Rule:Codd

@RULE Codd

Codd's cellular automaton.

Codd, E.F., _Cellular_Automata_, Academic Press 1968 (ACM Monograph #3).

Originally distributed with XLife as codd.r.

Several corrections have been made. Stasis transitions have been taken out. 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 (subordibate 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 ruleset

@TREE

num_states=8 num_neighbors=4 num_nodes=253 1 0 1 2 3 4 5 1 7 1 0 1 2 3 0 0 0 0 1 0 1 2 2 1 1 1 1 1 0 1 2 3 4 5 6 7 1 0 0 2 3 4 5 6 7 1 2 6 0 1 4 5 6 7 1 3 3 1 3 4 5 6 7 2 0 1 2 3 4 3 5 6 1 0 1 2 3 4 5 0 7 1 0 1 2 3 0 0 0 7 1 3 1 2 3 4 5 6 7 1 2 6 2 3 4 5 6 7 1 0 1 1 3 4 5 6 7 2 1 8 9 3 4 10 11 12 1 0 1 2 3 1 1 1 1 1 0 4 2 3 4 5 6 7 1 2 1 3 1 4 5 6 7 1 2 6 2 0 4 5 6 7 1 0 1 2 0 4 5 6 7 2 2 9 14 3 15 16 17 18 1 0 2 2 3 4 5 6 7 2 3 3 3 3 3 3 20 3 2 4 4 16 3 3 3 3 3 1 0 5 2 3 4 5 6 7 2 3 10 23 3 3 3 3 3 2 5 11 17 20 3 3 11 3 2 6 12 18 3 3 3 3 3 3 7 13 19 21 22 24 25 26 2 8 8 1 3 4 3 11 12 1 0 1 2 2 0 0 0 7 1 0 1 3 3 4 5 6 7 2 29 1 1 3 3 30 17 18 2 18 3 3 3 3 3 3 3 2 4 4 3 3 3 3 3 3 2 23 3 3 3 3 3 3 3 1 2 6 0 4 4 5 6 7 2 35 11 11 3 3 3 11 3 1 3 2 1 7 4 5 6 7 2 37 12 3 3 3 3 3 3 3 13 28 31 32 33 34 36 38 2 2 9 14 3 16 23 17 18 2 29 1 1 3 30 3 17 18 1 0 1 2 3 1 1 0 0 1 1 7 2 3 4 5 6 7 2 14 1 14 42 15 23 11 43 1 0 1 2 3 4 1 6 7 1 0 6 2 3 4 5 6 7 1 0 7 2 3 4 5 6 7 2 45 1 42 42 15 23 46 47 2 3 3 3 3 3 3 3 3 1 2 1 0 3 4 5 6 7 2 50 3 11 3 3 3 3 3 1 3 1 3 3 4 5 6 7 2 52 3 3 3 3 3 3 3 3 40 41 44 48 49 49 51 53 1 1 1 2 3 4 5 6 7 2 45 55 42 42 15 23 46 47 1 0 1 2 3 4 5 6 0 1 1 6 2 3 4 5 6 7 2 3 57 42 42 15 23 58 47 2 30 3 3 3 3 3 3 3 3 21 32 56 59 49 49 60 60 2 4 4 15 3 3 3 3 3 3 62 33 49 49 49 49 49 49 2 3 10 16 3 3 3 3 3 3 64 34 49 49 49 49 49 49 2 46 46 11 3 3 3 3 3 3 25 36 51 60 49 49 66 49 3 26 38 53 60 49 49 49 49 4 27 39 54 61 63 65 67 68 2 1 8 29 18 4 23 35 37 2 9 1 1 3 3 3 11 3 2 4 4 30 3 3 3 3 3 2 10 3 3 3 3 3 3 3 2 11 11 17 3 3 3 11 3 2 12 12 18 3 3 3 3 3 3 70 28 71 49 72 73 74 75 1 2 1 2 3 4 5 6 7 2 8 3 3 3 4 46 77 12 1 1 4 2 3 4 5 6 7 1 1 5 2 3 4 5 6 7 2 1 3 3 3 79 80 58 43 2 4 4 79 3 3 3 3 3 2 3 46 80 3 3 3 3 3 2 11 77 58 3 3 3 77 3 