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

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different representations of the reference square    revID: 179077   Purge
transition T001
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
 →  * * * * * * * * * * * (*)
values 0 to 15
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
 →  * * * * * * * * * * * (*)
complement of last
-1 -15 7 9
3 13 -5 -11
-7 -9 1 15
5 11 -3 -13
 →  * * * * * * * * * * * (*)
from: commons:Commons:Village pump#Most-perfect magic squares - Jain squares
(17:46, July 19, 2005 (UTC)): Template:4x4 type square/colors 00 and Template:4x4 type square/table updated there)
The 384 4x4 squares are known as Jain squares originating in India from the 11th - 12th centuary.
note: at [[:meta:]] width="100%" is used in the (main) table; it is not used at commons:
see the difference editing section 0, removing width="100%" and making a preview


template status:
templates
will be
updated
       
use arbitrary "shifting", "mirroring" and "rotations" {{{LINKS}}} *

Contents

Created using Mozilla Firefox. – revID: 179077

updates[edit]

stable versions in the template namespace:

  • last revision of templates modified before 00:34, July 15, 2005 (UTC) – see oldID: 177497#

stable versions in the user namespace:

  • last revision of user pages modified before 09:48, July 15, 2005 (UTC) – see oldID: 177788#

notes on history[edit]

  1. discarded oldID: 177497#using_the_.22none_of_the_new_introduced_parameters_are_named.22_method

"templates"[edit]

4x4 type squares[edit]

  1. User:Gangleri/tests/4x4 type square
    A – primary level - all parameters are named
    at the moment values are inserted at the primary level
    future use: an extra level B0 / C0 for value insertion could be added
    Template:4x4 type squarenot updated

using the "new introduced parameters are all named" method[edit]

  1. adding a "method" (METHOD) related to the generation or transition of original cell values
    1. "identification" of this method at User:Gangleri/tests/4x4 type square/method
      B1 – intermediate level - all old parameters are named - one named parameter skipped
      Template:4x4 type square/methodnot updated
    2. available methods:
      1. "trivial" – no changes: User:Gangleri/tests/4x4 type square/
        B2 – intermediate level - all old parameters are named - one named parameter skipped
        Template:4x4 type square/not updated
      2. future use: other methods to ilustrate the proprieties of these themplates
  2. adding a color pattern (COLORS) to ilustrate some properties related to cell values
    1. User:Gangleri/tests/4x4 type square/colors 00
      B3 – intermediate level - remaining old parameters are named - new parameters have been introduced - last are all named
      Template:4x4 type square/colors 00not updated
  3. modifying (METHODCOLORS) the color pattern defined previously – can "follow" the transition of original cell values or not
    since 02:14, July 15, 2005 (UTC)
    1. "identification" of this color pattern method at User:Gangleri/tests/4x4 type square/methodcolors
      User:Gangleri/tests/4x4 type square/methodcolors – (new) not available
    2. available color pattern methods:
      1. "trivial" – no changes: User:Gangleri/tests/4x4 type square/methodcolors/
        User:Gangleri/tests/4x4 type square/methodcolors/ – (new) not available
      2. future use: other methods to ilustrate the proprieties of these themplates
  4. generation of the square at User:Gangleri/tests/4x4 type square/table
    B4 – deepest level - remaining parameters (old and new) are named
    Template:4x4 type square/tablenot updated
  5. #embedding a 4x4 type square in an infinite planeUser:Gangleri/tests/4x4 type square/table (10x10)
    since 09:22, July 15, 2005 (UTC)
    Template:4x4 type square/table (10x10) – since 09:22, July 15, 2005 (UTC) – not available

examples[edit]

example B4 (deepest level - remaining parameters (old and new) are named) called directly[edit]

{{User:Gangleri/tests/4x4 type square/table|ALIGN=left|WIDTH=20px|A00=7|A01=12|A02=1|A03=10|A10=9|A11=2|A12=15|A13=4|A20=14|A21=5|A22=8|A23=3|A30=0|A31=11|A32=6|A33=13|C00=black|C01=violet|C02=black|C03=black|C10=green|C11=blue|C12=red|C13=black|C20=black|C21=black|C22=black|C23=violet|C30=red|C31=black|C32=green|C33=blue}}

generates:
User:Gangleri/tests/4x4 type square/table

{{{ALIGN}}}: left – {{{WIDTH}}}: 20px
{{{C00}}}: black – {{{C01}}}: violet – {{{C02}}}: black – {{{C03}}}: black
{{{C10}}}: green – {{{C11}}}: blue – {{{C12}}}: red – {{{C13}}}: black
{{{C20}}}: black – {{{C21}}}: black – {{{C22}}}: black – {{{C23}}}: violet
{{{C30}}}: red – {{{C31}}}: black – {{{C32}}}: green – {{{C33}}}: blue
{{{A00}}}: 7 – {{{A01}}}: 12 – {{{A02}}}: 1 – {{{A03}}}: 10 – Purge
{{{A10}}}: 9 – {{{A11}}}: 2 – {{{A12}}}: 15 – {{{A13}}}: 4
{{{A20}}}: 14 – {{{A21}}}: 5 – {{{A22}}}: 8 – {{{A23}}}: 3
{{{A30}}}: 0 – {{{A31}}}: 11 – {{{A32}}}: 6 – {{{A33}}}: 13
7 12 1 10
9 2 15 4
14 5 8 3
0 11 6 13


