Les automates cellulaires élémentaires

Jean-Baptiste
Rouquier

Work

Présentation

Programmation

Prépas

LaTeX


Accès direct à l'une des 256 règles

La règle choisie sera affichée ainsi.

Autres dynamiques

Notes

La table

space time diagram
00
255255
0000000000000000
1111111111111111
EFGHEFGH
ABCDABCD
linéaire affine « zéro » 
space time diagram
11
127127
0000000100000001
0111111101111111
AEFGHAEFGH
ABCDHABCDH
 
space time diagram
216
191247
0000001000010000
1011111111110111
BEFGHCEFGH
ABCDGABCDF
 
space time diagram
317
63119
0000001100010001
0011111101110111
ABEFGHACEFGH
ABCDGHABCDFH
 
space time diagram
44
223223
0000010000000100
1101111111011111
FGHFGH
ABCABC
 
space time diagram
55
9595
0000010100000101
0101111101011111
AFGHAFGH
ABCHABCH
 
space time diagram
620
159215
0000011000010100
1001111111010111
BFGHCFGH
ABCGABCF
 
space time diagram
721
3187
0000011100010101
0001111101010111
ABFGHACFGH
ABCGHABCFH
 
space time diagram
864
239253
0000100001000000
1110111111111101
EGHEFH
ABDACD
 
space time diagram
965
111125
0000100101000001
0110111101111101
AEGHAEFH
ABDHACDH
 
space time diagram
1080
175245
0000101001010000
1010111111110101
BEGHCEFH
ABDGACDF
 
space time diagram
1181
47117
0000101101010001
0010111101110101
ABEGHACEFH
ABDGHACDFH
 
space time diagram
1268
207221
0000110001000100
1100111111011101
GHFH
ABAC
 
space time diagram
1369
7993
0000110101000101
0100111101011101
AGHAFH
ABHACH
 
space time diagram
1484
143213
0000111001010100
1000111111010101
BGHCFH
ABGACF
 
space time diagram
1585
1585
0000111101010101
0000111101010101
ABGHACFH
ABGHACFH
affine « shift+non » 
space time diagram
1818
183183
0001001000010010
1011011110110111
BCEFGHBCEFGH
ABCDFGABCDFG
 
space time diagram
1919
5555
0001001100010011
0011011100110111
ABCEFGHABCEFGH
ABCDFGHABCDFGH
 
space time diagram
2222
151151
0001011000010110
1001011110010111
BCFGHBCFGH
ABCFGABCFG
 
space time diagram
2323
2323
0001011100010111
0001011100010111
ABCFGHABCFGH
ABCFGHABCFGH
« minorité » 
space time diagram
2466
231189
0001100001000010
1110011110111101
CEGHBEFH
ABDFACDG
 
space time diagram
2567
10361
0001100101000011
0110011100111101
ACEGHABEFH
ABDFHACDGH
 
space time diagram
2682
167181
0001101001010010
1010011110110101
BCEGHBCEFH
ABDFGACDFG
 
space time diagram
2783
3953
0001101101010011
0010011100110101
ABCEGHABCEFH
ABDFGHACDFGH
 
space time diagram
2870
199157
0001110001000110
1100011110011101
CGHBFH
ABFACG
 
space time diagram
2971
7129
0001110101000111
0100011100011101
ACGHABFH
ABFHACGH
 
space time diagram
3086
135149
0001111001010110
1000011110010101
BCGHBCFH
ABFGACFG
 
space time diagram
3232
251251
0010000000100000
1111101111111011
DEFGHDEFGH
ABCDEABCDE
 
space time diagram
3333
123123
0010000100100001
0111101101111011
ADEFGHADEFGH
ABCDEHABCDEH
 
space time diagram
3448
187243
0010001000110000
1011101111110011
BDEFGHCDEFGH
ABCDEGABCDEF
 
space time diagram
3549
59115
0010001100110001
0011101101110011
ABDEFGHACDEFGH
ABCDEGHABCDEFH
 
space time diagram
3636
219219
0010010000100100
1101101111011011
DFGHDFGH
ABCEABCE
 
space time diagram
3737
9191
0010010100100101
0101101101011011
ADFGHADFGH
ABCEHABCEH
 
space time diagram
3852
155211
0010011000110100
1001101111010011
BDFGHCDFGH
ABCEGABCEF
 
space time diagram
4096
235249
0010100001100000
1110101111111001
DEGHDEFH
ABDEACDE
 
space time diagram
4197
107121
0010100101100001
0110101101111001
ADEGHADEFH
ABDEHACDEH
 
space time diagram
42112
171241
0010101001110000
1010101111110001
BDEGHCDEFH
ABDEGACDEF
 
space time diagram
43113
43113
0010101101110001
0010101101110001
ABDEGHACDEFH
ABDEGHACDEFH
 
space time diagram
44100
203217
0010110001100100
1100101111011001
DGHDFH
ABEACE
 
space time diagram
45101
7589
0010110101100101
0100101101011001
ADGHADFH
ABEHACEH
 
space time diagram
46116
139209
0010111001110100
1000101111010001
BDGHCDFH
ABEGACEF
 
space time diagram
5050
179179
0011001000110010
1011001110110011
BCDEFGHBCDEFGH
ABCDEFGABCDEFG
 
