Difference between revisions of "Black/white reversal"
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Apple Bottom (talk | contribs) (New glossary entry) |
Apple Bottom (talk | contribs) m (Correct example) |
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# B = 36; S = 125 | # B = 36; S = 125 | ||
# B′ = 0124578; S′ = | # B′ = 0124578; S′ = 034678 | ||
# B″ = 0134678; S″ = | # B″ = 0134678; S″ = 012458 | ||
Therefore, the black/white reversal of B36/S125 is | Therefore, the black/white reversal of B36/S125 is B012458/S0134678. |
Revision as of 10:47, 2 July 2016
Black/white reversal (or complement) can refer to two related concepts:
- The black/white reversal of a pattern is the result of toggling the state of each cell in the universe: bringing dead cells to life, and killing live cells.
- The black/white reversal of a rule is a transformation of a rule in such a way that the black/white reversal of any pattern (in the previous sense) will behave the same way under the new rule as the unreversed pattern did under the original rule.
Each rule has precisely one black/white reversal; if this is the same as the rule itself, the rule is said to be self-complementary.
Determining the black/white reversal of a rule
To determine the black/white reversal of a given rule:
- Negate the rule's B and S conditions, yielding B′ and S′.
- Subtract each condition in B′ and S′ from 8, yielding B″ and S″.
- The black/white reversal of B/S is S″/B″.
For example, using the rule B36/S125:
- B = 36; S = 125
- B′ = 0124578; S′ = 034678
- B″ = 0134678; S″ = 012458
Therefore, the black/white reversal of B36/S125 is B012458/S0134678.