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 0

Rule 1

Rule 1

Rule 2

Rule 2

Rule 3

Rule 3

Rule 4

Rule 4

Rule 5

Rule 5

Rule 6

Rule 6

Rule 7

Rule 7

Rule 8

Rule 8

Rule 9

Rule 9

Rule 10

Rule 10

Rule 11

Rule 11

Rule 12

Rule 12

Rule 13

Rule 13

Rule 14

Rule 14

Rule 15

Rule 15

Rule 16

Rule 16

Rule 17

Rule 17

Rule 18

Rule 18

Rule 19

Rule 19

Rule 20

Rule 20

Rule 21

Rule 21

Rule 22

Rule 22

Rule 23

Rule 23

Rule 24

Rule 24

Rule 25

Rule 25

Rule 26

Rule 26

Rule 27

Rule 27

Rule 28

Rule 28

Rule 29

Rule 29

Rule 30

Rule 30

Rule 31

Rule 31

Rule 32

Rule 32

Rule 33

Rule 33

Rule 34

Rule 34

Rule 35

Rule 35

Rule 36

Rule 36

Rule 37

Rule 37

Rule 38

Rule 38

Rule 39

Rule 39

Rule 40

Rule 40

Rule 41

Rule 41

Rule 42

Rule 42

Rule 43

Rule 43

Rule 44

Rule 44

Rule 45

Rule 45

Rule 46

Rule 46

Rule 47

Rule 47

Rule 48

Rule 48

Rule 49

Rule 49

Rule 50

Rule 50

Rule 51

Rule 51

Rule 52

Rule 52

Rule 53

Rule 53

Rule 54

Rule 54

Rule 55

Rule 55

Rule 56

Rule 56

Rule 57

Rule 57

Rule 58

Rule 58

Rule 59

Rule 59

Rule 60

Rule 60

Rule 61

Rule 61

Rule 62

Rule 62

Rule 63

Rule 63

Rule 64

Rule 64

Rule 65

Rule 65

Rule 66

Rule 66

Rule 67

Rule 67

Rule 68

Rule 68

Rule 69

Rule 69

Rule 70

Rule 70

Rule 71

Rule 71

Rule 72

Rule 72

Rule 73

Rule 73

Rule 74

Rule 74

Rule 75

Rule 75

Rule 76

Rule 76

Rule 77

Rule 77

Rule 78

Rule 78

Rule 79

Rule 79

Rule 80

Rule 80

Rule 81

Rule 81

Rule 82

Rule 82

Rule 83

Rule 83

Rule 84

Rule 84

Rule 85

Rule 85

Rule 86

Rule 86

Rule 87

Rule 87

Rule 88

Rule 88

Rule 89

Rule 89

Rule 90

Rule 90

Rule 91

Rule 91

Rule 92

Rule 92

Rule 93

Rule 93

Rule 94

Rule 94

Rule 95

Rule 95

Rule 96

Rule 96

Rule 97

Rule 97

Rule 98

Rule 98

Rule 99

Rule 99

Rule 100

Rule 100

Rule 101

Rule 101

Rule 102

Rule 102

Rule 103

Rule 103

Rule 104

Rule 104

Rule 105

Rule 105

Rule 106

Rule 106

Rule 107

Rule 107

Rule 108

Rule 108

Rule 109

Rule 109

Rule 110

Rule 110

Rule 111

Rule 111

Rule 112

Rule 112

Rule 113

Rule 113

Rule 114

Rule 114

Rule 115

Rule 115

Rule 116

Rule 116

Rule 117

Rule 117

Rule 118

Rule 118

Rule 119

Rule 119

Rule 120

Rule 120

Rule 121

Rule 121

Rule 122

Rule 122

Rule 123

Rule 123

Rule 124

Rule 124

Rule 125

Rule 125

Rule 126

Rule 126

Rule 127

Rule 127

Rule 128

Rule 128

Rule 129

Rule 129

Rule 130

Rule 130

Rule 131

Rule 131

Rule 132

Rule 132

Rule 133

Rule 133

Rule 134

Rule 134

Rule 135

Rule 135

Rule 136