space time diagram
5151
5151
0011001100110011
0011001100110011
ABCDEFGHABCDEFGH
ABCDEFGHABCDEFGH
affine « non » 
space time diagram
5454
147147
0011011000110110
1001001110010011
BCDFGHBCDFGH
ABCEFGABCEFG
« universel ? » 
space time diagram
5698
227185
0011100001100010
1110001110111001
CDEGHBDEFH
ABDEFACDEG
 
space time diagram
5799
9957
0011100101100011
0110001100111001
ACDEGHABDEFH
ABDEFHACDEGH
 
space time diagram
58114
163177
0011101001110010
1010001110110001
BCDEGHBCDEFH
ABDEFGACDEFG
 
space time diagram
60102
195153
0011110001100110
1100001110011001
CDGHBDFH
ABEFACEG
linéaire affine « xor(xn-1,xn) » 
space time diagram
62118
131145
0011111001110110
1000001110010001
BCDGHBCDFH
ABEFGACEFG
 
space time diagram
7272
237237
0100100001001000
1110110111101101
EHEH
ADAD
 
space time diagram
7373
109109
0100100101001001
0110110101101101
AEHAEH
ADHADH
 
space time diagram
7488
173229
0100101001011000
1010110111100101
BEHCEH
ADGADF
 
space time diagram
7676
205205
0100110001001100
1100110111001101
HH
AA
 
space time diagram
7777
7777
0100110101001101
0100110101001101
AHAH
AHAH
 
space time diagram
7892
141197
0100111001011100
1000110111000101
BHCH
AGAF
 
space time diagram
9090
165165
0101101001011010
1010010110100101
BCEHBCEH
ADFGADFG
linéaire affine « xor(xn-1,xn+1) » 
space time diagram
9494
133133
0101111001011110
1000010110000101
BCHBCH
AFGAFG
 
space time diagram
104104
233233
0110100001101000
1110100111101001
DEHDEH
ADEADE
 
space time diagram
105105
105105
0110100101101001
0110100101101001
ADEHADEH
ADEHADEH
affine « non xor » 
space time diagram
106120
169225
0110101001111000
1010100111100001
BDEHCDEH
ADEGADEF
 
space time diagram
108108
201201
0110110001101100
1100100111001001
DHDH
AEAE
 
space time diagram
110124
137193
0110111001111100
1000100111000001
BDHCDH
AEGAEF
« universel » 
space time diagram
122122
161161
0111101001111010
1010000110100001
BCDEHBCDEH
ADEFGADEFG
 
space time diagram
126126
129129
0111111001111110
1000000110000001
BCDHBCDH
AEFGAEFG
 
space time diagram
128128
254254
1000000010000000
1111111011111110
EFGEFG
BCDBCD
captif « et » 
space time diagram
130144
190246
1000001010010000
1011111011110110
BEFGCEFG
BCDGBCDF
captif  
space time diagram
132132
222222
1000010010000100
1101111011011110
FGFG
BCBC
captif  
space time diagram
134148
158214
1000011010010100
1001111011010110
BFGCFG
BCGBCF
captif  
space time diagram
136192
238252
1000100011000000
1110111011111100
EGEF
BDCD
captif  
space time diagram
138208
174244
1000101011010000
1010111011110100
BEGCEF
BDGCDF
captif  
space time diagram
140196
206220
1000110011000100
1100111011011100
GF
BC
captif  
space time diagram
142212
142212
1000111011010100
1000111011010100
BGCF
BGCF
captif  
space time diagram
146146
182182
1001001010010010
1011011010110110
BCEFGBCEFG
BCDFGBCDFG
captif  
space time diagram
150150
150150
1001011010010110
1001011010010110
BCFGBCFG
BCFGBCFG
linéaire affine captif « xor » 
space time diagram
152194
230188
1001100011000010
1110011010111100
CEGBEF
BDFCDG
captif  
space time diagram
154210
166180
1001101011010010
1010011010110100
BCEGBCEF
BDFGCDFG
captif  
space time diagram
156198
198156
1001110011000110
1100011010011100
CGBF
BFCG
captif  
space time diagram
160160
250250
1010000010100000
1111101011111010
DEFGDEFG
BCDEBCDE
captif  
space time diagram
162176
186242
1010001010110000
1011101011110010
BDEFGCDEFG
BCDEGBCDEF
captif  
space time diagram
164164
218218
1010010010100100
1101101011011010
DFGDFG
BCEBCE
captif  
space time diagram
168224
234248
1010100011100000
1110101011111000
DEGDEF
BDECDE
captif  
space time diagram
170240
170240
1010101011110000
1010101011110000
BDEGCDEF
BDEGCDEF
linéaire affine captif « shift » 
space time diagram
172228
202216
1010110011100100
1100101011011000
DGDF
BECE
captif  
space time diagram
178178
178178
1011001010110010
1011001010110010
BCDEFGBCDEFG
BCDEFGBCDEFG
captif  
space time diagram
184226
226184
1011100011100010
1110001010111000
CDEGBDEF
BDEFCDEG
captif « embouteillages » 
space time diagram
200200
236236
1100100011001000
1110110011101100
EE
DD
captif  
space time diagram
204204
204204
1100110011001100
1100110011001100
linéaire affine captif « identité » 
space time diagram
232232
232232
1110100011101000
1110100011101000
DEDE
DEDE
captif « majorité »