## Clifford Algebra VoDou Physics of Wolfram's 256 Cellular Automata Rules

The 256 Cellular Automata Rules of Wolfram correspond to the 256 basis elements of the 256-dimensional Clifford Algebra of 16x16 Real Matrices, Cl(8) and Cl(1,7), and its discrete counterpart, as well as to the 256 Odu of IFA.

To visualize the correspondence, write the rule numbers in binary notation, put them with the pictures of the 30-level actions of each of the 256 rules as shown on pages 55 and 56 of Wolfram's book A New Kind of Science, and organize them with respect to the

1 + 8 + 28 + 56 + (35+35) + 56 + 28 + 8 + 1 = 256 = 16x16 = 2^8

Here are 78 of the 256, including:

• all 1+8+8+1 = 18 of grades 0, 1, 7, 8;
• 10 of the 28 in each of grades 2, 6;
• 10 of the 56 in each of grades 3, 5;
• 10+10 = 20 of the 35+35 = 70 in grade 4.

The vertical line is a symmetry line of the symmetry of exchanging 0s and 1s in the binary numbers.

Note that:

• the grade-1 vectors 1, 2, 4, 16 (the subset sequence 2^0 = 1, 2^1 = 2, 2^2 = 4, 2^4 = 16 related to Fermat primes)

correspond to the 4 dimensions of physical spacetime;

• 1 gives a succession of bands, the procession of time;
• 2 gives a slope to the left, one of three space dimensions;
• 4 gives a vertical slope, a second of three space dimensions;
• 16 gives a slope to the right, the third of three space dimensions;
• the grade-1 vectors 8, 32, 64, 128 (all giving all white)

correspond to the 4 dimensions of internal symmetry space;

• rule 18 = 00010010 is the first rule to include both 16 = 00010000 with right slope and 2 = 00000010 with left slope and is the first rule with traingular self-similar fractal structure;
• rule 30 = 00011110 is the first rule to include 16, 8, 4, and 2 and is in the self-dual grade-4 and is the first rule with triangular chaotic behavior.

Here are all 28 rules for each of grades 2 and 6.

Note that:

Here are all 56 rules for each of grades 3 and 5.

Note that:

Here are all 35+35 = 70 rules for grade 4.

Note that:

Here is a numerical (no pictures) list of all 256, with grade indicated:

```Grade: 0         1         2         3         4         5         6         7         8

000 00000000
001           00000001
002           00000010
003                     00000011
004           00000100
005                     00000101
006                     00000110
007                               00000111
008           00001000
009                     00001001
010                               00001010
011                               00001011
012                     00001100
013                               00001101
014                               00001110
015                                         00001111
016           00010000
017                     00010001
018                     00010010
019                               00010011
020                     00010100
021                               00010101
022                               00010110
023                                         00010111
024                     00011000
025                               00011001
026                               00011010
027                                         00011011
028                               00011100
029                                         00011101
030                                         00011110
031                                                   00011111
032           00100000
033                     00100001
034                     00100010
035                               00100011
036                     00100100
037                               00100101
038                               00100110
039                                         00100111
040                     00101000
041                               00101001
042                               00101010
043                                         00101011
044                               00101100
045                                         00101101
046                                         00101110
047                                                   00101111
048                     00110000
049                               00110001
050                               00110010
051                                         00110011
052                               00110100
053                                         00110101
054                                         00110110
055                                                   00110111
056                               00111000
057                                         00111001
058                                         00111010
059                                                   00111011
060                                         00111100
061                                                   00111101
062                                                   00111110
063                                                             00111111
064           01000000
065                     01000001
066                     01000010
067                               01000011
068                     01000100
069                               01000101
070                               01000110
071                                         01000111
072                     01001000
073                               01001001
074                     01001010
075                                         01001011
076                               01001100
077                                         01001101
078                                         01001110
079                                                   01001111
080                     01010000
081                               01010001
082                               01010010
083                                         01010011
084                               01010100
085                                         01010101
086                                         01010110
087                                                   01010111
088                               01011000
089                                         01011001
090                                         01011010
091                                                   01011011
092                                         01011100
093                                                   01011101
094                                                   01011110
095                                                             01011111
096                     01100000
097                               01100001
098                               01100010
099                                         01100011
100                               01100100
101                                         01100101
102                                         01100110
103                                                   01100111
104                               01101000
105                                         01101001
106                                         01101010
107                                                   01101011
108                                         01101100
109                                                   01101101
110                                                   01101110
111                                                             01101111
112                               01110000
113                                         01110001
114                                         01110010
115                                                   01110011
116                                         01110100
117                                                   01110101
118                                                   01110110
119                                                             01110111
120                                         01111000
121                                                   01111001
122                                                   01111010
123                                                             01111011
124                                                   01111100
125                                                             01111101
126                                                             01111110
127                                                                       01111111
128           10000000
129                     10000001
130                     10000010
131                               10000011
132                     10000100
133                               10000101
134                               10000110
135                                         10000111
136                     10001000
137                               10001001
138                               10001010
139                                         10001011
140                               10001100
141                                         10001101
142                                         10001110
143                                                   10001111
144                     10010000
145                               10010001
146                               10010010
147                                         10010011
148                               10010100
149                                         10010101
150                                         10010110
151                                                   10010111
152                               10011000
153                                         10011001
154                                         10011010
155                                                   10011011
156                                         10011100
157                                                   10011101
158                                                   10011110
159                                                             10011111
160                     10100000
161                               10100001
162                               10100010
163                                         10100011
164                               10100100
165                                         10100101
166                                         10100110
167                                                   10100111
168                               10101000
169                                         10101001
170                                         10101010
171                                                   10101011
172                                         10101100
173                                                   10101101
174                                                   10101110
175                                                             10101111
176                               10110000
177                                         10110001
178                                         10110010
179                                                   10110011
180                                         10110100
181                                                   10110101
182                                                   10110110
183                                                            10110111
184                                         10111000
185                                                   10111001
186                                                   10111010
187                                                            10111011
188                                                   10111100
189                                                            10111101
190                                                            10111110
191                                                                      10111111
192                     11000000
193                               11000001
194                               11000010
195                                         11000011
196                               11000100
197                                         11000101
198                                         11000110
199                                                   11000111
200                               11001000
201                                         11001001
202                                         11001010
203                                                   11001011
204                                         11001100
205                                                   11001101
206                                                   11001110
207                                                             11001111
208                               11010000
209                                         11010001
210                                         11010010
211                                                   11010011
212                                         11010100
213                                                   11010101
214                                                   11010110
215                                                             11010111
216                                         11011000
217                                                   11011001
218                                                   11011010
219                                                             11011011
220                                                   11011100
221                                                             11011101
222                                                             11011110
223                                                                       11011111
224                               11100000
225                                         11100001
226                                         11100010
227                                                   11100011
228                                         11100100
229                                                   11100101
230                                                   11100110
231                                                             11100111
232                                         11101000
233                                                   11101001
234                                                   11101010
235                                                             11101011
236                                                   11101100
237                                                             11101101
238                                                             11101110
239                                                                       11101111
240                                         11110000
241                                                   11110001
242                                                   11110010
243                                                             11110011
244                                                   11110100
245                                                             11110101
246                                                             11110110
247                                                                       11110111
248                                                   11111000
249                                                             11111001
250                                                             11111010
251                                                                       11111011
252                                                             11111100
253                                                                       11111101
254                                                                       11111110
255                                                                                 11111111```