OCA:2×2
| 2x2 | |
| View static image | |
| View animated image | |
| Rulestring | 125/36 B36/S125 |
|---|---|
| Character | Chaotic |
2x2 is a Life-like cellular automaton in which cell birth occurs with 3 or 6 neighbors, and survival occurs on 1, 2 or 5. Patterns in the rule have a similar chaotic evolution to the standard Life rules, although the chaos tends to die out much sooner.
Notable Patterns
A large variety of still lifes and oscillators appear spontaneously from randomly generated starting states. There is also a rare spaceship, which travels at c/8 diagonally.
Still Lifes
Still patterns are generally smaller in 2x2 than in Life; the smallest occuring have populations of only 2 cells. In 2x2, still patterns tend to be similar to Life in terms of structure; ie. forming patterns with islands stabilising each other. Many still patterns from life also work in 2x2, For example, the beehive, tub, loaf, pond and mango.
Enumerating the still lifes
So far little effort has gone into counting all possible still lifes in 2x2. The following results are based on patterns which have occured naturally.
| Size | Still lifes |
|---|---|
| 1 | 0 |
| 2 | 2 |
| 3 | 1 |
| 4 | 3 |
| 5 | 4 |
| 6 | 9 |
| 7 | 10 |
| 8 | ~25 |
| 9 | Unknown |
| 10 | Unknown |
Oscillators
A large variety of patterns of many periods occur naturally in 2x2.
P2 Oscillators
Many of the p2s in 2x2 have a single cell 'on-off' rotor, with small variations in the
still casing of the oscillator. These occur relatively frequently naturally.
High-period Oscillators
One of the most interesting aspects of this rule is the higher-period oscillators that
appear naturally. Patterns with p10, 11, 14, 17, 22 and 26 are all relatively frequent.
Other oscillators can be made from 2xn boxes. For example, when n=4 a p2 oscillator is
formed, and when n=8, the rectangle oscillates at p6.
Spaceships
There are a selection of ships known in 2x2 [1]. Of these, only one is known to occur naturally from random soups. It travels at c/8 diagonally.
Other patterns
No infinite-growth mechanisms (guns, puffers etc.) have yet been discovered in 2x2.
References
- ↑ "2x2 (B36/S125)". David Eppstein. Retrieved on March 18, 2009.