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A '''collision''' is an interaction between two or more [[pattern]]s that are initially disjoint and non-interacting.
A '''collision''' is an interaction between two or more [[pattern]]s that are initially disjoint and non-interacting.


Usually, each of participating patterns is a common, relatively simple [[object]] or [[reaction]]. It is often possible to [[rewind]] a collision back in time by finding [[predecessor]]s for each of the participating patterns, while preserving the moment of first interaction.
It is often possible to [[rewind]] a collision back in time by finding [[predecessor]]s for each of the participating patterns, while preserving the moment of first interaction.


Frequently discussed types of collisions include collisions between [[spaceship]]s (e.g. [[Glider synthesis|glider syntheses]]), collisions between a spaceship and a stationary pattern (e.g. [[one-glider seed]]s), collisions between several spaceships and a stationary pattern (e.g. [[synthesis component]]s).
Frequently discussed types of collisions include collisions between [[spaceship]]s (for example [[Glider synthesis|glider syntheses]]), collisions between a spaceship and a stationary pattern<ref>{{LinkForumThread|format=ref|f=2|t=3862|p=72365|title=Conjecture on collisions with small stable constellations}}</ref> (for example [[one-glider seed]]s), collisions between several spaceships and a stationary pattern (for example [[synthesis component]]s).


Less frequently, "collision" may refer to an arbitrary pattern interaction (for example, the interaction between [[queen bee shuttle]]s in the [[Gosper's glider gun]]).
Less frequently, "collision" may refer to an arbitrary pattern interaction (for example, the interaction between [[queen bee shuttle]]s in the [[Gosper's glider gun]]).
==Glider collisions==
{{related|Glider synthesis|2-glider collision|3-glider collision|4-glider collision}}
Collisions between [[glider]]s are frequently discussed in the context of [[glider synthesis]] and glider constructibility, where the aim is either to construct a specific object or pattern or to prove that it cannot be constructed.
In Life, there are 71 two-glider collisions. With three or more gliders, it is possible to construct an unbounded number of different patterns with different bounding boxes, for example pairs of [[traffic light]]s separated by different distances. With three gliders, it is still possible to describe the set of three-glider collisions systematically, as infinite families of collisions along with a finite set.<ref name="post151662">{{LinkForumThread|format=ref|p=151662|title=Re: Unproven conjectures|author=Dave Greene|date=October 2, 2022}}</ref>
=== Other rules ===
For [[alien rule]]s, the number of two-glider collisions may depend on the specific rule; the set of collisions with three or more gliders also depends on the [[evolution]] of each of two-glider collisions.<ref name="post151643">{{LinkForumThread|format=ref|p=151643|title=Re: Unproven conjectures|author=Dave Greene|date=October 1, 2022}}</ref>
The Life's [[glider]] works in 2{{sup|82}} isotropic rules expressible with [[Hensel notation]] (all of birth conditions in B2ikn3cekqry4aceijknqtwyz5aceijkqry678 and all of survival conditions in S02cikn3aceikqy4aceijnqrtwyz5678 are optional).
The set of two-glider collisions in a rule depends on presence of certain of these conditions (B2i, B2k, B2n); below are shown examples of collisions that are not collisions in Life.
{|style="margin:auto;width:300px;"
|{{EmbedViewer
|rle          = x = 13, y = 7, rule = B2i34c/S2-i3
obo$b2o$bo2$11bo$10bo$10b3o!
|viewerconfig = #C [[ HEIGHT 600 THUMBSIZE 4 ZOOM 24 X -1 Y 6 THEME Book GPS 15 AUTOSTART T 0 PAUSE 1 T 20 PAUSE 5 T 79 PAUSE 1 LOOP 80 ]]
|position    = center
|caption      = A B2i-dependent 2G collision in {{rl|Salad}} ({{cata|census/b2i34cs2-i3|B2i34c/S2-i3}})
}}
|{{EmbedViewer
|rle          = x = 14, y = 7, rule = B2k34c/S2-c34z8
11bobo$11b2o$12bo2$bo$2bo$3o!
|viewerconfig = #C [[ HEIGHT 600 THUMBSIZE 4 ZOOM 24 Y 6 THEME Book GPS 15 AUTOSTART T 0 PAUSE 1 T 20 PAUSE 5 T 79 PAUSE 1 LOOP 80 ]]
|position    = center
|caption      = A B2k-dependent 2G collision in {{rl|Simple Life}}<ref>{{LinkForumThread|format=ref|f=11|t=4411|title=Simple Life(B2k34c/S2-c34z8)}}</ref> ({{cata|census/b2k34cs2-c34z8|B2k34c/S2-c34z8}})
}}
|{{EmbedViewer
|rle          = x = 15, y = 7, rule = B2n3/S23-q
12bobo$12b2o$13bo2$bo$2bo$3o!
|viewerconfig = #C [[ HEIGHT 600 THUMBSIZE 4 ZOOM 24 X 1 Y 6 THEME Book GPS 15 AUTOSTART T 0 PAUSE 1 T 20 PAUSE 5 T 103 PAUSE 1 LOOP 104 ]]
|position    = center
|caption      = A B2n-dependent 2G collision in {{rl|LeapLife}} ({{cata|census/b2n3s23-q|B2n3/S23-q}})
}}
|}
==References==
<references>
</references>