temporary: User:Gangleri/tests/4x4 type square/table (code)Purge

compare with initial values

|A00=7|A01=12|A02=1|A03=10
|A10=9|A11=2|A12=15|A13=4
|A20=14|A21=5|A22=8|A23=3
|A30=0|A31=11|A32=6|A33=13

|C00=black|C01=violet|C02=black|C03=black
|C10=green|C11=blue|C12=red|C13=black
|C20=black|C21=black|C22=black|C23=violet
|C30=red|C31=black|C32=green|C33=blue

notes: works as expected – 07:48, July 15, 2005 (UTC)

example B3 calling ... B4 - all parameters are always named[edit]

{{User:Gangleri/tests/4x4 type square/colors 00|METHODCOLORS=/|ALIGN=left|WIDTH=20px|A00=7|A01=12|A02=1|A03=10|A10=9|A11=2|A12=15|A13=4|A20=14|A21=5|A22=8|A23=3|A30=0|A31=11|A32=6|A33=13}}

generates: (edit section or page, remove second pre ... /pre and make a preview)

{{User:Gangleri/tests/4x4 type square/colors 00|METHODCOLORS=/|ALIGN=left|WIDTH=20px|A00=7|A01=12|A02=1|A03=10|A10=9|A11=2|A12=15|A13=4|A20=14|A21=5|A22=8|A23=3|A30=0|A31=11|A32=6|A33=13}}


notes: works as expected – 07:48, July 15, 2005 (UTC)

example (emulated A calling B1 calling B2) calling B3 calling ... B4 - all parameters are always named[edit]

{{User:Gangleri/tests/4x4 type square/|COLORS=00|METHODCOLORS=/|ALIGN=left|WIDTH=20px|A00=7|A01=12|A02=1|A03=10|A10=9|A11=2|A12=15|A13=4|A20=14|A21=5|A22=8|A23=3|A30=0|A31=11|A32=6|A33=13}}

generates: (edit section or page, remove second pre ... /pre and make a preview)

{{User:Gangleri/tests/4x4 type square/|COLORS=00|METHODCOLORS=/|ALIGN=left|WIDTH=20px|A00=7|A01=12|A02=1|A03=10|A10=9|A11=2|A12=15|A13=4|A20=14|A21=5|A22=8|A23=3|A30=0|A31=11|A32=6|A33=13}}


notes: works as expected – 07:48, July 15, 2005 (UTC)

example A calling B1 calling B2 calling B3 calling ... B4 - all parameters are always named[edit]

{{User:Gangleri/tests/4x4 type square|METHOD=/|COLORS=00|METHODCOLORS=/|ALIGN=left|WIDTH=20px|A00=7|A01=12|A02=1|A03=10|A10=9|A11=2|A12=15|A13=4|A20=14|A21=5|A22=8|A23=3|A30=0|A31=11|A32=6|A33=13}}

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

{{{METHOD}}}: / – {{{COLORS}}}: 00
{{{METHODCOLORS}}}: /
{{{ALIGN}}}: left – {{{WIDTH}}}: 20px
{{{A00}}}: 7 – {{{A01}}}: 12 – {{{A02}}}: 1 – {{{A03}}}: 10 – Purge
{{{A10}}}: 9 – {{{A11}}}: 2 – {{{A12}}}: 15 – {{{A13}}}: 4
{{{A20}}}: 14 – {{{A21}}}: 5 – {{{A22}}}: 8 – {{{A23}}}: 3
{{{A30}}}: 0 – {{{A31}}}: 11 – {{{A32}}}: 6 – {{{A33}}}: 13

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

{{{METHOD}}}: / – {{{COLORS}}}: 00
{{{METHODCOLORS}}}: /
{{{ALIGN}}}: left – {{{WIDTH}}}: 20px
{{{A00}}}: 7 – {{{A01}}}: 12 – {{{A02}}}: 1 – {{{A03}}}: 10 – Purge
{{{A10}}}: 9 – {{{A11}}}: 2 – {{{A12}}}: 15 – {{{A13}}}: 4
{{{A20}}}: 14 – {{{A21}}}: 5 – {{{A22}}}: 8 – {{{A23}}}: 3
{{{A30}}}: 0 – {{{A31}}}: 11 – {{{A32}}}: 6 – {{{A33}}}: 13

User:Gangleri/tests/4x4 type square/

{{{COLORS}}}: 00
{{{METHODCOLORS}}}: /
{{{ALIGN}}}: left – {{{WIDTH}}}: 20px
{{{A00}}}: 7 – {{{A01}}}: 12 – {{{A02}}}: 1 – {{{A03}}}: 10 – Purge
{{{A10}}}: 9 – {{{A11}}}: 2 – {{{A12}}}: 15 – {{{A13}}}: 4
{{{A20}}}: 14 – {{{A21}}}: 5 – {{{A22}}}: 8 – {{{A23}}}: 3
{{{A30}}}: 0 – {{{A31}}}: 11 – {{{A32}}}: 6 – {{{A33}}}: 13

User:Gangleri/tests/4x4 type square/colors 00

{{{METHODCOLORS}}}: /
{{{ALIGN}}}: left – {{{WIDTH}}}: 20px
{{{A00}}}: 7 – {{{A01}}}: 12 – {{{A02}}}: 1 – {{{A03}}}: 10 – Purge
{{{A10}}}: 9 – {{{A11}}}: 2 – {{{A12}}}: 15 – {{{A13}}}: 4
{{{A20}}}: 14 – {{{A21}}}: 5 – {{{A22}}}: 8 – {{{A23}}}: 3
{{{A30}}}: 0 – {{{A31}}}: 11 – {{{A32}}}: 6 – {{{A33}}}: 13

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

{{{METHODCOLORS}}}: /
{{{ALIGN}}}: left – {{{WIDTH}}}: 20px
{{{C00}}}: black – {{{C01}}}: violet – {{{C02}}}: black – {{{C03}}}: black
{{{C10}}}: green – {{{C11}}}: blue – {{{C12}}}: red – {{{C13}}}: black
{{{C20}}}: black – {{{C21}}}: black – {{{C22}}}: black – {{{C23}}}: violet
{{{C30}}}: red – {{{C31}}}: black – {{{C32}}}: green – {{{C33}}}: blue
{{{A00}}}: 7 – {{{A01}}}: 12 – {{{A02}}}: 1 – {{{A03}}}: 10 – Purge
{{{A10}}}: 9 – {{{A11}}}: 2 – {{{A12}}}: 15 – {{{A13}}}: 4
{{{A20}}}: 14 – {{{A21}}}: 5 – {{{A22}}}: 8 – {{{A23}}}: 3
{{{A30}}}: 0 – {{{A31}}}: 11 – {{{A32}}}: 6 – {{{A33}}}: 13

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

{{{ALIGN}}}: left – {{{WIDTH}}}: 20px
{{{C00}}}: black – {{{C01}}}: violet – {{{C02}}}: black – {{{C03}}}: black
{{{C10}}}: green – {{{C11}}}: blue – {{{C12}}}: red – {{{C13}}}: black
{{{C20}}}: black – {{{C21}}}: black – {{{C22}}}: black – {{{C23}}}: violet
{{{C30}}}: red – {{{C31}}}: black – {{{C32}}}: green – {{{C33}}}: blue
{{{A00}}}: 7 – {{{A01}}}: 12 – {{{A02}}}: 1 – {{{A03}}}: 10 – Purge
{{{A10}}}: 9 – {{{A11}}}: 2 – {{{A12}}}: 15 – {{{A13}}}: 4
{{{A20}}}: 14 – {{{A21}}}: 5 – {{{A22}}}: 8 – {{{A23}}}: 3
{{{A30}}}: 0 – {{{A31}}}: 11 – {{{A32}}}: 6 – {{{A33}}}: 13

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

{{{ALIGN}}}: left – {{{WIDTH}}}: 20px
{{{C00}}}: black – {{{C01}}}: violet – {{{C02}}}: black – {{{C03}}}: black
{{{C10}}}: green – {{{C11}}}: blue – {{{C12}}}: red – {{{C13}}}: black
{{{C20}}}: black – {{{C21}}}: black – {{{C22}}}: black – {{{C23}}}: violet
{{{C30}}}: red – {{{C31}}}: black – {{{C32}}}: green – {{{C33}}}: blue
{{{A00}}}: 7 – {{{A01}}}: 12 – {{{A02}}}: 1 – {{{A03}}}: 10 – Purge
{{{A10}}}: 9 – {{{A11}}}: 2 – {{{A12}}}: 15 – {{{A13}}}: 4
{{{A20}}}: 14 – {{{A21}}}: 5 – {{{A22}}}: 8 – {{{A23}}}: 3
{{{A30}}}: 0 – {{{A31}}}: 11 – {{{A32}}}: 6 – {{{A33}}}: 13
7 12 1 10
9 2 15 4
14 5 8 3
0 11 6 13


