Difference between revisions of "OCA:Tlife"

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{{ambox|text=See forum thread [https://conwaylife.com/forums/viewtopic.php?f=16&t=6235 "Rule definition terminology"] for a discussion of which wording to use on LifeWiki to explain differences between rulestrings / rule definitions}}{{Rule
{{Rule
|name            = tlife
|name            = tlife
|char            = Chaotic
|char            = Chaotic
|b              = 3
|b              = 3
|s              = 2-i34q
|s              = 2-i34q
|hideimg        = true
}}
}}
'''tlife''' is a [[non-totalistic cellular automaton]] devised by [[M. I. Wright]] on September 6, 2015. It is very closely related to the much more commonly known rule [[Conway's Game of Life]], differing by only two survival conditions in [[Hensel notation]]. It is likely one of the best-studied non-totalistic rules in existence.
'''tlife''' is a [[non-totalistic cellular automaton]] devised by [[M. I. Wright]] on September 6, 2015. It is very closely related to the much more commonly known rule [[Conway's Game of Life]], differing by only two isotropic survival [[transition (rule definition)|transitions]]. It is likely one of the most-studied [[isotropic non-totalistic]] (INT) rules in existence.


== Rules ==
== Rules ==
tlife is identical to Life, save for two conditions expressed in [[Hensel notation]]:
tlife is identical to Life, save for two transitions expressed in [[Hensel notation]]:


* cells with two adjacent cells in a straight orthogonal line (as in [[blinker]]) will die (-S2i), and
* -S2i:  cells with two adjacent cells in a straight orthogonal line (as in [[blinker]]) will die.
* cells with four adjacent cells (as in the dense phase of [[beacon]]) will survive (+S4q).
* +S4q:  cells with four adjacent cells (as in the dense phase of [[beacon]]) will survive.


The two differing conditions, illustrated:
The two differing transitions, illustrated:




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== Patterns ==
== Patterns ==
Although many patterns from Conway Life still function identically in tlife, some do not; for example, the [[blinker]] dies in tlife, and the [[beacon]] (depending on the phase) is or evolves into an 8-cell still life. Conversely, some patterns from tlife work in normal Life, but some do not.
Although many patterns from Conway Life still function identically in tlife, some do not; for example, the [[blinker]] dies in tlife, and the [[beacon]] (depending on the phase) is or evolves into an 8-cell still life known as block-tie. Conversely, some patterns from tlife work in normal Life, but some do not.


{|style="float:right;margin-left:16px;margin-bottom:8px;width:100px;"
{|style="float:right;margin-left:16px;margin-bottom:8px;width:100px;"
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|caption      = "Gate Kid" (named after its apgcode), or "honeyloaf p5" (its original name), a period 5 oscillator which works in both tlife and tdrylife
|caption      = "Gate Kid" (named after its apgcode), or "honeyloaf p5" (its original name), a period 5 oscillator which works in both tlife and tdrylife
|apgcode      = xp5_g8kid52z121/b3s2-i34q
|apgcode      = xp5_g8kid52z121/b3s2-i34q
}}
|-
|{{EmbedViewer
|rle          = x = 5, y = 6, rule = B3/S2-i34q
$2b2o$b2o$o$b2o!
|viewerconfig = #C [[ HEIGHT 600 WIDTH 800 THUMBSIZE 3 ZOOM 40 GPS 2 TRACKLOOP 4 -1/4 -1/4 AUTOSTART ]]
|position    = center
|caption      = Ant, a c/4 diagonal spaceship only slightly larger than the glider.
|apgcode      = xq4_1ba4/b3s2-i34q
}}
}}
|}
|}


=== Spaceships ===
=== Spaceships ===
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Alongside these, other elementary spaceships have been discovered. One such spaceship, which travels at [[c/2 orthogonal]] (period 4), is dubbed the ''disemiMWSS'', referencing the fact it looks like two [[middleweight spaceship]]s interacting with each other; there is also a skewed variant. There is also another c/2 orthogonal spaceship that evolves from a phase of the [[queen bee]], which has several minor variants. Other important spaceships include chains of interacting Ts, a small 2c/6 orthogonal ship, a small-to-medium [[c/4 orthogonal]] ship, and a large 8c/282 orthogonal ship consisting of many copies of a puffer of the same speed.<ref name="ships1" /><ref name="hypership" /> There are [[eater]]s for the glider, T, and ant, as well as for the queen bee ship and its variants.<ref name="tmain"/>
Alongside these, other elementary spaceships have been discovered. One such spaceship, which travels at [[c/2 orthogonal]] (period 4), is dubbed the ''disemiMWSS'', referencing the fact it looks like two [[middleweight spaceship]]s interacting with each other; there is also a skewed variant. There is also another c/2 orthogonal spaceship that evolves from a phase of the [[queen bee]], which has several minor variants. Other important spaceships include chains of interacting Ts, a small 2c/6 orthogonal ship, a small-to-medium [[c/4 orthogonal]] ship, and a large 8c/282 orthogonal ship consisting of many copies of a puffer of the same speed.<ref name="ships1" /><ref name="hypership" /> There are [[eater]]s for the glider, T, and ant, as well as for the queen bee ship and its variants.<ref name="tmain"/>