==Also see==
==Also see==
* [[2-glider collision]], [[3-glider collision]], [[4-glider collision]]
* [[Collisions of a glider with common objects]]
* [[Collisions of a glider with common objects]]
* [[gencols]]
* [[gencols]]
* [[QuFince]]


[[Category:Collisions| ]]
[[Category:Collisions| ]]
__NOTOC__

Latest revision as of 07:17, 28 April 2023

A collision is an interaction between two or more patterns that are initially disjoint and non-interacting.

It is often possible to rewind a collision back in time by finding predecessors for each of the participating patterns, while preserving the moment of first interaction.

Frequently discussed types of collisions include collisions between spaceships (for example glider syntheses), collisions between a spaceship and a stationary pattern[1] (for example one-glider seeds), collisions between several spaceships and a stationary pattern (for example synthesis components).

Less frequently, "collision" may refer to an arbitrary pattern interaction (for example, the interaction between queen bee shuttles in the Gosper's glider gun).

Glider collisions

See also: Glider synthesis, 2-glider collision, 3-glider collision, 4-glider collision

Collisions between gliders are frequently discussed in the context of glider synthesis and glider constructibility, where the aim is either to construct a specific object or pattern or to prove that it cannot be constructed.

In Life, there are 71 two-glider collisions. With three or more gliders, it is possible to construct an unbounded number of different patterns with different bounding boxes, for example pairs of traffic lights separated by different distances. With three gliders, it is still possible to describe the set of three-glider collisions systematically, as infinite families of collisions along with a finite set.[2]

Other rules

For alien rules, the number of two-glider collisions may depend on the specific rule; the set of collisions with three or more gliders also depends on the evolution of each of two-glider collisions.[3] The Life's glider works in 282 isotropic rules expressible with Hensel notation (all of birth conditions in B2ikn3cekqry4aceijknqtwyz5aceijkqry678 and all of survival conditions in S02cikn3aceikqy4aceijnqrtwyz5678 are optional). The set of two-glider collisions in a rule depends on presence of certain of these conditions (B2i, B2k, B2n); below are shown examples of collisions that are not collisions in Life.

x = 13, y = 7, rule = B2i34c/S2-i3 obo$b2o$bo2$11bo$10bo$10b3o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 600 THUMBSIZE 4 ZOOM 24 X -1 Y 6 THEME Book GPS 15 AUTOSTART T 0 PAUSE 1 T 20 PAUSE 5 T 79 PAUSE 1 LOOP 80 ]]
A B2i-dependent 2G collision in Salad (B2i34c/S2-i3)
(click above to open LifeViewer)
x = 14, y = 7, rule = B2k34c/S2-c34z8 11bobo$11b2o$12bo2$bo$2bo$3o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 600 THUMBSIZE 4 ZOOM 24 Y 6 THEME Book GPS 15 AUTOSTART T 0 PAUSE 1 T 20 PAUSE 5 T 79 PAUSE 1 LOOP 80 ]]
A B2k-dependent 2G collision in Simple Life[4] (B2k34c/S2-c34z8)
(click above to open LifeViewer)
x = 15, y = 7, rule = B2n3/S23-q 12bobo$12b2o$13bo2$bo$2bo$3o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 600 THUMBSIZE 4 ZOOM 24 X 1 Y 6 THEME Book GPS 15 AUTOSTART T 0 PAUSE 1 T 20 PAUSE 5 T 103 PAUSE 1 LOOP 104 ]]
A B2n-dependent 2G collision in LeapLife (B2n3/S23-q)
(click above to open LifeViewer)

References

  1. ↑ Conjecture on collisions with small stable constellations (discussion thread) at the ConwayLife.com forums
  2. ↑ Dave Greene (October 2, 2022). Re: Unproven conjectures (discussion thread) at the ConwayLife.com forums
  3. ↑ Dave Greene (October 1, 2022). Re: Unproven conjectures (discussion thread) at the ConwayLife.com forums
  4. ↑ Simple Life(B2k34c/S2-c34z8) (discussion thread) at the ConwayLife.com forums

Also see

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