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

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

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Section XXI - Understanding Physical [ Quasi 24-Symmetry ] -- Phase I

Summary for the Section :

• In this Section and the next 2 Sections , we shall attempt to establish the following :
  • Whenever we convert a set of [ 24 QSM-Configurations ] into [ 8-colors sequences ] and [ 8-numbers strings ] ,
    • via using the [ Fu-Hei Scheme of Fixed-Positions ] and the [ ASCENDING Read-Off Scheme ] ;

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

    • to quantify the underlying [ Structural Mapping relations ]

      for both the set-of-24 [ 8-colors sequences ] and the set-of-24 [ 8-numbers strings ] .

• And in this 1st-of-3-Sections , we shall set up another set of 24 [ Quasi 24-Symmetric 8-colors configurations ] , namely :
  • the [ 24 QSM-Configurations --- Canadian Rockies Series ] .

  And we shall also up the associated [ 8-colors sequences ] and [ 8-numbers Strings ] ,

  • for our comparison in the next-Section-to-come .

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Bringing-in [ Configuration Mount Robson ] :

• Let us now bring-in a new [ 8-colors configuration ] ,
  • [ Configuration Mount Robson ] :

    

    • for our use in this Section and beyond .

  And we simply note here that :

  • [ Configuration Mount Robson ] is different from [ Configuration Annapurna ] , and

  • [ Configuration Mount Robson ] is not one of the [ 24 QSM-Configurations --- Himalaya Series ] .

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Expanding with [ Configuration Mount Robson ] as the base-configuration :

• Let us now use [ Configuration Mount Robson ] as the base-configuration of our expansion process ,

  i.e. :

  • we plug-in [ Configuration Mount Robson ] into [ Position A ] in the Linkage Diagram on-the-right , below ;

  

  • and start expanding , via using a sufficient number of :
    • [ 2-notch rotations in the -X / -Y / -Z Axial-Direction ] .

• And we would then arrive at this set of 24 [ 8-colors configurations ] :
  • as per the diagram on-the-left , below .

  

  And we shall name this set of 24 [ 8-colors configurations ] :

  • the [ 24 QSM-Configurations --- Canadian Rockies Series ] .

  

  ( QSM stands for Quasi-SymMetric and Mount Robson is a mountain the Canadian Rockies Mountain Range . )

Coverting the 24 [ QSM-Configurations ] to [ 8-Colors Sequences ] :

• Let us now quickly do the conversion to the [ 8-colors sequences ] ,
  • using the [ Fu-Hei Scheme of Fixed-Positions ] and the [ ASENDING Read-Off Order ] ;

    i.e. :

    • 

  to arrive at this set of 24 [ 8-colors sequences ] , as per the diagram on-the-right , below .

  

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Converting to the [ 8-numbers strings ] :

• Let us now convert the above 24 [ 8-colors sequences ] into the [ 8-numbers strings ] ,
  • using the [ FIRST-UP Colors-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

  • to arrive at the diagram on-the-right , below .

  

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Getting Ready for Future Comparisons :

• We also bring-in , at this point , this set of 2 diagrams for the [ 24 QSM-Configurations --- Canadian Rockies Series ] , below :

  

  • which will be useful in our comparisons to follow in later Sections .

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

go to the last section : Section XX - Quasi 24-Symmetry arising from the Half-On-Half Rotations

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

Original dated 2011-3-06