Quasi 24-Symmetry Phase IV

On 8-Colors Combinatorics and [ Quasi 24-Symmetry ]

by Frank C. Fung ( 1st published in March, 2011. )

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Section VIII - Demonstrating [ Quasi 24-Symmetry ] - Phase IV

Summary for the Section :

In this Section , we shall do another round of the Expansion-Mapping Procedure , same as before :
- but will now bring-in a new [ 8-colors circular-ring-pattern ] , [ Pattern ANITA ] , to serve as the [ Core Pattern ] ;
for the purpose of finding out :
- whether there exist other 24-elements [ Quasi 24-Symmetric Sets ] within
  
  the { Reduced Set of 5,040 [ 8-Colors Circular-Ring Patterns ] with the Red-Color in Fixed-Position [ FP-1 ] } framework .

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Selecting an [ Anchor Pattern ] for our Expansion-Mapping Process :

Let us now select again the [ Base Pattern ] in { Row 1 , Column 1 } as our [ Anchor Pattern ] ;
- i.e. :

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Bringing-in the pre-selected [ 8-colors circular-ring-pattern ] :

Let us now bring-in the pattern [ Pattern ANITA ] :
- a pattern different from the [ 24 QSM-Patterns ] in the ALPHA / BETA / GAMMA / DELTA series ;
and use this as the [ Core Pattern ] of our Expansion-Mapping Process .

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The Colors-to-Numbers Matching Process :

We then have , for the Colors-to-Numbers Matching Process , this set of 2 diagrams below :

matching the [ Anchor Pattern ] on-the-left against the [ Core Pattern ] on-the-right .

And the [ Colors-to-Numbers Assignment Scheme ] here , based on the above , is then :

Color #1	Color #2	Color #3	Color #4	Color #5	Color #6	Color #7	Color #8
***********	***********	***********	***********	***********	***********	***********	***********
RED	MAGENTA	YELLOW	ORANGE	CYAN	PURPLE	GREEN	BLUE

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The Expansion-Mapping Process :

Let us now do the full Expansion-Mapping process , using the [ Colors-to-Numbers Assignment Scheme ] from above ,
- to arrive at the full set of 24 patterns , as per the diagram on-the-right below .
And we shall name this particular [ set of 24 patterns ] as the [ 24 QSM-Patterns --- EPSILON Series ] ;
- for our comparison with the [ 24 QSM-Patterns --- IOTA Series ] , yet-to-come in the next Section .

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Identifying the pattern [ Pattern KARINA ] for our use :

Let us now also identify the [ 8-colors circular-ring-pattern ] in { Row 2 , Column 4 } in the diagram on-the-right above ,
- i.e. , this pattern :
  
  as the pattern [ Pattern KARINA ] , for our use in the next Section .

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go to the next section : Section IX - Demonstrating [ Quasi 24-Symmetry ] - Phase V

go to the last section : Section VII - Summarizing on the [ Quasi 24-Symmetry ] Criteria

return to the 8-Colors Combinatorics / Quasi 24-Symmetry HomePage

Original dated 2011-3-06