User:Pzq Alex/Rules 1 transition from Life
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This page documents isotropic non-totalistic rules that are only one transition (excluding B0) from Life.
| Rules by the toggled INT transition | ||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| B0 | B1c | B1e | B2c | B2e | B2k | B2a | B2i | B2n | B3c | B3e | B3k | B3a | B3i | B3n | B3y | B3q |
| B3j | B3r | B4c | B4e | B4k | B4a | B4i | B4n | B4y | B4q | B4j | B4r | B4t | B4w | B4z | B5c | B5e |
| B5k | B5a | B5i | B5n | B5y | B5q | B5j | B5r | B6c | B6e | B6k | B6a | B6i | B6n | B7c | B7e | B8 |
| S0 | S1c | S1e | S2c | S2e | S2k | S2a | S2i | S2n | S3c | S3e | S3k | S3a | S3i | S3n | S3y | S3q |
| S3j | S3r | S4c | S4e | S4k | S4a | S4i | S4n | S4y | S4q | S4j | S4r | S4t | S4w | S4z | S5c | S5e |
| S5k | S5a | S5i | S5n | S5y | S5q | S5j | S5r | S6c | S6e | S6k | S6a | S6i | S6n | S7c | S7e | S8 |
| With C1 census on Catagolue | Other | |||||||||||||||
Birth transitions
B1
B1c3/S23
An explosive rule characterized by the exploding dot replicator as a result of B1c.
B1e3/S23
Also explosive, but fills a growing diamond-shaped region with density of about 38%.
B2
B2c3/S23
Random soups expand and create some temporary stable objects.
B2e3/S23
Known as xvaLifeg. Random soups expand and emit some small five-bit spaceships.
| The common five-bitter in B2e3/S23 (click above to open LifeViewer) |
B2k3/S23
Similar to 3-4 Life, soups create expanding chaotic blobs, shooting gliders outwards.
B2a3/S23
Explosive, as with Seeds.
B2i3/S23
- See also B2i3/S23
Similar to DryLife, soups create expanding clouds of chaos, shooting gliders outwards.
| Common p20 in B2i3/S23 (click above to open LifeViewer) |
B2n3/S23
Similar to DryLife, soups create expanding clouds of chaos, shooting gliders and occasionally xWSSes outwards.
B3
B3-c/S23
Similar to Life, but honey farms do not form naturally.
B3-e/S23
Similar to Life. There is a natural p46 (not the twin bees shuttle!), a 2c/11 diagonal, and a c/14 diagonal. There is also a (58, 18)c/295 oblique puffer evolving from an R+block collision, a 15c/59 orthogonal puffer evolving from a pi+two tubs collision.
| Left: natural p46. Middle: natural 2c/11d. Right: natural c/14d (click above to open LifeViewer) |
| natural (58, 18)c/295 puffer (failed MMS breeder) starting from an R+block collision (click above to open LifeViewer) |
| natural 15c/59o puffer starting from a pi+two tubs collision (click above to open LifeViewer) |
B3-k/S23
Similar to Life, but with some special oscillators and a natural 5c/16o. A pentadecathlon can reflect gliders with its pipsquirted domino spark.
| Left to right: p2, p4, p4, 5c/16o (click above to open LifeViewer) |
| p15 glider loop (click above to open LifeViewer) |
B3-a/S23
Patterns never escape their bounding diamonds.
B3-i/S23
Patterns never escape their bounding boxes.
B3-n/S23
Similar to Life, with a p5, a p6, and a 27c/118 diagonal puffer.
| A p5 and a p6 (click above to open LifeViewer) |
| 27c/118d puffer starting from a B+block collision (click above to open LifeViewer) |
B3-y/S23
Dense ash, with a 3c/8o puffer arising from the twin bees.
| The 3c/8o puffer (click above to open LifeViewer) |
B3-q/S23
Very dense ash, especially considering that it doesn't tend to expand as much as regular Life. A few still lifes exist that can't in normal Life, but much more commonly, the absence of B3q allows objects to be closer together than they normally can be.