temporary: User:Gangleri/tests/4x4 type square/table (code)Purge

compare with initial values

|A00=7|A01=12|A02=1|A03=10
|A10=9|A11=2|A12=15|A13=4
|A20=14|A21=5|A22=8|A23=3
|A30=0|A31=11|A32=6|A33=13

|C00=black|C01=violet|C02=black|C03=black
|C10=green|C11=blue|C12=red|C13=black
|C20=black|C21=black|C22=black|C23=violet
|C30=red|C31=black|C32=green|C33=blue

notes: works as expected – 07:48, July 15, 2005 (UTC)

embedding a 4x4 type square in an infinite plane[edit]

example User:Gangleri/tests/4x4 type square/table (10x10) called directly

{{User:Gangleri/tests/4x4 type square/table (10x10)|BACKGROUND=#dfdfdf|ALIGN=left|WIDTH=20px|HEADER=demo|NOTE=use other sets of "''valid''" values|A00=7|A01=12|A02=1|A03=10|A10=9|A11=2|A12=15|A13=4|A20=14|A21=5|A22=8|A23=3|A30=0|A31=11|A32=6|A33=13|C00=black|C01=violet|C02=black|C03=black|C10=green|C11=blue|C12=red|C13=black|C20=black|C21=black|C22=black|C23=violet|C30=red|C31=black|C32=green|C33=blue}}

generates: (edit section or page, remove second pre ... /pre and make a preview)

{{User:Gangleri/tests/4x4 type square/table (10x10)|BACKGROUND=#dfdfdf|ALIGN=left|WIDTH=20px|HEADER=demo|NOTE=use other sets of "''valid''" values|A00=7|A01=12|A02=1|A03=10|A10=9|A11=2|A12=15|A13=4|A20=14|A21=5|A22=8|A23=3|A30=0|A31=11|A32=6|A33=13|C00=black|C01=violet|C02=black|C03=black|C10=green|C11=blue|C12=red|C13=black|C20=black|C21=black|C22=black|C23=violet|C30=red|C31=black|C32=green|C33=blue}}


notes: works as expected – 09:22, July 15, 2005 (UTC)

other methods - some examples of template magic and square magic[edit]

notes: should be demonstrated after bug is fixed

  1. adding a level imediatelly after "4x4 type square" to chose the set of values for one of the the 384 possible squares
    this considerably reduces the number of values in the top primary template(s) (the primary level template and its shortcut variants for different predefined settings / parameters)
  2. color patterns:
    1. adding some of the 24 possible color pattern for straight forward generation of the squares
    2. adding color "interpretative patterns" about diffs, sums, modulo, modulo and remainder, fix values
      1. some of them: either the "O-pattern" or one of the four "Y-patterns" (Y rotated iteratively 90°) or the X pattern, two of the subsqares (NE - SW or NW - SE); 2 color patterns for sums of two "neighbour values"

methods = transitions = morphisms#square magic using "methods = transitions = morphisms"

clasical methods[edit]

methods = transitions = morphisms#clasical methods

algebraic methods[edit]

methods = transitions = morphisms#algebraic methods

Kabbalah methods[edit]

methods = transitions = morphisms#Kabbalah methods

Kabbalah 4x4 square using templates[edit]

methods = transitions = morphisms#Kabbalah 4x4 square using templates

most-perfect magic squares methods[edit]

methods = transitions = morphisms#most-perfect magic squares methods

general most-perfect magic squares methods[edit]

methods = transitions = morphisms#general most-perfect magic squares methods

(composed?) most-perfect magic squares methods[edit]

methods = transitions = morphisms#(composed?) most-perfect magic squares methods

special 4x4 most-perfect magic squares methods methods / morphisms[edit]

methods = transitions = morphisms#special 4x4 most-perfect magic squares methods methods / morphisms

nothing new (Kohelet, Ecclesiastes)[edit]

methods = transitions = morphisms#nothing new (Kohelet, Ecclesiastes)

transitions to "leave" the Jain squares using other "descriptive patterns"[edit]

methods = transitions = morphisms#transitions to "leave" the Jain squares using other "descriptive patterns"

examples using these methods[edit]

4x4 type square/complement[edit]

{{User:Gangleri/tests/4x4 type square|METHOD=/complement|COLORS=00|METHODCOLORS=/complement|ALIGN=right|WIDTH=20px|A00=7|A01=12|A02=1|A03=10|A10=9|A11=2|A12=15|A13=4|A20=14|A21=5|A22=8|A23=3|A30=0|A31=11|A32=6|A33=13}}
{{4x4 type square|METHOD=/|COLORS=00|METHODCOLORS=/|ALIGN=left|WIDTH=20px|A00=7|A01=12|A02=1|A03=10|A10=9|A11=2|A12=15|A13=4|A20=14|A21=5|A22=8|A23=3|A30=0|A31=11|A32=6|A33=13}}

generates: (edit section or page, remove second pre ... /pre and make a preview)

