3-bit Walsh permutation/seeds

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Cluster of the neighbor graph, on the right the matrix sums and vertex types

There are 25 transforms that look similar to the neutral position.
This is the case when the view from one or two axes remains the same or almost the same.
Almost the same means, that the original square is sheared into a (simple) parallelogram.

124
125 (as inverse)
136 (binary)
125 and 136 look similar to the neutral position.
125 looks the same from x and almost the same from y (here shown from −y).
136 looks almost the same from x.

These are the 25 permutations in the middle cluster of the positive component of the neighbor graph.
Each of their matrices has a different set of columns. (I.e., each of their vectors has entries from a different set of integers.)

There are 3*6=18 transform that do not look like a square or simple parallelogram from any side, namely those who's matrices have seven 1s.
They are also shown in three rows of the table below. The choice which to put in the left column is somewhat random.
The ones chosen are those not connected to the central cluster in the positive component. (I.e. the three remaining ones with black circles.)


The table shows some properties of the permutations in the left column:

conjugacy class neut. 2+2 2+4
cycle shape London Rome Florence Lima 5 Lima 6 Rio +
sum 3 4 5a 5b 6 7
quantity 1 6 3 3 6 6 3
12 12


Permutations in the same row have the same complement pattern:

2+2
Rome
2+4
Lima 5
7a
Rio +
1
2
4
2+2
London
2+4
Lima 6
3
5
6
 
neut.
2+2
Florence
7


Each row contains the transform with the binary matrix above and that with an inverse matrix below.
(The latter is the same pattern of non-zero entries, but some 1s are negative.)
(The matrices for the first row are self-inverse.)

cc cs cp t stretch stretched seeds
&0 neut. &0 neut. 3 37 124 Walsh permutation 124 arrows.png


Walsh permutation 124 JF.png
124
Walsh permutation 214 JF.png
214
Walsh permutation 142 JF.png
142
Walsh permutation 412 JF.png
412
Walsh permutation 241 JF.png
241
Walsh permutation 421 JF.png
421
2+2 &1 London 4 26 134 Walsh permutation 134 arrows.png


Walsh permutation 134 JF.png
134
Walsh permutation 134 JF as inverse.png
Walsh permutation 314 JF.png
314
Walsh permutation 314 JF as inverse.png
Walsh permutation 143 JF.png
143
Walsh permutation 143 JF as inverse.png
Walsh permutation 413 JF.png
413
Walsh permutation 413 JF as inverse.png
Walsh permutation 341 JF.png
341
Walsh permutation 341 JF as inverse.png
Walsh permutation 431 JF.png
431
Walsh permutation 431 JF as inverse.png
2+2 &1 London 4 26 125 Walsh permutation 125 arrows.png


Walsh permutation 125 JF.png
125
Walsh permutation 125 JF as inverse.png
Walsh permutation 215 JF.png
215
Walsh permutation 215 JF as inverse.png
Walsh permutation 152 JF.png
152
Walsh permutation 152 JF as inverse.png
Walsh permutation 512 JF.png
512
Walsh permutation 512 JF as inverse.png
Walsh permutation 251 JF.png
251
Walsh permutation 251 JF as inverse.png
Walsh permutation 521 JF.png
521
Walsh permutation 521 JF as inverse.png
2+2 &1 London 4 25 234 Walsh permutation 324 arrows.png


Walsh permutation 324 JF.png
324
Walsh permutation 324 JF as inverse.png
Walsh permutation 234 JF.png
234
Walsh permutation 234 JF as inverse.png
Walsh permutation 342 JF.png
342
Walsh permutation 342 JF as inverse.png
Walsh permutation 432 JF.png
432
Walsh permutation 432 JF as inverse.png
Walsh permutation 243 JF.png
243
Walsh permutation 243 JF as inverse.png
Walsh permutation 423 JF.png
423
Walsh permutation 423 JF as inverse.png
2+2 &1 London 4 25 126 Walsh permutation 126 arrows.png


Walsh permutation 126 JF.png
126
Walsh permutation 126 JF as inverse.png
Walsh permutation 216 JF.png
216
Walsh permutation 216 JF as inverse.png
Walsh permutation 162 JF.png
162
Walsh permutation 162 JF as inverse.png
Walsh permutation 612 JF.png
612
Walsh permutation 612 JF as inverse.png
Walsh permutation 261 JF.png
261
Walsh permutation 261 JF as inverse.png
Walsh permutation 621 JF.png
621
Walsh permutation 621 JF as inverse.png
2+2 &1 London 4 23 245 Walsh permutation 524 arrows.png


