OCA:Gems
| Gems | |
| View static image | |
| Rulestring | 4568/3457 B3457/S4568 |
|---|---|
| Rule integer | 188600 |
| Character | Explosive |
| Black/white reversal | B15678/S02678 |
Gems is a Life-like cellular automaton in which dead cells are born if they have precisely three, four, five or seven live neighbors, and in which live cells will survive if they have precisely four, five, six or eight live neighbors. Small random initial configurations in Gems tend to turn into high-period oscillators (the "gems" the rule is named after); larger random initial configurations explode slowly.
Patterns
No odd period oscillators have been found in Gems.
Still lives
No finite still lifes can exist in Gems. 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 B3457/S4568 in the next tick, it must have at least 4 alive neighbours; the only possibility is that the alive neighbours are the cell to the right of C and three neighbouring cells in the next row:
0 0 0 0 0 0 0 0 0 0 0 1 1 ? ? ? < the first nonempty row; C is the leftmost alive cell ? x 1 1 1 ? ? ? state of cells denoted 'x' or '?' are unspecified ? ? ? ? ? ? ? ?
Then the dead cell to the left of C will be born in the next generation, either via B3 (if the cell 'x' is dead) or via B4 (if the cell 'x' is alive). This contradicts the assumption that C is the leftmost alive cell in the first nonempty row of a finite still life.
Spaceships
Gems has a single known spaceship moving orthogonally at a speed of c/5648, David Eppstein's glider 13047.[1] This is the slowest known elementary spaceship in any two-state outer-totalistic rule. It was also the slowest known across all two-state isotropic rules until it was surpassed by a c/5953 spaceship in the rule B2-an3acqry4cnw5-cj6cei78/S1c2n3-nqy4acknqtw5-ijkr6ei78, found by Arie Paap in July 2019.[2]
| Glider 13047 (click above to open LifeViewer) RLE: here Plaintext: here Catagolue: here |
Similar rules
A related rule is Gems Minor which removes eight from the survive list, but adds it to the birth list. It also has many high period oscillators and a slow spaceship, this one moving orthogonally at c/2068.
| Gems Minor | |
| Rulestring | 456/34578 B34578/S456 |
|---|---|
| Rule integer | 57784 |
| Character | Explosive |
| Black/white reversal | B015678/S2678 |
| c/2068 ship (click above to open LifeViewer) RLE: here Plaintext: here Catagolue: here |
References
- ↑ Glider 13047
- ↑ Arie Paap (July 24, 2019). Re: Smallest Spaceships Supporting Specific Speeds (5s) Project (discussion thread) at the ConwayLife.com forums
External links
- Gems: Long Live the Oscillators, and the Slowest Glider
- Gems at Adam P. Goucher's Catagolue
- Gems at David Eppstein's Glider Database
- Gems (B3457/S4568) (discussion thread) at the ConwayLife.com forums
- Gems Minor at Adam P. Goucher's Catagolue