2 12 12 47 3 3 3 3 3 3 28 78 81 49 82 83 84 85 2 1 3 3 3 79 80 58 47 1 7 1 2 3 4 5 6 0 1 6 1 3 2 4 5 0 7 2 1 55 88 89 79 80 58 43 2 55 3 3 3 55 55 55 55 2 3 79 79 55 80 3 3 3 2 3 80 80 55 3 58 3 3 2 3 58 58 3 3 3 58 3 2 3 43 43 3 3 3 3 79 3 71 87 90 91 92 93 94 95 2 1 3 3 3 15 80 46 43 2 57 3 3 3 47 47 47 43 2 3 3 55 3 3 3 3 3 3 49 49 97 98 49 99 49 49 2 3 79 79 3 80 3 3 3 2 3 3 80 3 3 3 3 3 3 33 82 101 99 102 49 49 49 2 10 3 30 3 3 3 3 3 2 3 3 58 3 3 3 3 3 3 104 83 93 49 49 105 49 49 2 46 3 58 3 3 3 3 3 3 74 84 94 49 49 49 107 49 2 12 12 43 3 3 3 3 3 2 3 3 79 3 3 3 3 3 3 75 109 95 49 49 49 49 110 4 76 86 96 100 103 106 108 111 2 2 29 14 45 3 3 50 52 2 9 1 1 55 3 3 3 3 2 14 1 14 42 3 3 11 3 2 3 3 42 42 3 3 3 3 2 15 3 15 15 3 3 3 3 2 16 30 23 23 3 3 3 3 2 17 17 11 46 3 3 3 3 2 18 18 43 47 3 3 3 3 3 113 114 115 116 117 118 119 120 2 9 1 1 1 3 3 3 3 2 1 3 55 3 79 80 58 43 2 1 3 88 3 79 80 58 43 2 3 3 89 3 3 55 3 3 2 3 79 79 15 80 3 3 3 2 3 80 80 80 3 58 3 3 2 11 58 58 46 3 3 58 3 2 3 43 43 43 3 3 3 79 3 122 123 124 125 126 127 128 129 2 14 88 3 3 15 23 11 47 2 42 3 3 3 3 23 46 47 2 3 79 15 15 15 3 3 3 2 3 80 23 23 3 23 3 3 2 11 58 11 46 3 3 11 3 2 3 43 47 47 3 3 3 47 3 115 124 131 132 133 134 135 136 2 3 3 89 3 55 55 3 3 2 42 3 3 3 15 23 46 47 1 0 4 3 2 4 5 6 7 2 3 55 140 15 3 3 3 3 1 0 5 3 2 4 5 6 7 2 3 3 142 23 3 3 3 3 1 0 6 3 2 4 5 6 7 2 3 3 144 46 3 3 3 3 1 0 7 3 2 4 5 6 7 2 3 3 146 47 3 3 3 3 3 116 138 139 139 141 143 145 147 2 16 30 15 15 3 3 3 3 2 3 79 15 3 15 3 3 3 2 3 3 140 15 3 3 3 3 2 3 80 3 3 3 3 3 3 3 149 92 150 151 152 49 49 49 2 23 3 23 23 3 3 3 3 2 3 55 142 23 3 3 3 3 2 3 58 23 3 3 3 3 3 3 154 93 134 155 49 156 49 49 2 11 58 58 55 3 3 58 3 2 11 58 46 3 3 3 3 3 3 119 158 135 145 49 49 159 49 2 3 47 43 55 3 3 3 79 2 3 79 47 3 3 3 3 3 3 120 161 136 147 49 49 49 162 4 121 130 137 148 153 157 160 163 2 3 18 45 3 3 3 30 30 2 3 3 1 57 3 3 3 3 2 3 3 15 15 3 3 3 3 2 3 3 23 23 3 3 3 3 2 20 3 46 58 3 3 3 3 2 3 3 47 47 3 3 3 3 3 165 166 116 116 167 168 169 170 2 3 3 55 57 3 3 3 3 2 3 3 3 3 55 3 3 3 2 3 3 55 47 3 3 3 3 2 3 3 55 43 3 3 3 3 3 172 49 173 49 174 174 174 175 2 3 3 3 3 3 55 3 3 2 42 89 3 3 140 142 