Walsh permutation 524 JF.png
524
Walsh permutation 524 JF as inverse.png
Walsh permutation 254 JF.png
254
Walsh permutation 254 JF as inverse.png
Walsh permutation 542 JF.png
542
Walsh permutation 542 JF as inverse.png
Walsh permutation 452 JF.png
452
Walsh permutation 452 JF as inverse.png
Walsh permutation 245 JF.png
245
Walsh permutation 245 JF as inverse.png
Walsh permutation 425 JF.png
425
Walsh permutation 425 JF as inverse.png
2+2 &1 London 4 23 146 Walsh permutation 164 arrows.png


Walsh permutation 164 JF.png
164
Walsh permutation 164 JF as inverse.png
Walsh permutation 614 JF.png
614
Walsh permutation 614 JF as inverse.png
Walsh permutation 146 JF.png
146
Walsh permutation 146 JF as inverse.png
Walsh permutation 416 JF.png
416
Walsh permutation 416 JF as inverse.png
Walsh permutation 641 JF.png
641
Walsh permutation 641 JF as inverse.png
Walsh permutation 461 JF.png
461
Walsh permutation 461 JF as inverse.png
2+2 &2 Rome 5a 11 247 Walsh permutation 724 arrows.png


Walsh permutation 724 JF.png
724
Walsh permutation 724 JF as inverse.png
Walsh permutation 274 JF.png
274
Walsh permutation 274 JF as inverse.png
Walsh permutation 742 JF.png
742
Walsh permutation 742 JF as inverse.png
Walsh permutation 472 JF.png
472
Walsh permutation 472 JF as inverse.png
Walsh permutation 247 JF.png
247
Walsh permutation 247 JF as inverse.png
Walsh permutation 427 JF.png
427
Walsh permutation 427 JF as inverse.png
2+2 &2 Rome 5a 12 147 Walsh permutation 174 arrows.png


Walsh permutation 174 JF.png
174
Walsh permutation 174 JF as inverse.png
Walsh permutation 714 JF.png
714
Walsh permutation 714 JF as inverse.png
Walsh permutation 147 JF.png
147
Walsh permutation 147 JF as inverse.png
Walsh permutation 417 JF.png
417
Walsh permutation 417 JF as inverse.png
Walsh permutation 741 JF.png
741
Walsh permutation 741 JF as inverse.png
Walsh permutation 471 JF.png
471
Walsh permutation 471 JF as inverse.png
2+2 &2 Rome 5a 14 127 Walsh permutation 127 arrows.png


Walsh permutation 127 JF.png
127
Walsh permutation 127 JF as inverse.png
Walsh permutation 217 JF.png
217
Walsh permutation 217 JF as inverse.png
Walsh permutation 172 JF.png
172
Walsh permutation 172 JF as inverse.png
Walsh permutation 712 JF.png
712
Walsh permutation 712 JF as inverse.png
Walsh permutation 271 JF.png
271
Walsh permutation 271 JF as inverse.png
Walsh permutation 721 JF.png
721
Walsh permutation 721 JF as inverse.png
2+2 &3 Florence 5a 37 135 Walsh permutation 135 arrows.png


Walsh permutation 135 JF.png
135
Walsh permutation 135 JF as inverse.png
Walsh permutation 315 JF.png
315
Walsh permutation 315 JF as inverse.png
Walsh permutation 153 JF.png
153
Walsh permutation 153 JF as inverse.png
Walsh permutation 513 JF.png
513
Walsh permutation 513 JF as inverse.png
Walsh permutation 351 JF.png
351
Walsh permutation 351 JF as inverse.png
Walsh permutation 531 JF.png
531
Walsh permutation 531 JF as inverse.png
2+2 &3 Florence 5a 37 236 Walsh permutation 326 arrows.png


Walsh permutation 326 JF.png
326
Walsh permutation 326 JF as inverse.png
Walsh permutation 236 JF.png
236
Walsh permutation 236 JF as inverse.png
Walsh permutation 362 JF.png
362
Walsh permutation 362 JF as inverse.png
Walsh permutation 632 JF.png
632
Walsh permutation 632 JF as inverse.png
Walsh permutation 263 JF.png
263
Walsh permutation 263 JF as inverse.png
Walsh permutation 623 JF.png
623
Walsh permutation 623 JF as inverse.png
2+2 &3 Florence 5a 37 456 Walsh permutation 564 arrows.png


Walsh permutation 564 JF.png
564
Walsh permutation 564 JF as inverse.png
Walsh permutation 654 JF.png
654
Walsh permutation 654 JF as inverse.png
Walsh permutation 546 JF.png
546
Walsh permutation 546 JF as inverse.png
Walsh permutation 456 JF.png
456
Walsh permutation 456 JF as inverse.png
Walsh permutation 645 JF.png
645
Walsh permutation 645 JF as inverse.png
Walsh permutation 465 JF.png
465
Walsh permutation 465 JF as inverse.png
2+4 &4 Lima 5 5b 12 156 Walsh permutation 165 arrows.png


