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

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

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Section XXII - Understanding Physical [ Quasi 24-Symmetry ] - Phase II

Summary for the Section :

• In this 2nd-of-3-Sections , we shall do another round of the Expansion-Mapping Procedure , same as in Part II of this paper ,
  • using again the [ 24 Base Structural Patterns ] from Section III ;

  and

  • the [ Core Pattern ] that we shall be using here is then [ Pattern RYAN ] ,
    • an [ 8-colors pattern ] related in a specific way to [ Configuration Mount Robson ] .

  And once we have completed the Expansion-Mapping process ,

  • we are ready for a quick comparison with the results from the last Section , i.e. :
    • the set-of-24 [ 8-colors sequences ] and the set-of-24 [ 8-numbers strings ]

      derived from the [ 24 QSM-Configurations --- Canadian Rockies Series ] .

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The 8-colors-pattern [ Pattern Ryan ] :

• Let us now bring-in the new 8-colors-pattern [ Pattern RYAN ] :
  • 
    • for our use in the Expansion-Mapping process below .

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The relation between [ Configuration Mount Robson ] and [ Pattern RYAN ] :

• It is important to state-out , at this point , the exact relation between [ Configuration Mount Robson ] and [ Pattern RYAN ] ,
  • ahead of the Expansion-Mapping process to follow .

  And the relation here is that :

  • Whenever we do the conversion of [ Configuration Mount Robson ] into a [ 8-colors sequence ] ;
    • using the [ Fu-Hei Scheme of Fixed-Positions ] and the [ ASCENDING Read-Off Order ] ;

  

  • the resultant [ 8-colors sequence ] and [ Pattern RYAN ] will always match exactly .

    

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Bringing-in the [ 24 Base Structural Patterns ] from before :

• Let us now bring-in the [ 24 Base Structural Patterns ] from Section III , and :
  • let us select , again , the [ Base Pattern ] in { Row 1 , Column 1 } 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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The Colors-to-Numbers Matching Process :

• Let us now bring-in [ Pattern RYAN ] from above , and
  • use this as the [ Core Pattern ] for our Expansion-Mapping process .

  Let us now do the [ Colors-to-Numbers Matching Process ] ,

  

  • 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	ORANGE	GREEN	BLUE	CYAN	YELLOW	PURPLE

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The Expansion-Mapping Process :

• Let us now do the 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 --- RHO Series ] .

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Converting the [ 24 QSM-Patterns --- RHO Series ] into the [ 8-numbers strings ] :

• Let us now do the conversion of the [ 24 QSM-Patterns --- RHO Series ] into [ 8-colors strings ] ,
  • using the [ FIRST-UP Color-to-Numbers Conversion Scheme ] :

    i.e. :

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

  

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A Quick Comparison :

• It is appropriate to bring-back , at this point ,
  • the results of the last Section for a quick comparison .

• First , we compare the 2 [ sets-of-24 ] for the [ 8-colors sequences ] :
  • on-the-left below is then the [ 24 QSM-Patterns --- RHO Series ] from this Section ,

  • on-theright below the set-of-24 [ 8-colors sequences ] from the last Section :
    • from the [ 24 QSM-Configurations --- Canadian Rockies Series ] converted via [ Fu-Hei / ASCENDING ] .

  

  • And we see here that the two (2) [ sets-of-24 ] matched exactly , on a grid-for-grid basis .

• Secondly , we compare the [ set-of-24 ] for the [ 8-numbers strings ] :
  • on-the-left below is then the set-of-24 [ 8-numbers strings ] from this Section ,

  • on-the-right below is then the set-of-24 [ 8-numbers strings ] from the last Section ,

  

  • And we see here that the two (2) [ sets-of-24 ] matched exactly , on a grid-for-grid basis .

  But this is really redundant , and this is because :

  • Once the 2 [ sets-of-24 ] matched at the [ 8-colors sequences ] level ,
    • applying the same [ Colors-to-Numbers Conversion Scheme ] to both sets will always yield :
      • matching [ sets-of-24 ] at the [ 8-numbers strings ] level .

  And in the case above , we applied the [ FIRST-UP Colors-to-Numbers Conversion Scheme ]

  • to both of the 2 matching sets at the [ 8-colors sequences ] level ,

    and :

    • exact-matches at the [ 8-numbers strings ] level are therefore inevitable .

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But what does this all mean :

• Let us bring-in again the 2 matching [ sets-of-24 ] at the [ 8-colors sequences ] level :

  

  Lets us recall that the diagram on-the-left above , the [ 24 QSM-Patterns --- RHO Series ] :

  • arose from an Expansion-Mapping procedure using the [ 24 Base Structural Patterns ] from Section III
    • with [ Pattern RYAN ] as the [ Core Pattern ] for the expansion .

  As such ,

  • the [ 24 Base Structural Patterns ] from Section III is therefore intrinsic to the [ Structural Mapping relations ] here .

• And the fact that the diagrams on-the-left and on-the-right matched exactly then tell us that :
  • the [ 24 Base Structural Patterns ] from Section III is also intrinsic to the [ Structural Mapping relations ]
    • for the diagram on-the-right .

• In short , when we do the conversion for the [ 24 QSM-Configurations --- Canadian Rockies Series ] ,
  • via using the [ Fu-Hei Scheme of Fixed-Positions ] and the [ ASCENDING Read-Off Scheme ] ;

  the [ 24 Base Structural Patterns ] from Section III is indeed the correct [ set-of-24 patterns ] to use :

  • to quantify the [ Structural Mapping relations ] of the derived set of [ 8-colors sequences ] .

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go to the next section : Section XXIII - Understanding Physical [ Quasi 24-Symmetry ] - Phase III

go to the last section : Section XXI - Understanding Physical [ Quasi 24-Symmetry ] - Phase I

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

Original dated 2011-3-06