144 146 2 3 3 3 15 3 3 3 3 2 3 55 23 23 3 3 3 3 2 3 3 46 46 3 3 3 3 3 116 177 178 139 179 180 181 170 3 116 49 139 139 167 168 181 170 2 3 3 15 47 3 3 3 3 2 3 55 15 15 3 3 3 3 3 167 184 185 167 49 49 49 49 2 3 3 80 47 3 3 3 3 3 168 187 180 168 49 49 49 49 2 3 3 46 47 3 3 3 3 3 169 189 181 181 49 49 49 49 2 3 3 43 43 3 3 3 3 3 170 191 170 170 49 49 49 49 4 171 176 182 183 186 188 190 192 2 16 3 3 3 3 3 3 3 3 33 33 194 49 49 49 49 49 2 30 79 79 3 80 3 3 3 3 33 82 196 99 102 49 49 49 2 15 3 3 3 3 3 3 3 2 15 79 15 140 3 3 3 3 2 15 15 15 15 3 3 3 3 2 3 80 15 3 3 3 3 3 3 198 92 199 200 201 49 49 49 2 15 55 3 15 3 3 3 3 2 15 47 15 15 3 3 3 3 3 49 49 203 204 49 49 49 49 3 49 102 201 49 49 49 49 49 3 49 49 49 49 49 49 49 49 4 195 197 202 205 206 207 207 207 2 3 23 3 3 3 3 3 3 3 209 73 34 49 49 49 49 49 3 73 83 93 99 49 105 49 49 2 30 80 80 3 3 58 3 3 2 23 80 23 142 3 23 3 3 2 23 80 23 23 3 3 3 3 3 194 212 213 214 49 156 49 49 2 23 55 23 23 3 3 3 3 2 23 47 23 23 3 3 3 3 3 49 99 216 217 49 49 49 49 3 49 105 156 49 49 49 49 49 4 210 211 215 218 207 219 207 207 2 5 35 50 30 3 3 46 3 2 11 11 3 3 3 3 46 3 2 17 11 11 3 3 3 11 3 2 20 3 3 3 3 3 3 3 2 11 11 3 3 3 3 3 3 3 221 222 223 224 49 49 225 49 2 11 77 58 3 3 3 3 3 2 17 58 58 3 3 3 58 3 3 222 227 228 49 49 49 227 49 2 11 58 11 144 3 3 46 3 2 46 46 46 46 3 3 3 3 2 3 58 11 3 3 3 3 3 3 223 228 230 231 49 49 232 49 2 46 55 46 46 3 3 3 3 2 58 47 46 46 3 3 3 3 3 224 49 234 235 49 49 49 49 3 225 227 232 49 49 49 49 49 4 226 229 233 236 207 207 237 207 2 6 37 52 30 3 3 3 3 2 12 12 3 3 3 3 3 3 3 239 240 32 49 49 49 49 49 2 18 47 43 3 3 3 3 79 3 240 109 242 49 49 49 49 110 2 18 43 43 3 3 3 3 79 2 43 43 47 146 3 3 3 47 2 47 43 47 47 3 3 3 3 3 32 244 245 246 49 49 49 162 2 47 55 47 47 3 3 3 3 3 49 49 248 246 49 49 49 49 3 49 110 162 49 49 49 49 49 4 241 243 247 249 207 207 207 250 5 69 112 164 193 208 220 238 251

@COLORS

1. colors from
2. http://necsi.org/postdocs/sayama/sdsr/java/loops.java
3. Color.black,Color.blue,Color.red,Color.green,
4. Color.yellow,Color.magenta,Color.white,Color.cyan,Color.orange

1 0 0 255 2 255 0 0 3 0 255 0 4 255 255 0 5 255 0 255 6 255 255 255 7 0 255 255