B3-j/S23
Patterns don't seem to escape their bounding boxes, although not strictly like B3-i/S23. A few highly varied rare still lifes appear more commonly, as well as a decent number that don't work in regular Life. Also has some unique oscillators and a unique c/4d. No familiar constellations form.
| The c/4d (click above to open LifeViewer) |
B3-r/S23
Fishhooks are more common, since they evolve from the procrastinator sequence.
| Left: a predecessor of a semi-common 22-cell still life. Right: the worker bee works without external support (click above to open LifeViewer) |
B4
B34c/S23
- See also 4diagonal
Similar to Life. There is a c/7o that consists of two copies of the bottom part of the loafer.
| The c/7o (click above to open LifeViewer) |
The century evolves into a 23c/110o puffer.
| (click above to open LifeViewer) |
B34e/S23
Fleets are instead a pair of eleveners. Other than that and the lack of working honey farms, not much difference from Life.
B34k/S23
Similar to Life, with a natural c/7d.
| (click above to open LifeViewer) |
The queen bee does not function as a shuttle but is an 8c/22 puffer.
| (click above to open LifeViewer) |
B34a/S23
Explosive, similar to 3-4 Life.
B34i/S23
Another "expanding chaos" rule, similar to DryLife.
B34n/S23
Similar to Life, with a natural c/2o puffer.
| (click above to open LifeViewer) |
- B34n/S23 at Adam P. Goucher's Catagolue
- B34n/S23 (klife) (discussion thread) at the ConwayLife.com forums
B34y/S23
Similar to Life.
B34q/S23
Similar to Life.
B34j/S23
Features a common breeder that is actually a failedrep.
| (click above to open LifeViewer) |
B34r/S23
Also called WetLife. Similar to DryLife, but patterns emit only xWSSes, hence its name, as opposed to DryLife.
B34t/S23
Similar to Life. There is a unique p8 and a p10.
| p8 and p10 (click above to open LifeViewer) |
B34w/S23
- See also Wlife
Features a quadratic failed replicator from the traffic light sequence, making it extremely common.
| c/2o, and p6 (click above to open LifeViewer) |
- B34w/S23 at Adam P. Goucher's Catagolue
- wlife (discussion thread) at the ConwayLife.com forums
B34z/S23
- See also Zlife
Similar to Life, with a unique p4, and a unique rotating p12.
| p4 and p12 (click above to open LifeViewer) |
B5
B35c/S23
Similar to DryLife.
B35e/S23
Similar to Life, but less active, with a p4.
| The p4 (click above to open LifeViewer) |
B35k/S23
Similar to Life.
B35a/S23
Similar to Life. The 4x4 solid block is a p4. Also has a p8, and a glide-reflective c/12d, and a glide reflective 5c/14o.
| The p4, the p8, the c/12d, and the 5c/14o (click above to open LifeViewer) |
B35i/S23
Similar to Life.
B35n/S23
Also called LifeWithoutGliders. There is a p60 rotating pre-pulsar hassler.
| The p60 (click above to open LifeViewer) |
B35y/S23
This rules is also called "hatlife", since a hat is a c/3o spaceship. Traffic lights are much more common because the 5-cell V spark (the one that defines B5y) becomes a T-tetromino. Similarly, since a line of six cells creates two of these, the same happens here, forming an interchange. Common beehive predecessors, such as the L-tetromino, also turn into an interchange. Long barges are more common since a fleet turns into two long barges and a bun becomes a fleet in two generations. This isn't to say that other still lifes don't exist, though; everything except the beehive still appears scattered throughout. Pulsars are more common, although they're not everywhere. Lifespan/explosiveness compared to Life is unchanged.
On September 30, 2021, forums user Inferno found a 3c/16 diagonal spaceship (Catagolue: here) by apgsearching a nearby rule B34e5y/S23.
- B35y/S23 at Adam P. Goucher's Catagolue
- B35y/S23 (hatlife) (discussion thread) at the ConwayLife.com forums
B35q/S23
Similar to Life, with a small c/4o.
| The c/4o (click above to open LifeViewer) |
B35j/S23
Similar to Life, with a natural c/3o puffer.
| The c/3o puffer (click above to open LifeViewer) |
B35r/S23
Similar to Life, with a 2c/20 diagonal spaceship.
| The 2c/20d (click above to open LifeViewer) |
B6
B36c/S23
Similar to Life, with a unique 2c/14o.
| The 2c/14o (click above to open LifeViewer) |
B36e/S23
B36k/S23
B36a/S23
B36i/S23
Pretty much indistinguishable from Life.
