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 \(t_0\) 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.
Rule 0
Rule 1
Rule 2
Rule 3
Rule 4
Rule 5
Rule 6
Rule 7
Rule 8
Rule 9
Rule 10
Rule 11
Rule 12
Rule 13
Rule 14
Rule 15
Rule 16
Rule 17
Rule 18
Rule 19
Rule 20
Rule 21
Rule 22
Rule 23
Rule 24
Rule 25
Rule 26
Rule 27
Rule 28
Rule 29
Rule 30
Rule 31
Rule 32
Rule 33
Rule 34
Rule 35
Rule 36
Rule 37
Rule 38
Rule 39
Rule 40
Rule 41
Rule 42
Rule 43
Rule 44
Rule 45
Rule 46
Rule 47
Rule 48
Rule 49
Rule 50
Rule 51
Rule 52
Rule 53
Rule 54
Rule 55
Rule 56
Rule 57
Rule 58
Rule 59
Rule 60
Rule 61
Rule 62
Rule 63
Rule 64
Rule 65
Rule 66
Rule 67
Rule 68
Rule 69
Rule 70
Rule 71
Rule 72
Rule 73
Rule 74
Rule 75
Rule 76
Rule 77
Rule 78
Rule 79
Rule 80
Rule 81
Rule 82
Rule 83
Rule 84
Rule 85
Rule 86
Rule 87
Rule 88
Rule 89
Rule 90
Rule 91
Rule 92
Rule 93
Rule 94
Rule 95
Rule 96
Rule 97
Rule 98
Rule 99
Rule 100
Rule 101
Rule 102
Rule 103
Rule 104
Rule 105
Rule 106
Rule 107
Rule 108
Rule 109
Rule 110
Rule 111
Rule 112
Rule 113
Rule 114
Rule 115
Rule 116
Rule 117
Rule 118
Rule 119
Rule 120
Rule 121
Rule 122
Rule 123
Rule 124
Rule 125
Rule 126
Rule 127
Rule 128
Rule 129
Rule 130
Rule 131
Rule 132
Rule 133
Rule 134
Rule 135
Rule 136
Rule 137
Rule 138
Rule 139
Rule 140
Rule 141
Rule 142
Rule 143
Rule 144
Rule 145
Rule 146
Rule 147
Rule 148
Rule 149
Rule 150
Rule 151
Rule 152
Rule 153
Rule 154
Rule 155
Rule 156
Rule 157
Rule 158
Rule 159
Rule 160
Rule 161
Rule 162
Rule 163
Rule 164
Rule 165
Rule 166
Rule 167
Rule 168
Rule 169
Rule 170
Rule 171
Rule 172
Rule 173
Rule 174
Rule 175
Rule 176
Rule 177
Rule 178
Rule 179
Rule 180
Rule 181
Rule 182
Rule 183
Rule 184
Rule 185
Rule 186
Rule 187
Rule 188
Rule 189
Rule 190
Rule 191
Rule 192
Rule 193
Rule 194
Rule 195
Rule 196
Rule 197
Rule 198
Rule 199
Rule 200
Rule 201
Rule 202
Rule 203
Rule 204
Rule 205
Rule 206
Rule 207
Rule 208
Rule 209
Rule 210
Rule 211
Rule 212
Rule 213
Rule 214
Rule 215
Rule 216
Rule 217
Rule 218
Rule 219
Rule 220
Rule 221
Rule 222
Rule 223
Rule 224
Rule 225
Rule 226
Rule 227
Rule 228
Rule 229
Rule 230
Rule 231
Rule 232
Rule 233
Rule 234
Rule 235
Rule 236
Rule 237
Rule 238
Rule 239
Rule 240
Rule 241
Rule 242
Rule 243
Rule 244
Rule 245
Rule 246
Rule 247
Rule 248
Rule 249
Rule 250
Rule 251
Rule 252
Rule 253
Rule 254
Rule 255
