tlife
tlife  


Rulestring  2i34q/3 B3/S2i34q 


Character  Chaotic 
tlife is a nontotalistic Lifelike 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 transitions. It is likely the beststudied nontotalistic Lifelike cellular automaton.
Contents
Rules
tlife is identical to Life in all transitions, save for two:
 Cells with two adjacent cells in a straight line (as in blinker) will die (2i), and
 Cells with four adjacent cells (as in the dense phase of beacon) will survive (4q).
The two differing transitions, illustrated:
000 110 111 > 0 110 > 1 000 001
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 is/evolves into an 8cell still life. Conversely, some patterns from tlife work in normal Life, but some do not.
Spaceships
The glider exists in tlife, and there are two other basic elementary spaceships: a slightly bigger c/4 diagonal called ant and a c/5 orthogonal (the Ttetromino, usually called simply T).
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, and a smalltomedium c/4 orthogonal ship. There exist eaters for the glider, T, and ant, as well as for the queen bee ship and its variants.
In all, c/2, 2c/5, 2c/4, 4c/8, c/3, 2c/6, c/4, and c/5 orthogonal, as well as c/4 diagonal, spaceships are known to exist, discounting higherperiod c/2 technology.
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. All known spaceships that function in both B3/S23 and B3/S2i34q travel at a velocity of (1,1)c/4.
Oscillators
There is a common unloopable (nonclassical) period160 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, higherperiod oscillators, and glider or T duplicators. A single copy can also reflect a glider or T, or convert it into the other. There is also a somewhat similar period 33, several p20s based on a failed replicator, a p14 shuttle, small rulespecific period 3, 4, 5, 6, and 8 oscillators, and an infinitely extensible family of oscillators consisting of replicating signals traveling up and down two diagonal lines of connected blocks. P4 and p6 sparkers have been found, allowing p16 Thassling oscillators and p6N glider loops for certain N > 4 (exactly which N is unexplored, but it is likely to be all N). Combinations of lowerperiod oscillators may lead to p12s and p15s; however, no examples have been explicitly constructed.
Infinite growth
As mentioned above, multiple copies of the period 160 oscillator can interact to form guns. There exist guns for the glider and the T consisting of only two copies, as well as two doublebarreled T guns. There is also a gun for the ant consisting of 3 interacting p160 oscillators. 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 overunity reaction supported by reflectors formed from the p33 oscillator.
Several puffers are known, all traveling at c/2 orthogonal and using one of two known engines: one or more Bheptominoes escorted by at least two disemiMWSSs, or a Schick enginelike tagalong to a pair of disemiMWSSs. 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.
A sawtooth has been constructed, Sawtooth 1761.
There is a breeder consisting of four Schick pufferbased glider rakes repeatedly synthesizing doublebarreled T guns.
No wickstretchers or spacefillers are known.
Similar rules
Various rules similar to tlife have been constructed.
B36/S2i34q
This rule is commonly known as "tHighLife" or "Thigh Life", 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. 'AbphzTa' used this to construct a 4c/11 orthogonal spaceship.
B37/S2i34q
This rule is commonly known as "tdrylife", taking its B7 from DryLife.
Unlike DryLife, it is not explosive, and has a lot of very interesting patterns. 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 wellknown rakes).
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 prebeehive. AbhpzTa 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.
A c/2 orthogonal spaceship based on 2 Bheptominoes has been seen to occur naturally.
It has a 11c/776 diagonal glide symmetric pond puffer, which is actually the century. It parallels the Rpentomino based 9c/28 orthogonal pond puffer from DryLife. In June 2017, AbhpzTa managed to build a 22c/1552 diagonal spaceship using pond puffer interactions.^{[1]} .
Most interestingly, there is a (2,6)c/21 (slope 3) ship puffer. This can be stabilised into various interesting patterns, such as a twoengine knightship. Also, 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.
External links
 tlife (discussion thread) at the ConwayLife.com forums
 thighlife (discussion thread) at the ConwayLife.com forums
 tdrylife (discussion thread) at the ConwayLife.com forums
 tlife at Adam P. Goucher's Catagolue
 thighlife at Adam P. Goucher's Catagolue
 tdrylife at Adam P. Goucher's Catagolue
References
 ↑ AbhpzTa (June 21, 2017). "Re: tDryLife". Retrieved on June 22, 2017.