B36n/S23
Also called Ship. The HighLife replicator works, but closer to Life in other respects.
B7
B37c/S23
Explosive, with dynamics comparable to DryLife, as exemplified by R-pentomino.
B37e/S23
Settles down similar to Life, but with a common infinite growth pattern arising from the I-heptomino. Also known as PiLife.
| I-heptomino becomes (11,11)c/52 puffer (click above to open LifeViewer) |
It can pull a beehive behind it to make a spaceship.
| The 11c/52d spaceship (click above to open LifeViewer) |
DryLife's 9c/28 pond puffer works in this rule, and there are numerous c/2 puffers arising from two B-heptominoes. A 74c/382o dirty puffer has been discovered as well.
- B37e/S23 at Adam P. Goucher's Catagolue
- Forums thread for B37e/S23 (discussion thread) at the ConwayLife.com forums
B8
B38/S23
For details see this article: Pedestrian Life.
- B38/S23 at Adam P. Goucher's Catagolue
- Forums thread for B38/S23 (discussion thread) at the ConwayLife.com forums
Survival transitions
S0
B3/S023
Has an article: DotLife.
- B3/S023 at Adam P. Goucher's Catagolue
- Dotlife(B3/S023) (discussion thread) at the ConwayLife.com forums
S1
B3/S1c23
Very explosive.
B3/S1e23
Very explosive.
S2
B3/S2-c3
Dynamics similar to Life, has some unique p2s and a unique p4.
B3/S2-e3
Dynamics similar to Life, has a c/4d and a 2c/8o.
B3/S2-k3
Dynamics similar to Life, has unique p3, p4, and p8.
B3/S2-a3
Abundant p2 oscillators exist, also has several c/3o's and a 2c/4o.
B3/S2-i3
Has both the glider and the c/5o T-ship from tlife. Honeycombs form from phi sparks. The cap is a period-4 oscillator.
B3/S2-n3
Settles much more quickly, but still has dense ash, with the main difference being that traffic lights and honey farms don't form, leaving fleets as the only common constellation.
| period-3 oscillator; appears approximately twice on average in a 1000×1000 soup (click above to open LifeViewer) |
S3
B3/S23-c
The pi is a 3c/10o puffer.
B3/S23-e
Has a unique p80, and a (12,6)c/40 knightship, and a c/3o.
- B3/S23-e at Adam P. Goucher's Catagolue
- B3/S23-e (discussion thread) at the ConwayLife.com forums
B3/S23-k
Similar to Life, with a unique c/4d.
B3/S23-a
Much more stable than Life, has two c/2o's based on the B-heptomino.
B3/S23-i
Settles quickly. Has a unique p10, and a rotating p8 (two of them can non-trivially interact to form a larger p8).
B3/S23-n
Settles quickly. Gliders don't work. Most honey farms die out, but one predecessor (the one that is two blocks too close to each other) is a p3.
B3/S23-y
Settles slightly quicker than Life. Traffic lights are rarer; the T-tetromino dies, but different sequences converging to the hollow or solid 3×3 square still work.
B3/S23-q
Interchange is a p6 oscillator. There is a fairly common p10 where one phase is two pi heptominoes facing each other with a bounding box of 3×9. Honey farms don't work (every predecessor does something different), fleets become four blocks, and the common Life spark of two touching preponds becomes two loaves. Glider is slightly more common because the 3o$3o$2bo! spark evolves to a glider.
B3/S23-j
Settles quickly. Ash differs from Life in the form of no gliders, fewer (but not no) honey farms, ship-ties appear by themselves instead of in pairs, more integrals, and the B-heptaplet is a 2c/4o spaceship. The 9-cell queen bee form is a c/2o true-period spaceship.
- B3/S23-j at Adam P. Goucher's Catagolue
- Integralife (B3/S23-j) (discussion thread) at the ConwayLife.com forums
B3/S23-r
Mangoes are very common, and beehive at beehive and bipond also more common than usual. Several relatives of the pi heptomino evolve into a constellation of four loaves via pre-pulsar. The fleet evolves into the super pond.
