Difference between revisions of "OCA:2×2"
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'''2x2''' is a [[cellular automaton#Well-known Life-like cellular automata|Life-like cellular automaton]] in which [[cell]]s 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. | '''2x2''' is a [[cellular automaton#Well-known Life-like cellular automata|Life-like cellular automaton]] in which [[cell]]s 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 | Patterns under the rule have a chaotic evolution similar to those under the [[Conway's Game of Life|standard Life rules]], but the chaos tends to die out much more quickly. | ||
==Notable Patterns== | ==Notable Patterns== | ||
A large variety of [[still life]]s and [[oscillators]] appear spontaneously from randomly generated starting states. There is also a somewhat rare [[spaceship]], which travels at c/8 diagonally. | A large variety of [[still life]]s 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=== | ||
Still lifes are generally smaller in 2x2 than in Life, with the smallest occurring having a | 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 | population of just 2 cells. These still life patterns still tend to be similar to Life patterns in terms | ||
of structure, for example having | of structure, for example often having islands that stabilise each other. | ||
Many still | Many still lifes from Life are also still lifes in 2x2, For example, the [[beehive]], [[tub]], [[loaf]], [[pond]] and [[mango]]. | ||
[[Image:2x2stills.png|framed|center|Some sample still lifes.<br />'''Manipulate via Java:''' [http://www.conwaylife.com/?p=2x2stills click here]<br />'''Download [[RLE]]:''' [http://www.conwaylife.com/pattern.asp?p=2x2stills click here] ]] | [[Image:2x2stills.png|framed|center|Some sample still lifes.<br />'''Manipulate via Java:''' [http://www.conwaylife.com/?p=2x2stills click here]<br />'''Download [[RLE]]:''' [http://www.conwaylife.com/pattern.asp?p=2x2stills click here] ]] | ||
====Enumerating the still lifes==== | ====Enumerating the still lifes==== | ||
Thus far, little effort has gone into counting all possible still lifes in 2x2. The following results are estimates based on patterns which have occurred naturally. | |||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
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===Oscillators=== | ===Oscillators=== | ||
A large variety of | A large variety of oscillators of various periods occur naturally in 2x2. | ||
====Period two oscillators==== | ====Period two oscillators==== | ||
Many of the [[period]] 2 oscillators in 2x2 have a single-cell 'on-off' [[rotor]], with small variations in the | 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 | [[stator]] of the oscillator. These occur fairly frequently naturally. | ||
[[Image:2x2_p2s.gif|framed|center|Some period 2 oscillators.<br />'''Manipulate via Java:''' [http://www.conwaylife.com/?p=2x2_p2s click here]<br />'''Download [[RLE]]:''' [http://www.conwaylife.com/pattern.asp?p=2x2_p2s.rle click here] ]] | [[Image:2x2_p2s.gif|framed|center|Some period 2 oscillators.<br />'''Manipulate via Java:''' [http://www.conwaylife.com/?p=2x2_p2s click here]<br />'''Download [[RLE]]:''' [http://www.conwaylife.com/pattern.asp?p=2x2_p2s.rle click here] ]] | ||
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Other oscillators can be made from 2×n boxes. For example, when n=4 a period 2 oscillator is | Other oscillators can be made from 2×n boxes. For example, when n=4 a period 2 oscillator is | ||
formed, and when n=8, the | formed, and when n=8, the rectangular oscillator formed has a period of 6. | ||
[[Image:2x2glider.gif|framed|right|The c/8 glider.<br />'''Manipulate via Java:''' [http://www.conwaylife.com/?p=2x2glider click here]<br />'''Download [[RLE]]:''' [http://www.conwaylife.com/pattern.asp?p=2x2glider.rle click here] ]] | [[Image:2x2glider.gif|framed|right|The c/8 glider.<br />'''Manipulate via Java:''' [http://www.conwaylife.com/?p=2x2glider click here]<br />'''Download [[RLE]]:''' [http://www.conwaylife.com/pattern.asp?p=2x2glider.rle click here] ]] | ||
Revision as of 10:51, 19 March 2009
| 2x2 | |
| View static image | |
| View animated image | |
| Rulestring | 125/36 B36/S125 |
|---|---|
| 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
Thus far, little effort has gone into counting all possible still lifes in 2x2. The following results are estimates based on patterns which have occurred naturally.
| Size | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| # of Still lifes | 0 | 2 | 1 | 3 | 4 | 9 | 10 | ~25 | Unknown | Unknown |
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.
High-period Oscillators
One of the most interesting aspects of this rule is the large number of naturally occurring higher-period oscillators. Patterns with periods 10, 11, 14, 17, 22 and 26 are all relatively frequent.
Manipulate via Java: click here
Download RLE: click here
Other oscillators can be made from 2×n boxes. For example, when n=4 a period 2 oscillator is formed, and when n=8, the rectangular oscillator formed has a period of 6.
Spaceships
There are a number of spaceships known to occur in 2x2 [1]. 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.
References
- ↑ "2x2 (B36/S125)". David Eppstein. Retrieved on March 18, 2009.