{{User:Gangleri/tests/4x4 type square|METHOD=/complement|COLORS=00|METHODCOLORS=/complement|ALIGN=right|WIDTH=20px|A00=7|A01=12|A02=1|A03=10|A10=9|A11=2|A12=15|A13=4|A20=14|A21=5|A22=8|A23=3|A30=0|A31=11|A32=6|A33=13}}
{{4x4 type square|METHOD=/|COLORS=00|METHODCOLORS=/|ALIGN=left|WIDTH=20px|A00=7|A01=12|A02=1|A03=10|A10=9|A11=2|A12=15|A13=4|A20=14|A21=5|A22=8|A23=3|A30=0|A31=11|A32=6|A33=13}}


notes: works as expected – 07:48, July 15, 2005 (UTC)

4x4 type square/fractional rotate clockwise NE - SW[edit]

{{User:Gangleri/tests/4x4 type square|METHOD=/fractional rotate clockwise NE - SW|COLORS=00|METHODCOLORS=/fractional rotate clockwise NE - SW|ALIGN=right|WIDTH=20px|A00=7|A01=12|A02=1|A03=10|A10=9|A11=2|A12=15|A13=4|A20=14|A21=5|A22=8|A23=3|A30=0|A31=11|A32=6|A33=13}}
{{4x4 type square|METHOD=/|COLORS=00|METHODCOLORS=/|ALIGN=left|WIDTH=20px|A00=7|A01=12|A02=1|A03=10|A10=9|A11=2|A12=15|A13=4|A20=14|A21=5|A22=8|A23=3|A30=0|A31=11|A32=6|A33=13}}

generates: (edit section or page, remove second pre ... /pre and make a preview)

{{User:Gangleri/tests/4x4 type square|METHOD=/fractional rotate clockwise NE - SW|COLORS=00|METHODCOLORS=/fractional rotate clockwise NE - SW|ALIGN=right|WIDTH=20px|A00=7|A01=12|A02=1|A03=10|A10=9|A11=2|A12=15|A13=4|A20=14|A21=5|A22=8|A23=3|A30=0|A31=11|A32=6|A33=13}}
{{4x4 type square|METHOD=/|COLORS=00|METHODCOLORS=/|ALIGN=left|WIDTH=20px|A00=7|A01=12|A02=1|A03=10|A10=9|A11=2|A12=15|A13=4|A20=14|A21=5|A22=8|A23=3|A30=0|A31=11|A32=6|A33=13}}


notes: works as expected – 07:48, July 15, 2005 (UTC)

4x4 type square/fractional rotate conterclockwise NE - SW[edit]

{{User:Gangleri/tests/4x4 type square|METHOD=/fractional rotate conterclockwise NE - SW|COLORS=00|METHODCOLORS=/fractional rotate conterclockwise NE - SW|ALIGN=right|WIDTH=20px|A00=7|A01=12|A02=1|A03=10|A10=9|A11=2|A12=15|A13=4|A20=14|A21=5|A22=8|A23=3|A30=0|A31=11|A32=6|A33=13}}
{{4x4 type square|METHOD=/|COLORS=00|METHODCOLORS=/|ALIGN=left|WIDTH=20px|A00=7|A01=12|A02=1|A03=10|A10=9|A11=2|A12=15|A13=4|A20=14|A21=5|A22=8|A23=3|A30=0|A31=11|A32=6|A33=13}}

generates: (edit section or page, remove second pre ... /pre and make a preview)

{{User:Gangleri/tests/4x4 type square|METHOD=/fractional rotate conterclockwise NE - SW|COLORS=00|METHODCOLORS=/fractional rotate conterclockwise NE - SW|ALIGN=right|WIDTH=20px|A00=7|A01=12|A02=1|A03=10|A10=9|A11=2|A12=15|A13=4|A20=14|A21=5|A22=8|A23=3|A30=0|A31=11|A32=6|A33=13}}
{{4x4 type square|METHOD=/|COLORS=00|METHODCOLORS=/|ALIGN=left|WIDTH=20px|A00=7|A01=12|A02=1|A03=10|A10=9|A11=2|A12=15|A13=4|A20=14|A21=5|A22=8|A23=3|A30=0|A31=11|A32=6|A33=13}}


notes: works as expected – 15:51, July 15, 2005 (UTC)

4x4 type square/fractional mirroring NE - SW[edit]

