The Wolfram Atlas of Simple Programs The Wolfram Atlas of Simple Programs

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Cellular Automata > One-dimensional > 

Elementary Cellular Automata

Rule properties:Rule descriptions:Algebraic form

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

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