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Supplement to Cellular Automata

The 256 Rules

As we have seen, in one-dimensional cellular automata with range = 1 and only two states there are 8 possible neighbors to be mapped to {1, 0}, giving a total of 256 possible rules. For illustration purposes, we collected the 200 time-steps evolution of all the 256 elementary rules (black = 1, white = 0), ordered by the Wolfram's code: for any CA, at t0 only the cell in the middle is black. To be sure, even if a rule is a Class 4 this does not guarantee that it will produce complex behavior starting from any possible configuration—as rule 54 clearly proves: compare its behavior below with the picture showed in the main entry.

Rule0 Rule1 Rule2 Rule3 Rule4 Rule5 Rule6 Rule7
Rule 0 Rule 1 Rule 2 Rule 3 Rule 4 Rule 5 Rule 6 Rule 7
Rule8 Rule9 Rule10 Rule11 Rule12 Rule13 Rule14 Rule15
Rule 8 Rule 9 Rule 10 Rule 11 Rule 12 Rule 13 Rule 14 Rule 15
Rule16 Rule17 Rule18 Rule19 Rule20 Rule21 Rule22 Rule23
Rule 16 Rule 17 Rule 18 Rule 19 Rule 20 Rule 21 Rule 22 Rule 23
Rule24 Rule25 Rule26 Rule27 Rule28 Rule29 Rule30 Rule31
Rule 24 Rule 25 Rule 26 Rule 27 Rule 28 Rule 29 Rule 30 Rule 31
Rule32 Rule33 Rule34 Rule35 Rule36 Rule37 Rule38 Rule39
Rule 32 Rule 33 Rule 34 Rule 35 Rule 36 Rule 37 Rule 38 Rule 39
Rule40 Rule41 Rule42 Rule43 Rule44 Rule45 Rule46 Rule47
Rule 40 Rule 41 Rule 42 Rule 43 Rule 44 Rule 45 Rule 46 Rule 47
Rule48 Rule49 Rule50 Rule51 Rule52 Rule53 Rule54 Rule55
Rule 48 Rule 49 Rule 50 Rule 51 Rule 52 Rule 53 Rule 54 Rule 55
Rule56 Rule57 Rule58 Rule59 Rule60 Rule61 Rule62 Rule63
Rule 56 Rule 57 Rule 58 Rule 59 Rule 60 Rule 61 Rule 62 Rule 63
Rule64 Rule65 Rule66 Rule67 Rule68 Rule69 Rule70 Rule71
Rule 64 Rule 65 Rule 66 Rule 67 Rule 68 Rule 69 Rule 70 Rule 71
Rule72 Rule73 Rule74 Rule75 Rule76 Rule77 Rule78 Rule79
Rule 72 Rule 73 Rule 74 Rule 75 Rule 76 Rule 77 Rule 78 Rule 79
Rule80 Rule81 Rule82 Rule83 Rule84 Rule85 Rule86 Rule87
Rule 80 Rule 81 Rule 82 Rule 83 Rule 84 Rule 85 Rule 86 Rule 87
Rule88 Rule89 Rule90 Rule91 Rule92 Rule93 Rule94 Rule95
Rule 88 Rule 89 Rule 90 Rule 91 Rule 92 Rule 93 Rule 94 Rule 95
Rule96 Rule97 Rule98 Rule99 Rule100 Rule101 Rule102 Rule103
Rule 96 Rule 97 Rule 98 Rule 99 Rule 100 Rule 101 Rule 102 Rule 103
Rule104 Rule105 Rule106 Rule107 Rule108 Rule109 Rule110 Rule111
Rule 104 Rule 105 Rule 106 Rule 107 Rule 108 Rule 109 Rule 110 Rule 111
Rule112 Rule113 Rule114 Rule115 Rule116 Rule117 Rule118 Rule119