In all, c/2, [[2c/5 orthogonal|2c/5]], 2c/4, 4c/8, [[c/3 orthogonal|c/3]], 2c/6, c/4, c/5, and 8c/282 orthogonal, as well as c/4 diagonal, spaceships are known to exist, discounting higher-period c/2 technology.<ref name="ships1"/>
In all, c/2, [[2c/5 orthogonal|2c/5]], 2c/4, 4c/8, [[c/3 orthogonal|c/3]], 2c/6, c/4, c/5, 8c/282, and 8c/187 orthogonal, as well as c/4 and c/5 diagonal<ref name="Luveelc5d" /> spaceships, are known to exist, discounting higher-period c/2 technology.<ref name="ships1"/>


The only named spaceship other than the glider known to function in both CGoL and tlife is the [[crab]]; however, several other, unnamed c/4 diagonal spaceships work in both rules.<ref name="crab">{{LinkForumThread|f=11|t=1831|p=23029|title=Re: tlife (B3/S2-i34q)|author=praosylen|date=September 27, 2015|format=ref}}</ref><ref name="lifeships">{{LinkForumThread|p=39575|title=Re: tlife (B3/S2-i34q)|author=praosylen|date=January 20, 2017|format=ref}}</ref> All known spaceships that function in both B3/S23 and B3/S2-i34q travel at a velocity of (1,1)c/4.
The only named spaceship other than the glider known to function in both CGoL and tlife is the [[crab]]; however, several other, unnamed c/4 diagonal spaceships work in both rules.<ref name="crab">{{LinkForumThread|f=11|t=1831|p=23029|title=Re: tlife (B3/S2-i34q)|author=praosylen|date=September 27, 2015|format=ref}}</ref><ref name="lifeships">{{LinkForumThread|p=39575|title=Re: tlife (B3/S2-i34q)|author=praosylen|date=January 20, 2017|format=ref}}</ref> All known spaceships that function in both B3/S23 and B3/S2-i34q travel at a velocity of c/4d.


