Bracketope (EntityClass, 3)
From Hi.gher. Space
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;[[Partially useless bracketope]]s (*, asterisk) | ;[[Partially useless bracketope]]s (*, asterisk) | ||
| - | :A ''partially | + | :A ''partially useless bracketope'' is a bracketope whose [[vertex graph]] is identical to that of a pure bracketope. |
;[[Pure bracketope]]s | ;[[Pure bracketope]]s | ||
Revision as of 08:57, 15 March 2008
A bracketope is any shape which can be defined using bracket notation.
Sets of bracketopes by complexity
- Totally useless bracketopes (&, ampersand)
- A totally useless bracketope is a bracketope which is similar to a pure bracketope.
- Partially useless bracketopes (*, asterisk)
- A partially useless bracketope is a bracketope whose vertex graph is identical to that of a pure bracketope.
- Pure bracketopes
- A pure bracketope is a bracketope which is not partially or totally useless.
- A question mark indicates that it is unknown whether this bracketope is pure.
Determining bracketopes' purity
If two or more bracketopes are similar to each other, the one with the lowest bracketopic index is pure and all others are totally useless.
Bracketopic statistics
Here is a table to show the number and percentage of various types of bracketopes in each dimension.
| Dimension | Bracketopes | Totally useless | Partially useless | Pure | Rotopes | Strange rotopes | Pure rotopes |
| 1 | 1 | 0 (0%) | 0 (0%) | 1 (100%) | 1 (100%) | 0 (0%) | 1 (100%) |
| 2 | 3 | 1 (33%) | 0 (0%) | 2 (67%) | 2 (67%) | 0 (0%) | 2 (67%) |
| 3 | 9 | 0 (0%) | 3 (33%) | 6 (67%) | 3 (33%) | 0 (0%) | 3 (33%) |
| 4 | 36 | 3 (8%) | 9 (25%) | 24 (67%) | 5 (14%) | 1 (3%) | 4 (11%) |
| 5 | 144 | 0 (0%) | 65 (45%) | 79 (55%) | 7 (5%) | 2 (1%) | 5 (3%) |
| Trend | Increasing | Unknown | Unknown | Decreasing % | Decreasing % | Unknown | Decreasing % |
Finding bracketopes
There is currently one main method for finding bracketopes:
