 # pe 1,2,7,2,7,7 # c 1,2,7,3,3,7 # pe 1,3,3,3,7,7 # pe 2,0,h,0,6,0 # k,k,g 2,0,0,f,7,1 # s,x 2,0,0,7,1,1 # x = extend 2,0,1,0,7,1 # s 2,0,1,1,7,1 # x 2,0,1,7,1,1 # x 2,0,7,1,1,1 # x 2,1,1,1,7,1 # x

2,0,0,2,5,3 # qm = cell q change of state 2,0,0,4,2,3 # pm = cell p change of state 2,0,1,4,2,3 # pm (was missing in codd.r) 2,0,2,0,7,3 # g 2,0,2,5,1,3 # qm 2,0,3,0,n,3 # g 2,2,3,2,d,3 # g (was missing in codd.r) 3,0,0,2,n,0 # r,m 3,0,0,6,2,0 # r 3,0,0,7,2,0 # m 3,0,1,6,2,0 # pm 3,0,1,7,2,0 # m 3,0,2,6,1,0 # qm 3,0,2,7,1,0 # m 3,0,0,0,6,1 # s 3,0,0,2,5,1 # qm 3,0,0,4,2,1 # pm 3,2,3,2,d,2 # g

3,0,1,0,6,4 # e 3,0,1,0,7,7 # j 4,0,0,0,1,0 # e 4,0,0,1,2,0 # fi 4,0,0,2,1,0 # fi 4,0,1,0,2,0 # fi 4,0,1,1,2,0 # fo 4,0,1,2,1,0 # fo 4,0,1,2,2,0 # p 4,0,2,1,1,0 # fo 4,0,2,1,2,0 # p 4,0,2,2,1,0 # p 4,0,3,1,2,0 # pg 4,0,0,0,2,1 # xr 4,0,0,2,2,1 # c 4,0,2,0,2,1 # pe 4,0,2,2,2,1 # pe 4,0,2,2,3,1 # pe 4,0,2,3,2,1 # pe 4,0,2,3,3,1 # pe 4,0,3,2,2,1 # pe 4,0,3,2,3,1 # pe 4,0,3,3,2,1 # pe 4,0,3,3,3,1 # pe 5,0,0,0,1,0 # i 5,0,0,1,2,0 # fi 5,0,0,2,1,0 # fi 5,0,1,0,2,0 # fi 5,0,1,1,2,0 # fo 5,0,1,2,1,0 # fo 5,0,1,2,2,0 # p 5,0,2,1,1,0 # fo 5,0,2,1,2,0 # p 5,0,2,2,1,0 # p 5,0,3,1,2,0 # pg 5,0,0,0,2,1 # xl 5,0,0,2,2,1 # c 5,0,2,p,b,1 # pe 5,0,3,b,c,1 # pe (was missing in codd.r) 6,0,0,0,1,0 # sh 6,0,0,1,1,0 # sh 6,0,0,1,2,0 # fi 6,0,0,2,1,0 # fi 6,0,1,0,1,0 # sh 6,0,1,0,2,0 # fi 6,0,1,1,1,0 # i 6,0,1,1,2,0 # fo 6,0,1,2,1,0 # fo 6,0,1,2,2,0 # p 6,0,2,1,1,0 # fo 6,0,2,1,2,0 # p 6,0,2,2,1,0 # p 6,0,2,2,3,0 # pe 6,0,2,3,2,0 # pe 6,0,2,3,3,0 # pe 6,0,3,1,2,0 # pg 6,0,3,2,2,0 # pe 6,0,3,2,3,0 # pe 6,0,3,3,2,0 # pe 6,0,3,3,3,0 # pe 6,1,2,3,2,0 # s 6,0,0,0,0,1 # sh 6,0,0,0,2,1 # sh 6,0,0,2,2,1 # c 6,0,2,0,2,1 # pe 6,0,2,2,2,1 # sh 7,0,0,0,1,0 # j 7,0,1,1,2,0 # fo 7,0,1,2,1,0 # fo 7,0,1,2,2,0 # p 7,0,2,1,1,0 # fo 7,0,2,1,2,0 # p 7,0,2,2,1,0 # p 7,0,2,2,3,0 # pe 7,0,2,3,2,0 # pe 7,0,2,3,3,0 # pe 7,0,3,1,2,0 # pg 7,0,3,1,3,0 # pe 7,0,3,2,2,0 # pe 7,0,3,2,3,0 # pe 7,0,3,3,2,0 # pe 7,0,3,3,3,0 # pe 7,1,2,2,2,0 # s 7,0,0,0,2,1 # pe 7,0,0,2,2,1 # c 7,0,2,0,2,1 # pe 7,0,2,2,2,1 # x

1. End of Codd's original ruleset

1. TJH added some extra cases for collisions between sheathing-signals:
2. (see top of file)
3. for 2-way collisions:

0,0,6,6,2,2 # sh 0,6,6,0,2,2 # sh (reflected form of above)

1. for 3-way collisions:

1,6,6,6,0,6 # sh