=== Oscillators ===
=== Oscillators ===


There is a common unloopable (non-classical) [[period]]-160 [[reflectorless rotating oscillator]] that often evolves from (what would, in normal Life, be) a [[loaf]] predecessor or a [[honey farm]] predecessor. Multiple copies of this oscillator can be combined to form interesting patterns such as guns, higher-period oscillators, and glider or T duplicators. A single copy can also reflect a glider or T, or convert one into the other.<ref name="tmain"/> There is also a somewhat similar period 33,<ref>{{LinkForumThread|p=30352|title=Re: tlife (B3/S2-i34q)|author=Nico Brown (glider_rider)|date=April 23, 2016|format=ref}}</ref> several p20s based on a failed replicator, a p14 shuttle, a variety of p2 oscillators, small rule-specific period 3, 4, 5, 6, and 8 oscillators,<ref name="tmain"/><ref>{{LinkForumThread|p=24323|title=Re: tlife (B3/S2-i34q)|author=Sphenocorona|date=October 29, 2015|format=ref}}</ref> larger billiard tables of all periods up to 10,<ref name="billiards1">{{LinkForumThread|p=54077|title=Re: tlife (B3/S2-i34q)|author=praosylen|date=December 14, 2017|format=ref}}</ref><ref>{{LinkForumThread|p=53676|title=Re: tlife (B3/S2-i34q)|author=praosylen|date=December 22, 2017|format=ref}}</ref> and an infinitely extensible family of oscillators consisting of replicating signals traveling up and down two diagonal lines of connected blocks.<ref>{{LinkForumThread|p=27818|title=Re: tlife (B3/S2-i34q)|author=praosylen|date=February 28, 2016|format=ref}}</ref> p4, p6, and p8 [[sparker]]s have also been found, allowing p16 T-hassling oscillators and p6N glider loops for certain N > 4 (exactly which N is unexplored, but it is likely to be all N), as well as p96+40N T shuttles for all N.<ref name="billiards1"/><ref>{{LinkForumThread|p=53787|title=Re: tlife (B3/S2-i34q)|author=praosylen|date=December 16, 2017|format=ref}}</ref><ref>{{LinkForumThread|p=44057|title=Re: tlife (B3/S2-i34q)|author=praosylen|date=June 4, 2017|format=ref}}</ref> Combinations of lower-period oscillators may lead to p12s and p15s; however, no examples have been explicitly constructed.
There is a common unloopable [[period]]-160 rotating [[oscillator]] that often evolves from (what would, in normal Life, be) a [[loaf]] predecessor or a [[honey farm]] predecessor. Multiple copies of this oscillator can be combined to form interesting patterns such as guns, higher-period oscillators, and glider or T duplicators. A single copy can also reflect a glider or T, or convert one into the other.<ref name="tmain"/> There is also a somewhat similar period 33,<ref>{{LinkForumThread|p=30352|title=Re: tlife (B3/S2-i34q)|author=Nora Brown (glider_rider)|date=April 23, 2016|format=ref}}</ref> several p20s based on a failed replicator, a p14 shuttle, a variety of p2 oscillators, small rule-specific period 3, 4, 5, 6, and 8 oscillators,<ref name="tmain"/><ref>{{LinkForumThread|p=24323|title=Re: tlife (B3/S2-i34q)|author=Sphenocorona|date=October 29, 2015|format=ref}}</ref> larger billiard tables of all periods up to 10,<ref name="billiards1">{{LinkForumThread|p=54077|title=Re: tlife (B3/S2-i34q)|author=praosylen|date=December 14, 2017|format=ref}}</ref><ref>{{LinkForumThread|p=53676|title=Re: tlife (B3/S2-i34q)|author=praosylen|date=December 22, 2017|format=ref}}</ref> and an infinitely extensible family of oscillators consisting of replicating signals traveling up and down two diagonal lines of connected blocks.<ref>{{LinkForumThread|p=27818|title=Re: tlife (B3/S2-i34q)|author=praosylen|date=February 28, 2016|format=ref}}</ref> p4, p6, and p8 [[sparker]]s have also been found, allowing p16 T-hassling oscillators and p6N glider loops for certain N > 4 (exactly which N is unexplored, but it is likely to be all N), as well as p96+40N T shuttles for all N.<ref name="billiards1"/><ref>{{LinkForumThread|p=53787|title=Re: tlife (B3/S2-i34q)|author=praosylen|date=December 16, 2017|format=ref}}</ref><ref>{{LinkForumThread|p=44057|title=Re: tlife (B3/S2-i34q)|author=praosylen|date=June 4, 2017|format=ref}}</ref> Combinations of lower-period oscillators have also allowed for p12 and p15 [[LCM]]s.


{{EmbedViewer
{{EmbedViewer
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|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 10 GPS 20 AUTOSTART ]]
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 10 GPS 20 AUTOSTART ]]
|position    = center
|position    = center
|caption      = The period-160 reflectorless rotating oscillator
|caption      = The period-160 rotating oscillator
|style        = width:300px;
|style        = width:300px;
|apgcode      = xp160_3v/b3s2-i34q
|apgcode      = xp160_3v/b3s2-i34q
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A [[sawtooth]] has been constructed, Sawtooth 1761.<ref>{{LinkForumThread|p=24988|title=Re: tlife (B3/S2-i34q)|author=EricG|date=November 12, 2015|format=ref}}</ref>
A [[sawtooth]] has been constructed, Sawtooth 1761.<ref>{{LinkForumThread|p=24988|title=Re: tlife (B3/S2-i34q)|author=EricG|date=November 12, 2015|format=ref}}</ref>


There is a breeder consisting of four Schick puffer-based glider rakes repeatedly synthesizing double-barreled T guns.<ref>{{LinkForumThread|p=23565|title=Re: tlife (B3/S2-i34q)|author=EricG|date=October 9, 2015|format=ref}}</ref>
There is a [[breeder]] consisting of four Schick puffer-based glider rakes repeatedly synthesizing double-barreled T guns.<ref>{{LinkForumThread|p=23565|title=Re: tlife (B3/S2-i34q)|author=EricG|date=October 9, 2015|format=ref}}</ref>


No wickstretchers or spacefillers are known.
The [[crab]]-based tubstretcher works in tlife.
 
No spacefillers are currently known.