{{User:Gangleri/tests/4x4 type square|METHOD=/fractional mirroring NE - SW|COLORS=00|METHODCOLORS=/fractional mirroring NE - SW|ALIGN=right|WIDTH=20px|A00=7|A01=12|A02=1|A03=10|A10=9|A11=2|A12=15|A13=4|A20=14|A21=5|A22=8|A23=3|A30=0|A31=11|A32=6|A33=13}}
{{4x4 type square|METHOD=/|COLORS=00|METHODCOLORS=/|ALIGN=left|WIDTH=20px|A00=7|A01=12|A02=1|A03=10|A10=9|A11=2|A12=15|A13=4|A20=14|A21=5|A22=8|A23=3|A30=0|A31=11|A32=6|A33=13}}

generates: (edit section or page, remove second pre ... /pre and make a preview)

{{User:Gangleri/tests/4x4 type square|METHOD=/fractional mirroring NE - SW|COLORS=00|METHODCOLORS=/fractional mirroring NE - SW|ALIGN=right|WIDTH=20px|A00=7|A01=12|A02=1|A03=10|A10=9|A11=2|A12=15|A13=4|A20=14|A21=5|A22=8|A23=3|A30=0|A31=11|A32=6|A33=13}}
{{4x4 type square|METHOD=/|COLORS=00|METHODCOLORS=/|ALIGN=left|WIDTH=20px|A00=7|A01=12|A02=1|A03=10|A10=9|A11=2|A12=15|A13=4|A20=14|A21=5|A22=8|A23=3|A30=0|A31=11|A32=6|A33=13}}


notes: works as expected – 08:44, July 15, 2005 (UTC)

4x4 type square/fractional mirroring NW - SE[edit]

{{User:Gangleri/tests/4x4 type square|METHOD=/fractional mirroring NW - SE|COLORS=00|METHODCOLORS=/fractional mirroring NW - SE|ALIGN=right|WIDTH=20px|A00=7|A01=12|A02=1|A03=10|A10=9|A11=2|A12=15|A13=4|A20=14|A21=5|A22=8|A23=3|A30=0|A31=11|A32=6|A33=13}}
{{4x4 type square|METHOD=/|COLORS=00|METHODCOLORS=/|ALIGN=left|WIDTH=20px|A00=7|A01=12|A02=1|A03=10|A10=9|A11=2|A12=15|A13=4|A20=14|A21=5|A22=8|A23=3|A30=0|A31=11|A32=6|A33=13}}

generates: (edit section or page, remove second pre ... /pre and make a preview)

{{User:Gangleri/tests/4x4 type square|METHOD=/fractional mirroring NW - SE|COLORS=00|METHODCOLORS=/fractional mirroring NW - SE|ALIGN=right|WIDTH=20px|A00=7|A01=12|A02=1|A03=10|A10=9|A11=2|A12=15|A13=4|A20=14|A21=5|A22=8|A23=3|A30=0|A31=11|A32=6|A33=13}}
{{4x4 type square|METHOD=/|COLORS=00|METHODCOLORS=/|ALIGN=left|WIDTH=20px|A00=7|A01=12|A02=1|A03=10|A10=9|A11=2|A12=15|A13=4|A20=14|A21=5|A22=8|A23=3|A30=0|A31=11|A32=6|A33=13}}


notes:

works as expected – 20:57, July 15, 2005 (UTC)
to do ilustrate the "O-pattern"

4x4 type square/mirroring of the two 2x2 NE - SW subsquares[edit]

{{User:Gangleri/tests/4x4 type square|METHOD=/mirroring of the two 2x2 NE - SW subsquares|COLORS=00|METHODCOLORS=/mirroring of the two 2x2 NE - SW subsquares|ALIGN=right|WIDTH=20px|A00=7|A01=12|A02=1|A03=10|A10=9|A11=2|A12=15|A13=4|A20=14|A21=5|A22=8|A23=3|A30=0|A31=11|A32=6|A33=13}}
{{4x4 type square|METHOD=/|COLORS=00|METHODCOLORS=/|ALIGN=left|WIDTH=20px|A00=7|A01=12|A02=1|A03=10|A10=9|A11=2|A12=15|A13=4|A20=14|A21=5|A22=8|A23=3|A30=0|A31=11|A32=6|A33=13}}

generates: (edit section or page, remove second pre ... /pre and make a preview)

{{User:Gangleri/tests/4x4 type square|METHOD=/mirroring of the two 2x2 NE - SW subsquares|COLORS=00|METHODCOLORS=/mirroring of the two 2x2 NE - SW subsquares|ALIGN=right|WIDTH=20px|A00=7|A01=12|A02=1|A03=10|A10=9|A11=2|A12=15|A13=4|A20=14|A21=5|A22=8|A23=3|A30=0|A31=11|A32=6|A33=13}}
{{4x4 type square|METHOD=/|COLORS=00|METHODCOLORS=/|ALIGN=left|WIDTH=20px|A00=7|A01=12|A02=1|A03=10|A10=9|A11=2|A12=15|A13=4|A20=14|A21=5|A22=8|A23=3|A30=0|A31=11|A32=6|A33=13}}


notes: works as expected – 12:14, July 15, 2005 (UTC)