S4
B3/S234c
Pretty much indistinguishable from Life.
- B3/S234c at Adam P. Goucher's Catagolue
- B3/S234c (discussion thread) at the ConwayLife.com forums
B3/S234e
Traffic lights become four blinkers with a tub in the middle. Honey farms don't work.
B3/S234k
Mildly explosive. Gliders don't work.
B3/S234a
Explosive enough that it's just one single expanding blob.
B3/S234i
Moderately explosive. Still lifes and blinkers do appear in the expanding mass, but they don't survive for long.
B3/S234n
Moderately explosive. Traffic lights become small lakes instead.
B3/S234y
Explosive, as exemplified by R-pentomino, which is a failed (20,7)c/68 puffer and explodes chaotically in a breeder-like manner.
B3/S234q
Mildly explosive. Pairs of mirrored buns appear quite frequently. Has two c/4 diagonal spaceships, the one that's not the glider is described in tlife.
B3/S234j
Almost indistinguishable from Life.
B3/S234r
Highly explosive.
B3/S234t
Mildly explosive. Mangoes are more common; otherwise, the ash is almost indistinguishable from Life. Occasionally, a still life will appear that relies on S4t.
B3/S234w
Not explosive. There is a unique p6, p9 and 2c/7d, among many other interesting patterns.
| From top-left to top-right: p6, p9, p10, 2c/7d; from bottom-left to bottom-right: p46, p30, glider tagalong (click above to open LifeViewer) RLE: here Plaintext: here |
The diagonal speed limit is c/3, not c/4, and there is an explicit example of a c/3d.
| A 3c/7 and 6c/14 puffer, c/3d, 2c/7d and c/4d (click above to open LifeViewer) |
B3/S234z
- See also Zlife
Lasts longer and expands more than Life, but still not explosive. The pi heptomino becomes a dead spark coil and a beehive. Hats are also more common.
S5
B3/S235c
B3/S235e
Traffic lights form small lakes, and honey farms from with a tub in the middle. Explosive on first glance, but actually just very chaotic.
- B3/S235e at Adam P. Goucher's Catagolue
- LakeLife (discussion thread) at the ConwayLife.com forums
B3/S235k
B3/S235a
An expanding blob of chaos, which is active in most places (more than in DryLife but less than in B3/S235i); stable patterns can be seen in the active region. Gliders are fast enough to escape the expansion, and there's a 2c/4 orthogonal spaceship that's much more common than the three XWSSes (which all work).
B3/S235i
An expanding blob of chaos, which is active pretty much everywhere, although patterns can be seen in the active region; it doesn't look like grey goo. Gliders are fast enough to escape the expansion. The T-pentomino is a period-14 oscillator.
- B3/S235i at Adam P. Goucher's Catagolue
- ilife (discussion thread) at the ConwayLife.com forums
B3/S235n
B3/S235y
B3/S235q
B3/S235j
B3/S235r
Pi-heptominoes form 3c/10 block puffers. The Eater 3 can be reduced to a loaf and canoe, resulting in very small hasslers. Sailboat, 120P34 and p52 R-pentomino hassler can be reduced this way.
S6
B3/S236c
Explosive, as exemplified by bobo$o2b2o$o2bo! .
B3/S236e
B3/S236k
Explosive, as exemplified by R-pentomino.
B3/S236a
Explosive, as exemplified by pi-heptomino.
B3/S236i
B3/S236n
Explosive, as exemplified by R-pentomino.
S7
B3/S237c
Explosive, as exemplified by century.
B3/S237e
Appears explosive, but actually just extremely chaotic.
S8
B3/S238
For details see Article: EightLife.
- B3/S238 at Adam P. Goucher's Catagolue
- B3/S238 (discussion thread) at the ConwayLife.com forums
External links
- Rules 1 transition from Life (discussion thread) at the ConwayLife.com forums
- Oscillator Discussion Thread (1-transition) (discussion thread) at the ConwayLife.com forums
- Oscillators in Near-Life rules not supported by Life (discussion thread) at the ConwayLife.com forums