== Similar rules ==
== Similar rules ==
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|hideimg        = true
|hideimg        = true
}}
}}
This rule is commonly known as "tHighLife", due to it sharing a B6 condition with {{rl|HighLife}}.
This rule is commonly known as "tHighLife", due to it sharing a B6 transition with {{rl|HighLife}}.


Very interestingly, it has a simple orthogonal [[replicator]] which replicates at 4c/11 orthogonal, very similarly to HighLife's own replicator. [[Luka Okanishi]] used this to construct a 4c/11 orthogonal spaceship.
Very interestingly, it has a simple orthogonal [[replicator]] which replicates at 4c/11 orthogonal, very similarly to HighLife's own replicator. [[Luka Okanishi]] used this to construct a 4c/11 orthogonal spaceship.
Line 117: Line 128:
|position    = center
|position    = center
|imgname      = thighlife4c11spaceship
|imgname      = thighlife4c11spaceship
|caption      = The 4c/11 spaceship
|caption      = The 16c/44 spaceship
|style        = width:300px;
|style        = width:300px;
|apgcode      = xq44_4sxokk772ueeyfeeeeexeeeeezw7fdheybgzx11w1y58ca7033y7sssssynssssszy4c6796x133x88ogwgya102zyggd2499221y24ahhha404ahhha4zyh1223/b36s2-i34q
|apgcode      = xq44_4sxokk772ueeyfeeeeexeeeeezw7fdheybgzx11w1y58ca7033y7sssssynssssszy4c6796x133x88ogwgya102zyggd2499221y24ahhha404ahhha4zyh1223/b36s2-i34q
Line 132: Line 143:
|hideimg        = true
|hideimg        = true
}}
}}
This rule is commonly known as "tdrylife", taking its B7 from {{rl|DryLife}}.
This rule is commonly known as "tDryLife" due to its additional B7 transition, analogous to {{rl|DryLife}}.


Unlike DryLife, it is not explosive, and has a lot of very interesting patterns. However, only two relatively common oscillators are the [[cap]] and the [[toad]], neither with a usable spark, resulting in no guns having been discovered so far (as opposed to the well-known rakes). [[Mango]]es are also much more common than in Life.
Unlike DryLife, it is not explosive, and has a lot of very interesting patterns. However, the only two relatively common oscillators are the [[cap]] and the [[toad]], neither with a usable spark, resulting in no guns having been discovered so far (as opposed to the well-known rakes). [[Mango]]es are also much more common than in Life.


Many interesting spaceships have been constructed in this rule. For example, there is a naturally occurring 2c/23 orthogonal spaceship involving the T trying to escape a [[pre-beehive]]. [[Luka Okanishi]] used this spaceship to create other patterns moving at this speed. A T forward rake was also built using known reflections for gliders and Ts when colliding with the 2c/23 spaceship.
Many interesting spaceships have been constructed in this rule. For example, there is a naturally occurring 2c/23 orthogonal spaceship involving the T trying to escape a [[pre-beehive]]. [[Luka Okanishi]] used this spaceship to create other patterns moving at this speed. A T forward rake was also built using known reflections for gliders and Ts when colliding with the 2c/23 spaceship.
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}}
}}


Most interestingly, there is a (2,6)c/21 ([[:category:spaceships with slope 3|slope 3]]) [[ship]] [[puffer]]. This can be stabilised into various interesting patterns, such as a two-[[engine]] [[knightship]]. [[Alexey Nigin]] has created a [[quadratic growth]] pattern which uses [[oblique]] spaceships to create pond puffers, based on a reaction discovered by [[Rhombic]]. A much slower quadratic growth pattern was discovered later by Rhombic, based on the synthesis of pond puffers with a T and a pond.
Most interestingly, there is a (2,6)c/21 ([[:category:spaceships with slope 3|slope 3]]) [[ship]] [[puffer]]. This can be stabilised into various interesting patterns, such as a two-[[engine]] [[oblique spaceship]] (specifically a camelship). [[Alexey Nigin]] has created a [[quadratic growth]] pattern which uses [[oblique]] spaceships to create pond puffers, based on a reaction discovered by [[Rhombic]]. A much slower quadratic growth pattern was discovered later by Rhombic, based on the synthesis of pond puffers with a T and a pond.


{{EmbedViewer
{{EmbedViewer
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|hideimg        = true
|hideimg        = true
}}
}}
This rule is commonly known as "SilverLife", it combines B6 and B7.
This rule is commonly known as "SilverLife"; it adds the B6 and B7 outer-totalistic transitions to tlife's rule specification.


