OCA:2×2
| 2x2 | |
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| Rulestring | 125/36 B36/S125 |
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| Character | Chaotic |
2x2 is a Life-like cellular automaton in which cells survive from one generation to the next if they have 1, 2 or 5 neighbours, and are born if they have 3 or 6 neighbours. Its name comes from the fact that it sends patterns made up of 2x2 blocks to patterns made up of 2x2 blocks.
Patterns under the rule have a chaotic evolution similar to those under the standard Life rules, but the chaos tends to die out much more quickly.
Notable Patterns
A large variety of still lifes and oscillators appear spontaneously from randomly generated starting states. There is also a somewhat rare naturally-occurring spaceship, which travels at c/8 diagonally.
Still Lifes
Still lifes are generally smaller in 2x2 than in Life, with the smallest occurring having a population of just 2 cells. These still life patterns still tend to be similar to Life patterns in terms of structure, for example often having islands that stabilise each other. Many still lifes from Life are also still lifes in 2x2, For example, the beehive, tub, loaf, pond and mango.
Enumerating the still lifes
The following table catalogs all still lifes in the 2x2 rule with 10 or fewer cells.[1]
| Size | Count | Image | Links |
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| 1 | 0 | ||
| 2 | 2 | 
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Download RLE: click here |
| 3 | 1 | 
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| 4 | 3 | 
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Download RLE: click here |
| 5 | 4 | 
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| 6 | 9 | 
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| 7 | 10 | 
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| 8 | 27 | 
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| 9 | 48 | 
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| 10 | 126 | 
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Download RLE: click here |
Common still lifes
The following table lists the twenty most common strict still lifes that arise after several generations of a random starting pattern.[2] The "approx. rel. freq." column gives an estimate of the proportion of all randomly-occurring still lifes that will be of the given type.
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Oscillators
A large variety of oscillators of various periods occur naturally in 2x2.
Period two oscillators
Many of the period 2 oscillators in 2x2 have a single-cell 'on-off' rotor, with small variations in the stator of the oscillator. These occur fairly frequently naturally.
Higher-period oscillators
One of the most interesting aspects of the 2x2 rule is the large number of naturally-occurring higher-period oscillators. Oscillators with periods 3, 4, 6, 8, 10, 14, 22 and 26 are all relatively frequent, and oscillators are also known for periods 5, 11, 12, 17, and 60.
One simple infinite family of oscillators is given by the 2×(4n) boxes of alive cells. The period of such oscillators for n = 1, 2, 3, ... is given by the sequence 2, 6, 14, 14, 62, 126, 30, 30, 1022, ...
Naturally occurring oscillators
The following table lists the twenty most common oscillators that arise after several generations of a random starting pattern.[2] The "approx. rel. freq." column gives an estimate of the proportion of all randomly-occurring oscillators that will be of the given type.
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Spaceships
There are a number of spaceships known to occur in 2x2 [3]. Of these, only one is known to occur naturally from soup. It travels at c/8 diagonally.
Other patterns
No infinite-growth mechanisms (guns, puffers etc.) have yet been discovered in 2x2.