Rule 112 Rule 113 Rule 114 Rule 115 Rule 116 Rule 117 Rule 118 Rule 119
Rule120 Rule121 Rule122 Rule123 Rule124 Rule125 Rule126 Rule127
Rule 120 Rule 121 Rule 122 Rule 123 Rule 124 Rule 125 Rule 126 Rule 127
Rule128 Rule129 Rule130 Rule131 Rule132 Rule133 Rule134 Rule135
Rule 128 Rule 129 Rule 130 Rule 131 Rule 132 Rule 133 Rule 134 Rule 135
Rule136 Rule137 Rule138 Rule139 Rule140 Rule141 Rule142 Rule143
Rule 136 Rule 137 Rule 138 Rule 139 Rule 140 Rule 141 Rule 142 Rule 143
Rule144 Rule145 Rule146 Rule147 Rule148 Rule149 Rule150 Rule151
Rule 144 Rule 145 Rule 146 Rule 147 Rule 148 Rule 149 Rule 150 Rule 151
Rule152 Rule153 Rule154 Rule155 Rule156 Rule157 Rule158 Rule159
Rule 152 Rule 153 Rule 154 Rule 155 Rule 156 Rule 157 Rule 158 Rule 159
Rule160 Rule161 Rule162 Rule163 Rule164 Rule165 Rule166 Rule167
Rule 160 Rule 161 Rule 162 Rule 163 Rule 164 Rule 165 Rule 166 Rule 167
Rule168 Rule169 Rule170 Rule171 Rule172 Rule173 Rule174 Rule175
Rule 168 Rule 169 Rule 170 Rule 171 Rule 172 Rule 173 Rule 174 Rule 175
Rule176 Rule177 Rule178 Rule179 Rule180 Rule181 Rule182 Rule183
Rule 176 Rule 177 Rule 178 Rule 179 Rule 180 Rule 181 Rule 182 Rule 183
Rule184 Rule185 Rule186 Rule187 Rule188 Rule189 Rule190 Rule191
Rule 184 Rule 185 Rule 186 Rule 187 Rule 188 Rule 189 Rule 190 Rule 191
Rule192 Rule193 Rule194 Rule195 Rule196 Rule197 Rule198 Rule199
Rule 192 Rule 193 Rule 194 Rule 195 Rule 196 Rule 197 Rule 198 Rule 199
Rule200 Rule201 Rule202 Rule203 Rule204 Rule205 Rule206 Rule207
Rule 200 Rule 201 Rule 202 Rule 203 Rule 204 Rule 205 Rule 206 Rule 207
Rule208 Rule209 Rule210 Rule211 Rule212 Rule213 Rule214 Rule215
Rule 208 Rule 209 Rule 210 Rule 211 Rule 212 Rule 213 Rule 214 Rule 215
Rule216 Rule217 Rule218 Rule219 Rule220 Rule221 Rule222 Rule223
Rule 216 Rule 217 Rule 218 Rule 219 Rule 220 Rule 221 Rule 222 Rule 223
Rule224 Rule225 Rule226 Rule227 Rule228 Rule229 Rule230 Rule231
Rule 224 Rule 225 Rule 226 Rule 227 Rule 228 Rule 229 Rule 230 Rule 231
Rule232 Rule233 Rule234 Rule235 Rule236 Rule237 Rule238 Rule239
Rule 232 Rule 233 Rule 234 Rule 235 Rule 236 Rule 237 Rule 238 Rule 239
Rule240 Rule241 Rule242 Rule243 Rule244 Rule245 Rule246 Rule247
Rule 240 Rule 241 Rule 242 Rule 243 Rule 244 Rule 245 Rule 246 Rule 247
Rule248 Rule249 Rule250 Rule251 Rule252 Rule253 Rule254 Rule255
Rule 248 Rule 249 Rule 250 Rule 251 Rule 252 Rule 253 Rule 254 Rule 255

Copyright © 2012 by
Francesco Berto <F.Berto@uva.nl>
Jacopo Tagliabue <tagliabue.jacopo@gmail.com>

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