It is rich in exotic speeds, including a p91 flamingoship.
It is rich in exotic speeds, including a p91 [[flamingoship]].


{{EmbedViewer
{{EmbedViewer
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}}
}}


There's also a 7c/55 diagonal pond puffer.
There is also a 7c/55 diagonal pond puffer.
{{EmbedViewer
{{EmbedViewer
|rle = x = 8, y = 8, rule = B367/S2-i34q
|rle = x = 8, y = 8, rule = B367/S2-i34q
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<ref name="ships1">{{LinkForumThread
<ref name="ships1">{{LinkForumThread
|f=11|t=1831|p=210251
|title  = Re: tlife (B3/S2-i34q)
|author = LuveelVoom
|date  = April 19, 2025
|format = raw
}}, in which the first two c/5 diagonals found were shown (at 27 and 29 half-diagonals wide)</ref>
<ref name="Luveelc5d">{{LinkForumThread
|p      = 23546
|p      = 23546
|title  = Re: tlife (B3/S2-i34q)
|title  = Re: tlife (B3/S2-i34q)
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|format = ref
|format = ref
}}</ref>
}}</ref>
<ref name="hypership">{{LinkForumThread
<ref name="hypership">{{LinkForumThread
|p      = 63228
|p      = 63228

Latest revision as of 16:41, 23 March 2026

tlife
x=64, y = 64, rule = B3/S2-i34q ! #C [[ THEME Inverse ]] #C [[ RANDOMIZE2 THUMBLAUNCH THUMBNAIL THUMBSIZE 2 GRID ZOOM 6 WIDTH 600 HEIGHT 600 LABEL 90 -20 2 "#G" AUTOSTART PAUSE 2 GPS 8 LOOP 256 ]]
LifeViewer-generated pseudorandom soup
Rulestring 2-i34q/3
B3/S2-i34q
Character Chaotic

tlife is a non-totalistic cellular automaton devised by M. I. Wright on September 6, 2015. It is very closely related to the much more commonly known rule Conway's Game of Life, differing by only two isotropic survival transitions. It is likely one of the most-studied isotropic non-totalistic (INT) rules in existence.

Rules

tlife is identical to Life, save for two transitions expressed in Hensel notation:

  • -S2i: cells with two adjacent cells in a straight orthogonal line (as in blinker) will die.
  • +S4q: cells with four adjacent cells (as in the dense phase of beacon) will survive.

The two differing transitions, illustrated: 


INT Moore R1 2i.png -> 0    

INT Moore R1 4q.png -> 1


Patterns

Although many patterns from Conway Life still function identically in tlife, some do not; for example, the blinker dies in tlife, and the beacon (depending on the phase) is or evolves into an 8-cell still life known as block-tie. Conversely, some patterns from tlife work in normal Life, but some do not.

x = 3, y = 2, rule = B3/S2-i34q 3o$bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 600 WIDTH 800 THUMBSIZE 3 ZOOM 60 Y -1 AUTOSTART GPS 2 TRACKLOOP 5 0 1/5 ]]
The T-tetromino spaceship
(click above to open LifeViewer)
Catagolue: here
x = 7, y = 7, rule = B3/S2-i34q 4b2o$3bo2bo$2bob2o$bo2bo$ob2o$obo$bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 600 WIDTH 800 THUMBSIZE 3 ZOOM 36 AUTOSTART GPS 2 ]]
"Gate Kid" (named after its apgcode), or "honeyloaf p5" (its original name), a period 5 oscillator which works in both tlife and tdrylife
(click above to open LifeViewer)
Catagolue: here
x = 5, y = 6, rule = B3/S2-i34q $2b2o$b2o$o$b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 600 WIDTH 800 THUMBSIZE 3 ZOOM 40 GPS 2 TRACKLOOP 4 -1/4 -1/4 AUTOSTART ]]
Ant, a c/4 diagonal spaceship only slightly larger than the glider.
(click above to open LifeViewer)
Catagolue: here


Spaceships

For other uses of "Ant", see ants.

