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

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

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Section V - Demonstrating [ Quasi 24-Symmetry ] - Phase II

Summary for the Section :

• In this Section , we shall use again the pattern [ Pattern AARON ] as the [ Core Pattern ] for our Expansion-Mapping Process ,
  • but with a different choice for the [ Anchor Pattern ] .

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

• Let us now select the [ Base Pattern ] in { Row 3 , Column 3 } as our [ Anchor Pattern ] ;
  • i.e. :

  

  • the [ Base Structural Pattern ] as marked-off in [ dark-grey color ] in the diagram above .

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

• Let us now bring-in the pattern [ Pattern AARON ] :

  

  • 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	PURPLE	BLUE	YELLOW	CYAN	MAGENTA	ORANGE	GREEN

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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 resultant set of 24 patterns , as per the diagram on-the-right above .

  And we shall name this particular [ set of 24 patterns ] as the [ 24 QSM-Patterns --- GAMMA Series ] .

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Comparing the [ ALPHA Series ] and the [ GAMMA Series ] :

• Let us bring-in the two (2) sets of [ 24 QSM-Patterns ] :
  • the [ 24 QSM-Patterns --- ALPHA Series ] and the [ 24 QSM-Patterns --- GAMMA Series ] ,
    • for a quick comparison :

  

• Do we have a match here ?
  • And the answer is YES .

  

  • We see here that all of the 24 patterns are fully accounted-for in both the [ ALPHA Series ] and the [ GAMMA Series ] .

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go to the next section : Section VI - Demonstrating [ Quasi 24-Symmetry ] - Phase III

go to the last section : Section IV - Demonstrating [ Quasi 24-Symmetry ] - Phase I

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

Original dated 2011-3-06