4x4 type square/mirroring of the two 2x2 NW - SE subsquares[edit]

{{User:Gangleri/tests/4x4 type square|METHOD=/mirroring of the two 2x2 NW - SE subsquares|COLORS=00|METHODCOLORS=/mirroring of the two 2x2 NW - SE subsquares|ALIGN=right|WIDTH=20px|A00=7|A01=12|A02=1|A03=10|A10=9|A11=2|A12=15|A13=4|A20=14|A21=5|A22=8|A23=3|A30=0|A31=11|A32=6|A33=13}}
{{4x4 type square|METHOD=/|COLORS=00|METHODCOLORS=/|ALIGN=left|WIDTH=20px|A00=7|A01=12|A02=1|A03=10|A10=9|A11=2|A12=15|A13=4|A20=14|A21=5|A22=8|A23=3|A30=0|A31=11|A32=6|A33=13}}

generates: (edit section or page, remove second pre ... /pre and make a preview)

{{User:Gangleri/tests/4x4 type square|METHOD=/mirroring of the two 2x2 NW - SE subsquares|COLORS=00|METHODCOLORS=/mirroring of the two 2x2 NW - SE subsquares|ALIGN=right|WIDTH=20px|A00=7|A01=12|A02=1|A03=10|A10=9|A11=2|A12=15|A13=4|A20=14|A21=5|A22=8|A23=3|A30=0|A31=11|A32=6|A33=13}}
{{4x4 type square|METHOD=/|COLORS=00|METHODCOLORS=/|ALIGN=left|WIDTH=20px|A00=7|A01=12|A02=1|A03=10|A10=9|A11=2|A12=15|A13=4|A20=14|A21=5|A22=8|A23=3|A30=0|A31=11|A32=6|A33=13}}


notes: works as expected – 21:00, July 15, 2005 (UTC)

one key "Inputbox previews"[edit]

  • ...

references[edit]

others:

Would like to have the time to read these articles. – ;-) Gangleri | Th | T 21:37, July 15, 2005 (UTC)

reference square[edit]

Special thanks:

to T.V.Padmakumar, India for his work about the ‘Sri Rama Chakra’ like squares
library#reference square

using templates[edit]

reference

availability at other wiki's[edit]

migration and update issues[edit]

  • to add new functionality modifications to the templates are required from time to time; adding new parameters will break temporarily all pages where they are used;
  • in order to minimizy this outage time it would be necessary to
  1. have an overview about what version / variant is used where
  2. have an overview about the pages where they are used; a list or working "backlinks"
  3. evaluate the order which should be used update if this can minimize outage time

references about similar work[edit]

miscellaneous[edit]

User:Gangleri/tests/9x9 type square called directly[edit]
{{User:Gangleri/tests/9x9 type square|BACKGROUND=#dfdfdf|ALIGN=left|WIDTH=20px|A00=31|A01=36|A02=29|A03=76|A04=81|A05=74|A06=13|A07=18|A08=11|A10=30|A11=32|A12=34|A13=75|A14=77|A15=79|A16=12|A17=14|A18=16|A20=35|A21=28|A22=33|A23=80|A24=73|A25=78|A26=17|A27=10|A28=15|A30=22|A31=27|A32=20|A33=40|A34=45|A35=38|A36=58|A37=63|A38=56|A40=21|A41=23|A42=25|A43=39|A44=41|A45=43|A46=57|A47=59|A48=61|A50=26|A51=19|A52=24|A53=44|A54=37|A55=42|A56=62|A57=55|A58=60|A60=67|A61=72|A62=65|A63=4|A64=9|A65=2|A66=49|A67=54|A68=47|A70=66|A71=68|A72=70|A73=3|A74=5|A75=7|A76=48|A77=50|A78=52|A80=71|A81=64|A82=69|A83=8|A84=1|A85=6|A86=53|A87=46|A88=51|C00=black|C01=black|C02=black|C03=black|C04=black|C05=black|C06=black|C07=black|C08=black|C10=black|C11=black|C12=black|C13=black|C14=black|C15=black|C16=black|C17=black|C18=black|C20=black|C21=black|C22=black|C23=black|C24=black|C25=black|C26=black|C27=black|C28=black|C30=black|C31=black|C32=black|C33=black|C34=black|C35=black|C36=black|C37=black|C38=black|C40=black|C41=black|C42=black|C43=black|C44=black|C45=black|C46=black|C47=black|C48=black|C50=black|C51=black|C52=black|C53=black|C54=black|C55=black|C56=black|C57=black|C58=black|C60=black|C61=black|C62=black|C63=blue|C64=blue|C65=blue|C66=black|C67=black|C68=black|C70=black|C71=black|C72=black|C73=blue|C74=blue|C75=blue|C76=black|C77=black|C78=black|C80=black|C81=black|C82=black|C83=blue|C84=blue|C85=blue|C86=black|C87=black|C88=black}}

generates: (edit section or page, remove second pre ... /pre and make a preview)