The glider exists in tlife, and there are two other basic elementary spaceships: a slightly bigger c/4 diagonal called ant and a non-monotonic c/5 orthogonal (the T-tetromino, usually called simply T or T-ship).[1]

Alongside these, other elementary spaceships have been discovered. One such spaceship, which travels at c/2 orthogonal (period 4), is dubbed the disemiMWSS, referencing the fact it looks like two middleweight spaceships interacting with each other; there is also a skewed variant. There is also another c/2 orthogonal spaceship that evolves from a phase of the queen bee, which has several minor variants. Other important spaceships include chains of interacting Ts, a small 2c/6 orthogonal ship, a small-to-medium c/4 orthogonal ship, and a large 8c/282 orthogonal ship consisting of many copies of a puffer of the same speed.[2][3] There are eaters for the glider, T, and ant, as well as for the queen bee ship and its variants.[1]

In all, c/2, 2c/5, 2c/4, 4c/8, c/3, 2c/6, c/4, c/5, 8c/282, and 8c/187 orthogonal, as well as c/4 and c/5 diagonal[4] spaceships, are known to exist, discounting higher-period c/2 technology.[2]

The only named spaceship other than the glider known to function in both CGoL and tlife is the crab; however, several other, unnamed c/4 diagonal spaceships work in both rules.[5][6] All known spaceships that function in both B3/S23 and B3/S2-i34q travel at a velocity of c/4d.

Oscillators

There is a common unloopable period-160 rotating oscillator that often evolves from (what would, in normal Life, be) a loaf predecessor or a honey farm predecessor. Multiple copies of this oscillator can be combined to form interesting patterns such as guns, higher-period oscillators, and glider or T duplicators. A single copy can also reflect a glider or T, or convert one into the other.[1] There is also a somewhat similar period 33,[7] several p20s based on a failed replicator, a p14 shuttle, a variety of p2 oscillators, small rule-specific period 3, 4, 5, 6, and 8 oscillators,[1][8] larger billiard tables of all periods up to 10,[9][10] and an infinitely extensible family of oscillators consisting of replicating signals traveling up and down two diagonal lines of connected blocks.[11] p4, p6, and p8 sparkers have also been found, allowing p16 T-hassling oscillators and p6N glider loops for certain N > 4 (exactly which N is unexplored, but it is likely to be all N), as well as p96+40N T shuttles for all N.[9][12][13] Combinations of lower-period oscillators have also allowed for p12 and p15 LCMs.

x = 8, y = 8, rule = B3/S2-i34q 3bo$b2o$b2o3b2o$o2bo$bob2obo$bo3b2o$2b2ob2o$4bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 10 GPS 20 AUTOSTART ]]
The period-160 rotating oscillator
(click above to open LifeViewer)
Catagolue: here

Infinite growth

As mentioned above, multiple copies of the period 160 oscillator can interact to form guns. There exist many guns for the glider and the T consisting of only two copies, as well as two double-barreled T guns.[14] There is also a gun for the ant consisting of 3 interacting p160 oscillators.[1] By combining multiple basic guns, larger guns have been formed for the c/2, 2c/6, disemiMWSS and skewed variants, as well as pairs of interacting T's. A period 231 T gun is also known, using an over-unity reaction supported by reflectors formed from the p33 oscillator.[15]

Several puffers are known. Most known puffers travel at c/2 orthogonal and use one of three engines: one or more B-heptominoes escorted by at least two disemiMWSSs, a Schick engine-like tagalong to a pair of disemiMWSSs, or a p8 engine derived from a 4c/8 ship.[16][17][2] These engines can be perturbed by still more disemiMWSSs to form rakes for the glider and the T, as well as presumably for other spaceships.[17][18] There is also an 8c/282 (mod 141) puffer made up of an ant bouncing between two boats, displacing each in a forward direction while creating a block and a forward T, discovered by dani; Luka Okanishi used this to construct a large 8c/282 ship.[19][3]

A sawtooth has been constructed, Sawtooth 1761.[20]

There is a breeder consisting of four Schick puffer-based glider rakes repeatedly synthesizing double-barreled T guns.[21]

The crab-based tubstretcher works in tlife.

No spacefillers are currently known.

Similar rules

Various rules similar to tlife have been explored, such as B36/S2-i34q (tHighlife), B37/S2-i34q (tDrylife), and B367/S2-i34q (SilverLife).

B36/S2-i34q

Ambox notice.png It has been suggested that this page or section be split into OCA:tHighLife. (Discuss)
tHighLife
Rulestring 2-i34q/36
B36/S2-i34q
Character Chaotic

This rule is commonly known as "tHighLife", due to it sharing a B6 transition with HighLife.