Rule 136

Rule 137

Rule 137

Rule 138

Rule 138

Rule 139

Rule 139

Rule 140

Rule 140

Rule 141

Rule 141

Rule 142

Rule 142

Rule 143

Rule 143

Rule 144

Rule 144

Rule 145

Rule 145

Rule 146

Rule 146

Rule 147

Rule 147

Rule 148

Rule 148

Rule 149

Rule 149

Rule 150

Rule 150

Rule 151

Rule 151

Rule 152

Rule 152

Rule 153

Rule 153

Rule 154

Rule 154

Rule 155

Rule 155

Rule 156

Rule 156

Rule 157

Rule 157

Rule 158

Rule 158

Rule 159

Rule 159

Rule 160

Rule 160

Rule 161

Rule 161

Rule 162

Rule 162

Rule 163

Rule 163

Rule 164

Rule 164

Rule 165

Rule 165

Rule 166

Rule 166

Rule 167

Rule 167

Rule 168

Rule 168

Rule 169

Rule 169

Rule 170

Rule 170

Rule 171

Rule 171

Rule 172

Rule 172

Rule 173

Rule 173

Rule 174

Rule 174

Rule 175

Rule 175

Rule 176

Rule 176

Rule 177

Rule 177

Rule 178

Rule 178

Rule 179

Rule 179

Rule 180

Rule 180

Rule 181

Rule 181

Rule 182

Rule 182

Rule 183

Rule 183

Rule 184

Rule 184

Rule 185

Rule 185

Rule 186

Rule 186

Rule 187

Rule 187

Rule 188

Rule 188

Rule 189

Rule 189

Rule 190

Rule 190

Rule 191

Rule 191

Rule 192

Rule 192

Rule 193

Rule 193

Rule 194

Rule 194

Rule 195

Rule 195

Rule 196

Rule 196

Rule 197

Rule 197

Rule 198

Rule 198

Rule 199

Rule 199

Rule 200

Rule 200

Rule 201

Rule 201

Rule 202

Rule 202

Rule 203

Rule 203

Rule 204

Rule 204

Rule 205

Rule 205

Rule 206

Rule 206

Rule 207

Rule 207

Rule 208

Rule 208

Rule 209

Rule 209

Rule 210

Rule 210

Rule 211

Rule 211

Rule 212

Rule 212

Rule 213

Rule 213

Rule 214

Rule 214

Rule 215

Rule 215

Rule 216

Rule 216

Rule 217

Rule 217

Rule 218

Rule 218

Rule 219

Rule 219

Rule 220

Rule 220

Rule 221

Rule 221

Rule 222

Rule 222

Rule 223

Rule 223

Rule 224

Rule 224

Rule 225

Rule 225

Rule 226

Rule 226

Rule 227

Rule 227

Rule 228

Rule 228

Rule 229

Rule 229

Rule 230

Rule 230

Rule 231

Rule 231

Rule 232

Rule 232

Rule 233

Rule 233

Rule 234

Rule 234

Rule 235

Rule 235

Rule 236

Rule 236

Rule 237

Rule 237

Rule 238

Rule 238

Rule 239

Rule 239

Rule 240

Rule 240

Rule 241

Rule 241

Rule 242

Rule 242

Rule 243

Rule 243

Rule 244

Rule 244

Rule 245

Rule 245

Rule 246

Rule 246

Rule 247

Rule 247

Rule 248

Rule 248

Rule 249

Rule 249

Rule 250

Rule 250

Rule 251

Rule 251

Rule 252

Rule 252

Rule 253

Rule 253

Rule 254

Rule 254

Rule 255

Rule 255

Copyright © 2017 by
Francesco Berto <F.Berto@uva.nl>
Jacopo Tagliabue <tagliabue.jacopo@gmail.com>

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