Category:3-ary Boolean functions in octeract matrix; faction clusters
See also category: 3-ary Boolean functions; graphs of faction clusters.
Entries with the same color belong to the same faction.
The colors are basically red, blue, yellow and green, indicating the four quadrants.
The shade of this color is determined by the consul weight. The smaller one corresponds to the light shade.
The light and dark part of each matrix is the intersection of truth tables and Zhegalkin indices of great dominions. (See here.)
E.g. the dark part of this matrix is the intersection of T 14 and Z 8. In the caption this is expressed by the pair (14, 8).
The other shade in the same matrix has the reversed pair. (Gentle factions have pairs with equal entries.)
Different small clusters in the same big cluster have the same patron dominion.
small clusters[edit]
Small clusters are defined with the complement and twin relationships. There are 13 of them.
4 factions[edit]
| faction size 1 federations 0 | 42 consul weights 0 | 3 | |||
|---|---|---|---|
.svg) |
.svg) | ||
| |||
| faction size 3 federations 44 | 6 consul weights 1 | 2 | |||
|---|---|---|---|
.svg) |
.svg) | ||
| |||
| faction size 6 federations 2 | 26 consul weights 1 | 2 | |||
|---|---|---|---|
.svg) |
.svg) | ||
| |||
8 factions[edit]
| faction size 1 federations 22, 104 consul weights 0, 3 |
|---|
.svg) dark: (22, 104) (consul weight 3) |
| faction size 3 federations 8, 42 | 14, 44 consul weights 0, 1 | 2, 3 | |||
|---|---|---|---|
.svg) dark: (42, 8) (consul weight 1) |
.svg) dark: (44, 14) (consul weight 3) | ||
| |||
| faction size 3 federations 8, 14 | 2, 22 consul weights 0, 2 | 1, 3 | |||
|---|---|---|---|
.svg) dark: (14, 8) (consul weight 2) |
.svg) dark: (2, 22) (consul weight 3) | ||
| |||
| faction size 3 federations 2, 110 consul weights 1, 2 |
|---|
.svg) dark: (110, 2) (consul weight 2) |
| faction size 6 federations 26, 44 consul weights 1, 2 |
|---|
.svg) dark: (26, 44) (consul weight 2) |
big clusters[edit]
.svg)
A third relationship between factions is flipping the highest bit. (Flipping of the lowest bit is implied from the two others.)
Big clusters are defined with all three relationships. There are 8 of them.
Their entries in the 16×16 matrix form 2×2 squares, essentially making them entries of an 8×8 matrix.
(This means, that the lowest and highest bit are irrelevant to big clusters.)
| 8 factions in two small clusters obtuse | ||
|---|---|---|
_(3).svg) consul weights 0, 3 |
_(2).svg) consul weights 1, 2 |
_(2).svg) consul weights 1, 2 |
| 8 factions in one small cluster acute | ||
|---|---|---|
consul weights 0, 3 |
consul weights 1, 2 |
consul weights 1, 2 |
| 16 factions in two small clusters | |
|---|---|
_(2_3).svg) consul weights 0, 1 (white numbers) and 2, 3 (black numbers) acute |
_(1_3).svg) consul weights 0, 2 (white numbers) and 1, 3 (black numbers) obtuse |
Subcategories
This category has only the following subcategory.
Pages in category "3-ary Boolean functions in octeract matrix; faction clusters"
This category contains only the following page.
Media in category "3-ary Boolean functions in octeract matrix; faction clusters"
The following 10 files are in this category, out of 10 total.
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3-ary Boolean functions; faction cluster 4x1 (0).svg 870 × 870; 15 KB
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3-ary Boolean functions; faction cluster 4x1 (3).svg 870 × 870; 15 KB
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3-ary Boolean functions; faction cluster 4x3 (1).svg 870 × 870; 15 KB
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3-ary Boolean functions; faction cluster 4x3 (2).svg 870 × 870; 15 KB
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3-ary Boolean functions; faction cluster 4x6 (1).svg 870 × 870; 15 KB
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3-ary Boolean functions; faction cluster 4x6 (2).svg 870 × 870; 15 KB
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3-ary Boolean functions; faction cluster 8x3 (0 1).svg 870 × 870; 15 KB
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3-ary Boolean functions; faction cluster 8x3 (0 2).svg 870 × 870; 15 KB
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3-ary Boolean functions; faction cluster 8x3 (1 3).svg 870 × 870; 15 KB
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3-ary Boolean functions; faction cluster 8x3 (2 3).svg 870 × 870; 15 KB