Walsh permutation 165 JF.png
165
Walsh permutation 165 JF as inverse.png
Walsh permutation 615 JF.png
615
Walsh permutation 615 JF as inverse.png
Walsh permutation 156 JF.png
156
Walsh permutation 156 JF as inverse.png
Walsh permutation 516 JF.png
516
Walsh permutation 516 JF as inverse.png
Walsh permutation 651 JF.png
651
Walsh permutation 651 JF as inverse.png
Walsh permutation 561 JF.png
561
Walsh permutation 561 JF as inverse.png
2+4 &4 Lima 5 5b 14 136 Walsh permutation 136 arrows.png


Walsh permutation 136 JF.png
136
Walsh permutation 136 JF as inverse.png
Walsh permutation 316 JF.png
316
Walsh permutation 316 JF as inverse.png
Walsh permutation 163 JF.png
163
Walsh permutation 163 JF as inverse.png
Walsh permutation 613 JF.png
613
Walsh permutation 613 JF as inverse.png
Walsh permutation 361 JF.png
361
Walsh permutation 361 JF as inverse.png
Walsh permutation 631 JF.png
631
Walsh permutation 631 JF as inverse.png
2+4 &4 Lima 5 5b 14 235 Walsh permutation 325 arrows.png


Walsh permutation 325 JF.png
325
Walsh permutation 325 JF as inverse.png
Walsh permutation 235 JF.png
235
Walsh permutation 235 JF as inverse.png
Walsh permutation 352 JF.png
352
Walsh permutation 352 JF as inverse.png
Walsh permutation 532 JF.png
532
Walsh permutation 532 JF as inverse.png
Walsh permutation 253 JF.png
253
Walsh permutation 253 JF as inverse.png
Walsh permutation 523 JF.png
523
Walsh permutation 523 JF as inverse.png
2+4 &4 Lima 5 5b 11 256 Walsh permutation 526 arrows.png


Walsh permutation 526 JF.png
526
Walsh permutation 526 JF as inverse.png
Walsh permutation 256 JF.png
256
Walsh permutation 256 JF as inverse.png
Walsh permutation 562 JF.png
562
Walsh permutation 562 JF as inverse.png
Walsh permutation 652 JF.png
652
Walsh permutation 652 JF as inverse.png
Walsh permutation 265 JF.png
265
Walsh permutation 265 JF as inverse.png
Walsh permutation 625 JF.png
625
Walsh permutation 625 JF as inverse.png
2+4 &4 Lima 5 5b 12 345 Walsh permutation 534 arrows.png


Walsh permutation 534 JF.png
534
Walsh permutation 534 JF as inverse.png
Walsh permutation 354 JF.png
354
Walsh permutation 354 JF as inverse.png
Walsh permutation 543 JF.png
543
Walsh permutation 543 JF as inverse.png
Walsh permutation 453 JF.png
453
Walsh permutation 453 JF as inverse.png
Walsh permutation 345 JF.png
345
Walsh permutation 345 JF as inverse.png
Walsh permutation 435 JF.png
435
Walsh permutation 435 JF as inverse.png
2+4 &4 Lima 5 5b 11 346 Walsh permutation 364 arrows.png


Walsh permutation 364 JF.png
364
Walsh permutation 364 JF as inverse.png
Walsh permutation 634 JF.png
634
Walsh permutation 634 JF as inverse.png
Walsh permutation 346 JF.png
346
Walsh permutation 346 JF as inverse.png
Walsh permutation 436 JF.png
436
Walsh permutation 436 JF as inverse.png
Walsh permutation 643 JF.png
643
Walsh permutation 643 JF as inverse.png
Walsh permutation 463 JF.png
463
Walsh permutation 463 JF as inverse.png
2+4 &5 Lima 6 6 23 157 Walsh permutation 175 arrows.png


Walsh permutation 175 JF.png
175
Walsh permutation 175 JF as inverse.png
Walsh permutation 715 JF.png
715
Walsh permutation 715 JF as inverse.png
Walsh permutation 157 JF.png
157
Walsh permutation 157 JF as inverse.png
Walsh permutation 517 JF.png
517
Walsh permutation 517 JF as inverse.png
Walsh permutation 751 JF.png
751
Walsh permutation 751 JF as inverse.png
Walsh permutation 571 JF.png
571
Walsh permutation 571 JF as inverse.png
2+4 &5 Lima 6 6 25 137 Walsh permutation 137 arrows.png