{{User:Gangleri/tests/9x9 type square|BACKGROUND=#dfdfdf|ALIGN=left|WIDTH=20px|A00=31|A01=36|A02=29|A03=76|A04=81|A05=74|A06=13|A07=18|A08=11|A10=30|A11=32|A12=34|A13=75|A14=77|A15=79|A16=12|A17=14|A18=16|A20=35|A21=28|A22=33|A23=80|A24=73|A25=78|A26=17|A27=10|A28=15|A30=22|A31=27|A32=20|A33=40|A34=45|A35=38|A36=58|A37=63|A38=56|A40=21|A41=23|A42=25|A43=39|A44=41|A45=43|A46=57|A47=59|A48=61|A50=26|A51=19|A52=24|A53=44|A54=37|A55=42|A56=62|A57=55|A58=60|A60=67|A61=72|A62=65|A63=4|A64=9|A65=2|A66=49|A67=54|A68=47|A70=66|A71=68|A72=70|A73=3|A74=5|A75=7|A76=48|A77=50|A78=52|A80=71|A81=64|A82=69|A83=8|A84=1|A85=6|A86=53|A87=46|A88=51|C00=black|C01=black|C02=black|C03=black|C04=black|C05=black|C06=black|C07=black|C08=black|C10=black|C11=black|C12=black|C13=black|C14=black|C15=black|C16=black|C17=black|C18=black|C20=black|C21=black|C22=black|C23=black|C24=black|C25=black|C26=black|C27=black|C28=black|C30=black|C31=black|C32=black|C33=black|C34=black|C35=black|C36=black|C37=black|C38=black|C40=black|C41=black|C42=black|C43=black|C44=black|C45=black|C46=black|C47=black|C48=black|C50=black|C51=black|C52=black|C53=black|C54=black|C55=black|C56=black|C57=black|C58=black|C60=black|C61=black|C62=black|C63=blue|C64=blue|C65=blue|C66=black|C67=black|C68=black|C70=black|C71=black|C72=black|C73=blue|C74=blue|C75=blue|C76=black|C77=black|C78=black|C80=black|C81=black|C82=black|C83=blue|C84=blue|C85=blue|C86=black|C87=black|C88=black}}


notes: works as expected – 11:06, July 15, 2005 (UTC)

31 36 29 76 81 74 13 18 11
30 32 34 75 77 79 12 14 16
35 28 33 80 73 78 17 10 15
22 27 20 40 45 38 58 63 56
21 23 25 39 41 43 57 59 61
26 19 24 44 37 42 62 55 60
67 72 65 4 9 2 49 54 47
66 68 70 3 5 7 48 50 52
71 64 69 8 1 6 53 46 51

question: Can you find 27 subsquares (nxn cells in n rows and n columns; values must not be consecutive) where the sum of the new diagonals, the sum of the new raws and the sum of the new columns is the identical for that particular subsquare?

usefull code[edit]

library

tasks[edit]

  1. color should follow methods; workaround: two templates available at the moment
  2. common code for changing value and color methods (transitions)
  3. generate code for next transition with User:Gangleri/tests/4x4 type square/codeTemplate:4x4 type square/code and a new parameter
  4. add an additional parameter to use either 4x4 type square/tabletemplate or 4x4 type square/table (10x10)template for the display of "final results
  5. update many of the "available since"
  6. it is probably possible to add "RTL" links to te called templates in the last line of the table Gangleri | Th | T 08:53, July 17, 2005 (UTC)

algebraic background[edit]

  1. algebraic structure of the transitions (raw and column permutations) between two of the 384 squares
    1. transitions should be supported with templates
    2. just to know: T^8 = I (reverts to the original square)

open questions[edit]

  1. in the algebraic structure of all transitions there are elements where T^n <> I for n < 8
    1. question: Is it possible to call "the same" template 8 times without being disqualified as "infinite recursion"? A workaround would be to make 8 copies but ths would be painfull solution.
  2. the sequence in which templates are called use both "diversification" (for methods and colors) and "meeting points"; it is questionable if this is somthing to benefit or not; it allows to minimize required changes and updates but increases the number of nesting levels
    1. question: What are the opinions about this?

comments[edit]

  • The greatest hindrance implementing the templates was using parameters at places / levels where they have not been defined. Gangleri | Th | T 07:28, July 14, 2005 (UTC)
  • Another hindrance is dealing with redundand (multiple) information. An example: I often change the code aonly inside the "< ... >" and wonder about strange results. Using a template would help. Anyhow temlates in templates are not supported at the moment.
see bugzilla:00662 – "Templates inside template parameters" Gangleri | Th | T 08:44, July 15, 2005 (UTC)