Very interestingly, it has a simple orthogonal replicator which replicates at 4c/11 orthogonal, very similarly to HighLife's own replicator. Luka Okanishi used this to construct a 4c/11 orthogonal spaceship.

x = 7, y = 5, rule = B36/S2-i34q 2b3o$bo3bo$o5bo$bo3bo$2b3o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 10 GPS 8 AUTOSTART T 0 PAUSE 2 T 44 PAUSE 1 LOOP 45 ]]
The replicator
(click above to open LifeViewer)
Catagolue: here
x = 72, y = 27, rule = B36/S2-i34q 8b2o$8b6o19b5o3b5o$2o4b4ob3o19b5o3b5o$bo3bo5b3o19b5o3b5o$bo3b3o3bo$2b 4o$2b2o2bo$2b3obo$3b2obo$5bo16bo$3b2o2bo12bob2o$19b2ob2o$18bobo14b5o27b 5o$17b3o15b5o27b5o$35b5o27b5o$10b2o4b3o24bo$9b2obo4b2o26bo$8b3obo$8bo 2bo10b3o$24b2o2bo$21bo2b2o2bo8b3o5b3o$22bo3b2o8bo3bo3bo3bo$21bobo11bo 5bobo5bo$21bo2b2o10bo3bo3bo3bo$20bo16b3o5b3o$21bo2bo$22b3o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 8 ]]
The 16c/44 spaceship
(click above to open LifeViewer)
Catagolue: here


B37/S2-i34q

Ambox notice.png It has been suggested that this page or section be split into OCA:tDryLife. (Discuss)
tDryLife
Rulestring 2-i34q/37
B37/S2-i34q
Character Chaotic

This rule is commonly known as "tDryLife" due to its additional B7 transition, analogous to DryLife.

Unlike DryLife, it is not explosive, and has a lot of very interesting patterns. However, the only two relatively common oscillators are the cap and the toad, neither with a usable spark, resulting in no guns having been discovered so far (as opposed to the well-known rakes). Mangoes are also much more common than in Life.

Many interesting spaceships have been constructed in this rule. For example, there is a naturally occurring 2c/23 orthogonal spaceship involving the T trying to escape a pre-beehive. Luka Okanishi used this spaceship to create other patterns moving at this speed. A T forward rake was also built using known reflections for gliders and Ts when colliding with the 2c/23 spaceship.

x = 8, y = 4, rule = B37/S2-i34q bobo$o2bo2b2o$bobo2b2o$6b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]
The 2c/23 ship
(click above to open LifeViewer)
Catagolue: here

A c/2 orthogonal spaceship based on 2 B-heptominoes has been seen to occur naturally.

x = 13, y = 17, rule = B37/S2-i34q 5b2o$2b5o$b2obo$b2o3$bo4bo3bo$bo5bo2bo$2bo8bo$8bo2b2o$2b2o4bob3o$bobo 8bo$bo2b2o$o3bo$bo2bo3b2obo$b3o5b3o$10bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]
The c/2 ship
(click above to open LifeViewer)
Catagolue: here

It has a 11c/776 diagonal glide symmetric pond puffer, which is actually the century. It parallels the R-pentomino based 9c/28 orthogonal pond puffer from DryLife. In June 2017, Luka Okanishi managed to build a 22c/1552 diagonal spaceship using pond puffer interactions.[22]

x = 61, y = 45, rule = B37/S2-i34q 41b2o$40bo2bo$40bo2bo$41b2o3$58b2o$57bo2bo$57bo2bo$58b2o2$30b2o$29bo2b o$29bo2bo$30b2o3$47b2o$46bo2bo$46bo2bo$47b2o2$19b2o$18bo2bo$18bo2bo$ 19b2o2$3o$obo33b2o$o2bo31bo2bo$2o3bo29bo2bo$bo4bo29b2o$5bobo3bo$4b3o4b 2o$12bo$11bo$7b2o2bo$b2o7b2o$b2o4b2o2bo$7bo3bo$8bo3b2o$8bo5bo2$10bob2o $11b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]
The pond puffer
(click above to open LifeViewer)
Catagolue: here

Most interestingly, there is a (2,6)c/21 (slope 3) ship puffer. This can be stabilised into various interesting patterns, such as a two-engine oblique spaceship (specifically a camelship). Alexey Nigin has created a quadratic growth pattern which uses oblique spaceships to create pond puffers, based on a reaction discovered by Rhombic. A much slower quadratic growth pattern was discovered later by Rhombic, based on the synthesis of pond puffers with a T and a pond.

x = 56, y = 24, rule = B37/S2-i34q 53bo$48bo2b4o$49b2o4bo$52bobo$42bo8bobo$36b3o3b2ob2o$42b2ob2o3$35bobo$ 36bobo$37b2o2$24b2o$24bobo$25b2o2$12b2o$12bobo$13b2o2$2o$obo$b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]
The (12, 4)c/42 ship puffer
(click above to open LifeViewer)
Catagolue: here

B367/S2-i34q

Ambox notice.png It has been suggested that this page or section be split into OCA:SilverLife. (Discuss)
SilverLife
Rulestring 2-i34q/367
B367/S2-i34q
Character Chaotic

This rule is commonly known as "SilverLife"; it adds the B6 and B7 outer-totalistic transitions to tlife's rule specification.