Walsh permutation 137 JF.png
137
Walsh permutation 137 JF as inverse.png
Walsh permutation 317 JF.png
317
Walsh permutation 317 JF as inverse.png
Walsh permutation 173 JF.png
173
Walsh permutation 173 JF as inverse.png
Walsh permutation 713 JF.png
713
Walsh permutation 713 JF as inverse.png
Walsh permutation 371 JF.png
371
Walsh permutation 371 JF as inverse.png
Walsh permutation 731 JF.png
731
Walsh permutation 731 JF as inverse.png
2+4 &5 Lima 6 6 23 267 Walsh permutation 726 arrows.png


Walsh permutation 726 JF.png
726
Walsh permutation 726 JF as inverse.png
Walsh permutation 276 JF.png
276
Walsh permutation 276 JF as inverse.png
Walsh permutation 762 JF.png
762
Walsh permutation 762 JF as inverse.png
Walsh permutation 672 JF.png
672
Walsh permutation 672 JF as inverse.png
Walsh permutation 267 JF.png
267
Walsh permutation 267 JF as inverse.png
Walsh permutation 627 JF.png
627
Walsh permutation 627 JF as inverse.png
2+4 &5 Lima 6 6 26 237 Walsh permutation 327 arrows.png


Walsh permutation 327 JF.png
327
Walsh permutation 327 JF as inverse.png
Walsh permutation 237 JF.png
237
Walsh permutation 237 JF as inverse.png
Walsh permutation 372 JF.png
372
Walsh permutation 372 JF as inverse.png
Walsh permutation 732 JF.png
732
Walsh permutation 732 JF as inverse.png
Walsh permutation 273 JF.png
273
Walsh permutation 273 JF as inverse.png
Walsh permutation 723 JF.png
723
Walsh permutation 723 JF as inverse.png
2+4 &5 Lima 6 6 25 467 Walsh permutation 764 arrows.png


Walsh permutation 764 JF.png
764
Walsh permutation 764 JF as inverse.png
Walsh permutation 674 JF.png
674
Walsh permutation 674 JF as inverse.png
Walsh permutation 746 JF.png
746
Walsh permutation 746 JF as inverse.png
Walsh permutation 476 JF.png
476
Walsh permutation 476 JF as inverse.png
Walsh permutation 647 JF.png
647
Walsh permutation 647 JF as inverse.png
Walsh permutation 467 JF.png
467
Walsh permutation 467 JF as inverse.png
2+4 &5 Lima 6 6 26 457 Walsh permutation 574 arrows.png


Walsh permutation 574 JF.png
574
Walsh permutation 574 JF as inverse.png
Walsh permutation 754 JF.png
754
Walsh permutation 754 JF as inverse.png
Walsh permutation 547 JF.png
547
Walsh permutation 547 JF as inverse.png
Walsh permutation 457 JF.png
457
Walsh permutation 457 JF as inverse.png
Walsh permutation 745 JF.png
745
Walsh permutation 745 JF as inverse.png
Walsh permutation 475 JF.png
475
Walsh permutation 475 JF as inverse.png
7a &6 Rio +7 11 357 Walsh permutation 753 arrows.png


Walsh permutation 753 JF.png
753
Walsh permutation 753 JF as inverse.png
Walsh permutation 735 JF.png
735
Walsh permutation 735 JF as inverse.png
Walsh permutation 573 JF.png
573
Walsh permutation 573 JF as inverse.png
Walsh permutation 537 JF.png
537
Walsh permutation 537 JF as inverse.png
Walsh permutation 375 JF.png
375
Walsh permutation 375 JF as inverse.png
Walsh permutation 357 JF.png
357
Walsh permutation 357 JF as inverse.png
7a &6 Rio +7 12 367 Walsh permutation 673 arrows.png


Walsh permutation 673 JF.png
673
Walsh permutation 673 JF as inverse.png
Walsh permutation 637 JF.png
637
Walsh permutation 637 JF as inverse.png
Walsh permutation 763 JF.png
763
Walsh permutation 763 JF as inverse.png
Walsh permutation 736 JF.png
736
Walsh permutation 736 JF as inverse.png
Walsh permutation 367 JF.png
367
Walsh permutation 367 JF as inverse.png
Walsh permutation 376 JF.png
376
Walsh permutation 376 JF as inverse.png
7a &6 Rio +7 14 567 Walsh permutation 657 arrows.png


Walsh permutation 657 JF.png
657
Walsh permutation 657 JF as inverse.png
Walsh permutation 675 JF.png
675
Walsh permutation 675 JF as inverse.png
Walsh permutation 567 JF.png
567
Walsh permutation 567 JF as inverse.png
Walsh permutation 576 JF.png
576
Walsh permutation 576 JF as inverse.png
Walsh permutation 765 JF.png
765
Walsh permutation 765 JF as inverse.png
Walsh permutation 756 JF.png
756
Walsh permutation 756 JF as inverse.png