Category:8-ary Walsh functions in octeract matrix

From Wikimedia Commons, the free media repository
Jump to navigation Jump to search
This category is an image set. It should contain only images that have the same style, and should have a parent category that is purely topical.
highlighted pattern

See also Quadrant colors in hypercube matrices (image set).

Each of these matrices can be interpreted as a set of 128 3-ary Boolean functions. As such it has a set of twins.
The relationship is described by self-inverse Walsh permutation (1, 3, 5, 15, 17, 51, 85, 255):   (It corresponds to the 8×8 top right Sierpinski triangle).

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

It has 16 fixed points: [0, 1, 6, 7, 18, 19, 20, 21, 106, 107, 108, 109, 120, 121, 126, 127]
They are highlighted with orange background. These are the Zhegalkin indices of Boolean functions with quaestor 0.


0
128
64
192
32
160
96
224
16
144
80
208
48
176
112
240

1
129
65
193
33
161
97
225
17
145
81
209
49
177
113
241

2
130
66
194
34
162
98
226
18
146
82
210
50
178
114
242

3
131
67
195
35
163
99
227
19
147
83
211
51
179
115
243

4
132
68
196
36
164
100
228
20
148
84
212
52
180
116
244

5
133
69
197
37
165
101
229
21
149
85
213
53
181
117
245

6
134
70
198
38
166
102
230
22
150
86
214
54
182
118
246

7
135
71
199
39
167
103
231
23
151
87
215
55
183
119
247

8
136
72
200
40
168
104
232
24
152
88
216
56
184
120
248

9
137
73
201
41
169
105
233
25
153
89
217
57
185
121
249

10
138
74
202
42
170
106
234
26
154
90
218
58
186
122
250

11
139
75
203
43
171
107
235
27
155
91
219
59
187
123
251

12
140
76
204
44
172
108
236
28
156
92
220
60
188
124
252

13
141
77
205
45
173
109
237
29
157
93
221
61
189
125
253

14
142
78
206
46
174
110
238
30
158
94
222
62
190
126
254

15
143
79
207
47
175
111
239
31
159
95
223
63
191
127
255

Pages in category "8-ary Walsh functions in octeract matrix"

This category contains only the following page.

8

Media in category "8-ary Walsh functions in octeract matrix"

The following 200 files are in this category, out of 256 total.

(previous page) (next page)(previous page) (next page)
Retrieved from "https://commons.wikimedia.org/w/index.php?title=Category:8-ary_Walsh_functions_in_octeract_matrix&oldid=836750216"