OCA:tlife

tlife
x=0, y = 0, rule = B3/S2-i34q ! #C [[ THEME Inverse ]] #C [[ RANDOMIZE2 RANDSEED 1729 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 survival transitions in Hensel notation. It is likely one of the best-studied non-totalistic rules in existence.

Rules

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
• cells with four adjacent cells (as in the dense phase of beacon) will survive (+S4q).

The two differing transitions, illustrated:

 -> 0    

 -> 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

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).

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. There are 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, c/5, and 8c/282 orthogonal, as well as c/4 diagonal, spaceships are known to exist, discounting higher-period 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/S2-i34q travel at a velocity of (1,1)c/4.

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. There is also a somewhat similar period 33, 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, larger billiard tables of all periods up to 10, and an infinitely extensible family of oscillators consisting of replicating signals traveling up and down two diagonal lines of connected blocks. 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. Combinations of lower-period oscillators may lead to p12s and p15s; however, no examples have been explicitly constructed.

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 reflectorless 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. 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 over-unity reaction supported by reflectors formed from the p33 oscillator.

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. 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. 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.

A sawtooth has been constructed, Sawtooth 1761.

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

No wickstretchers or 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

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 4c/11 spaceship (click above to open LifeViewer) Catagolue: here

B37/S2-i34q

tDryLife
Rulestring	2-i34q/37 B37/S2-i34q
Character	Chaotic

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. 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). 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.

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 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.

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

SilverLife
Rulestring	2-i34q/367 B367/S2-i34q
Character	Chaotic

This rule is commonly known as "SilverLife", it combines B6 and B7.

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's 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

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
• SilverLife (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
• SilverLife at Adam P. Goucher's Catagolue