Quasi 24-Symmetry Phase V

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

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

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

Summary for the Section :

In this Section , we shall use the pattern [ Pattern KARINA ] as the [ Core Pattern ] for our Expansion-Mapping Process ,
- but with the same choice for the [ Anchor Pattern ] as in the last Section ,
  - to see what we might possibly come up with .

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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 KARINA ] :
- 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	BLUE	YELLOW	PURPLE	MAGENTA	GREEN	ORANGE	CYAN

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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 --- IOTA Series ] .

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Comparing the [ EPSILON Series ] and the [ IOTA Series ] :

Let us bring-in the two (2) sets of [ 24 QSM-Patterns ] :
- the [ 24 QSM-Patterns --- EPSILON Series ] and the [ 24 QSM-Patterns --- IOTA 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 [ EPSILON Series ] and the [ IOTA Series ] .

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The question here on [ Quasi 24-Symmetry ] :

The question , at this point , is :
- Whether we have the same kind of [ Quasi 24-Symmetry ] here in the [ 24 QSM-Pattern --- EPSILON Series ]
  
  that we have previouly for the [ 24 QSM-Patterns --- ALPHA Series ] ?
And the answer here is Yes .

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go to the next section : Section X - Splitting the 5,040 [ Circular-Ring Patterns ] into 210 x [ sets of 24 ]

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

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

Original dated 2011-3-06