OCA:LongLife
| LongLife | |
| View static image | |
| Rulestring | 5/345 B345/S5 |
|---|---|
| Rule integer | 16440 |
| Character | Stable |
| Black/white reversal | B01245678/S012678 |
|
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LongLife (also Long Life) is a Life-like cellular automaton in which cells survive from one generation to the next if they have 5 neighbours, and are born if they have 3, 4, or 5 neighbours. The rule has been studied by Andrew Trevorrow.
LongLife is characterized by abundant natural high-period oscillators, composed of alternating rows, that appear to be unable to escape their bounding diamond. There are no known spaceships in LongLife, but the rule is on David Eppstein's "most-wanted" list.[1]
| The "White Whale", an example of a period-160,000,346 oscillator in LongLife given by Andrew Trevorrow (click above to open LifeViewer) RLE: here Plaintext: here |
No finite still lifes can exist in LongLife. Assume (for contradiction) that a finite still life exists, and let C denote the leftmost alive cell in the first nonempty row. For the cell C to survive under the rule B345/S5 in the next tick, it must have exactly 5 alive neighbours, including at least one of the positions marked 'x' below:
0 0 x x x 0 0 0 0 0 x 1 ? ? ? ? < the first nonempty row; C is the leftmost alive cell (the '1') ? ? ? ? ? ? ? ? state of cells denoted 'x' or '?' are unspecified
This contradicts the assumption that C is the leftmost alive cell in the first nonempty row of a finite still life.
References
- ↑ David Eppstein. "Most Wanted". Which "Life"-Like Systems Have Gliders?. Retrieved on 2016-09-29.
External links
- LongLife at Adam P. Goucher's Catagolue
- LongLife at David Eppstein's Glider Database
- MCell built-in Life rules: Long life at Mirek Wójtowicz's Cellebration page