It is rich in exotic speeds, including a p91 flamingoship.

x = 7, y = 9, rule = B367/S2-i34q 3b3o$2b2ob2o$bobob2o$4b2o$bo2bo$3bo$2o$o$o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]
The (6, 1)c/91 flamingoship
(click above to open LifeViewer)
Catagolue: here

There is also a 7c/55 diagonal pond puffer.

x = 8, y = 8, rule = B367/S2-i34q 6bo$4bo2bo$3b2o$2b3o$b3o2$o$bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]
7c/55 diagonal pond puffer
(click above to open LifeViewer)
Catagolue: here

References

  1. ↑ 1.0 1.1 1.2 1.3 1.4 M. I. Wright (September 13, 2015). tlife (B3/S2-i34q) (discussion thread) at the ConwayLife.com forums
  2. ↑ 2.0 2.1 2.2 LuveelVoom (April 19, 2025). Re: tlife (B3/S2-i34q), in which the first two c/5 diagonals found were shown (at 27 and 29 half-diagonals wide)
  3. ↑ 3.0 3.1 Luka Okanishi (AbhpzTa) (September 1, 2018). Re: tlife (B3/S2-i34q) (discussion thread) at the ConwayLife.com forums
  4. ↑ Arie Paap (wildmyron) (November 29, 2016). Re: tlife (B3/S2-i34q) (discussion thread) at the ConwayLife.com forums
  5. ↑ praosylen (September 27, 2015). Re: tlife (B3/S2-i34q) (discussion thread) at the ConwayLife.com forums
  6. ↑ praosylen (January 20, 2017). Re: tlife (B3/S2-i34q) (discussion thread) at the ConwayLife.com forums
  7. ↑ Nora Brown (glider_rider) (April 23, 2016). Re: tlife (B3/S2-i34q) (discussion thread) at the ConwayLife.com forums
  8. ↑ Sphenocorona (October 29, 2015). Re: tlife (B3/S2-i34q) (discussion thread) at the ConwayLife.com forums
  9. ↑ 9.0 9.1 praosylen (December 14, 2017). Re: tlife (B3/S2-i34q) (discussion thread) at the ConwayLife.com forums
  10. ↑ praosylen (December 22, 2017). Re: tlife (B3/S2-i34q) (discussion thread) at the ConwayLife.com forums
  11. ↑ praosylen (February 28, 2016). Re: tlife (B3/S2-i34q) (discussion thread) at the ConwayLife.com forums
  12. ↑ praosylen (December 16, 2017). Re: tlife (B3/S2-i34q) (discussion thread) at the ConwayLife.com forums
  13. ↑ praosylen (June 4, 2017). Re: tlife (B3/S2-i34q) (discussion thread) at the ConwayLife.com forums
  14. ↑ praosylen (September 20, 2016). Re: tlife (B3/S2-i34q) (discussion thread) at the ConwayLife.com forums
  15. ↑ Luka Okanishi (AbhpzTa) (May 14, 2016). Re: tlife (B3/S2-i34q) (discussion thread) at the ConwayLife.com forums
  16. ↑ praosylen (October 9, 2015). Re: tlife (B3/S2-i34q) (discussion thread) at the ConwayLife.com forums
  17. ↑ 17.0 17.1 Sphenocorona (October 9, 2015). Re: tlife (B3/S2-i34q) (discussion thread) at the ConwayLife.com forums
  18. ↑ EricG (October 9, 2015). Re: tlife (B3/S2-i34q) (discussion thread) at the ConwayLife.com forums
  19. ↑ dani (August 29, 2018). Re: tlife (B3/S2-i34q) (discussion thread) at the ConwayLife.com forums
  20. ↑ EricG (November 12, 2015). Re: tlife (B3/S2-i34q) (discussion thread) at the ConwayLife.com forums
  21. ↑ EricG (October 9, 2015). Re: tlife (B3/S2-i34q) (discussion thread) at the ConwayLife.com forums
  22. ↑ Luka Okanishi (AbhpzTa) (June 21, 2017). Re: tDryLife (discussion thread) at the ConwayLife.com forums

External links

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