User:Gangleri/tests/4x4 type square/patterns

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different representations of the reference square    revID: - diff · PAGEID: 82792 links here · #focus · W3C CSS Validator   Purge ↺
 

transition T001
00 01 02 03
10 11 12 13
20 21 22 23
30 31 32 33
 →  * * * * * * * * * * * (*)
:|00|01|02|03|10|11|12|13|20|21|22|23|30|31|32|33|:
 

values 1 to 16
09 16 05 04
07 02 11 14
12 13 08 01
06 03 10 15
 →  * * * * * * * * * * * (*)
:|09|16|05|04|07|02|11|14|12|13|08|01|06|03|10|15|:
 

values 0 to 15
08 15 04 03
06 01 10 13
11 12 07 00
05 02 09 14
 →  * * * * * * * * * * * (*)
:|08|15|04|03|06|01|10|13|11|12|07|00|05|02|09|14|:
 

values -15 to 15
1 15 -7 -9
-3 -13 5 11
7 9 -1 -15
-5 -11 3 13
 →  * * * * * * * * * * * (*)
:|1|15|-7|-9|-3|-13|5|11|7|9|-1|-15|-5|-11|3|13|:
 
complement of last
-1 -15 7 9
3 13 -5 -11
-7 -9 1 15
5 11 -3 -13
 →  * * * * * * * * * * * (*)
:|-1|-15|7|9|3|13|-5|-11|-7|-9|1|15|5|11|-3|-13|:


Created using Mozilla Firefox. – revID: - diff · PAGEID: 82792 links here · #focus · W3C CSS Validator

updates

stable versions in the template namespace:

  • last revision of templates modified before ---- – see oldID: 0#

stable versions in the user namespace:

  • last revision of user pages modified before ---- – see oldID: 0#

notes on history

  1. discarded {{oldid|ID=|anchor}}

analysis

  1. User:Gangleri/tests/4x4 type square/method/reference/signed binary ---X
    Template:4x4 type square/method/reference/signed binary ---X
  2. User:Gangleri/tests/4x4 type square/method/reference/signed binary --X-
    Template:4x4 type square/method/reference/signed binary --X-
  3. User:Gangleri/tests/4x4 type square/method/reference/signed binary -X--
    Template:4x4 type square/method/reference/signed binary -X--
  4. User:Gangleri/tests/4x4 type square/method/reference/signed binary X---
    Template:4x4 type square/method/reference/signed binary X---

binary analysis of reference table

binary analysis of the reference table using the "odd values -15 to 15" representation


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binary analysis of the "complement" of the "odd values -15 to 15" representation using "---X", "--X-", "-X--", "X---" as before


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neighbourship


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use arbitrary "shifting", "mirroring" and "rotations"
neighbours of analysis object: EWNS
15 is surrounded by: 8421
15 is surrounded by:
2^32^22^12^0
0 is surrounded by: 7111314
0 – ¡its complement is 15! is surrounded by:
15-2^315-2^215-2^115-2^0 {{{LINKS}}} *
neighbourship in directions E W N S at an arbitrary field
relation to the complement value of that field

(using the "odd values -15 to 15" representation)
value complement value binary generic pattern E W N S
15 0 1 1 1 1 +8 +4 +2 +1 8 4 2 1
14 1 1 1 1 0 +8 +4 +2 -1 9 5 3 0
13 2 1 1 0 1 +8 +4 -2 +1 10 6 0 3
12 3 1 1 0 0 +8 +4 -2 -1 11 7 1 2
11 4 1 0 1 1 +8 -4 +2 +1 12 0 6 5
10 5 1 0 1 0 +8 -4 +2 -1 13 1 7 4
9 6 1 0 0 1 +8 -4 -2 +1 14 2 4 7
8 7 1 0 0 0 +8 -4 -2 -1 15 3 5 6
7 8 0 1 1 1 -8 +4 +2 +1 0 12 10 9
6 9 0 1 1 0 -8 +4 +2 -1 1 13 11 8
5 10 0 1 0 1 -8 +4 -2 +1 2 14 8 11
4 11 0 1 0 0 -8 +4 -2 -1 3 15 9 10
3 12 0 0 1 1 -8 -4 +2 +1 4 8 14 13
2 13 0 0 1 0 -8 -4 +2 -1 5 9 15 12
1 14 0 0 0 1 -8 -4 -2 +1 6 10 12 15
0 15 0 0 0 0 -8 -4 -2 -1 7 11 13 14
note: the EWNS color code will change if the reference square is rotated or mirrored


special 4x4 most-perfect magic squares methods methods / morphisms

0) table (code) and /
Template:4x4 type square/colors analysis


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1) table (code) and /fractional mirroring NW - SE
Template:4x4 type square/colors analysis fractional mirroring NW - SE


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2) table (code) and /mirroring of the two 2x2 NE - SW subsquares
Template:4x4 type square/colors analysis mirroring of the two 2x2 NE - SW subsquares


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3) table (code) and /fractional rotate clockwise NE - SW
Template:4x4 type square/colors analysis fractional rotate clockwise NE - SW


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note this is the same pattern as #2) table (code) and /mirroring of the two 2x2 NE - SW subsquares rotated clockwise with 90°

384

384 most-perfect magic squares using the "values 1 to 16" representation and color code: (16 & 1) – ( 9 & 8) – ( 5 & 12) – ( 3 & 14) – ( 2 & 15)    revID: - diff · PAGEID: 82792 links here · #focus · W3C CSS Validator   Purge ↺
fractional mirroring NW - SE
02 11 05 16 02 11 05 16 02 11
13 08 10 03 13 08 10 03 13 08
12 01 15 06 12 01 15 06 12 01
07 14 04 09 07 14 04 09 07 14
02 11 05 16 02 11 05 16 02 11
13 08 10 03 13 08 10 03 13 08
12 01 15 06 12 01 15 06 12 01
07 14 04 09 07 14 04 09 07 14
02 11 05 16 02 11 05 16 02 11
13 08 10 03 13 08 10 03 13 08
use arbitrary "shifting", "mirroring" and "rotations"
(129) →  * * * * * * * * * * * (*)
reference table
02 11 14 07 02 11 14 07 02 11
13 08 01 12 13 08 01 12 13 08
03 10 15 06 03 10 15 06 03 10
16 05 04 09 16 05 04 09 16 05
02 11 14 07 02 11 14 07 02 11
13 08 01 12 13 08 01 12 13 08
03 10 15 06 03 10 15 06 03 10
16 05 04 09 16 05 04 09 16 05
02 11 14 07 02 11 14 07 02 11
13 08 01 12 13 08 01 12 13 08
use arbitrary "shifting", "mirroring" and "rotations"
(001) →  * * * * * * * * * * * (*)
fractional mirror NW - SE
shift 0 3
fractional rotate NW and SE clockwise
05 11 14 04 05 11 14 04 05 11
10 08 01 15 10 08 01 15 10 08
03 13 12 06 03 13 12 06 03 13
16 02 07 09 16 02 07 09 16 02
05 11 14 04 05 11 14 04 05 11
10 08 01 15 10 08 01 15 10 08
03 13 12 06 03 13 12 06 03 13
16 02 07 09 16 02 07 09 16 02
05 11 14 04 05 11 14 04 05 11
10 08 01 15 10 08 01 15 10 08
use arbitrary "shifting", "mirroring" and "rotations"
(324) →  * * * * * * * * * * * (*)