Create your own terminology

[muzik]

Gutteroid: Of oscillators, a region of cells in a time-symmetric oscillator which must necessarily oscillate at a subperiod rather than at the full period. (I would have called these "gutroids" for shortness, but the google search results were weird.)

For example, in the 4-block twin bees shuttle, the entire configuration appears reflected across an orthogonal line that passes through the center of cells. These cells must necessarily oscillate at half the period (23 instead of 46) due to the reaction passing through them twice as often. This creates a gutter-like line of lower-period cells (hence "gutteroid" or "gutroid") where this happens. Were the line of time symmetry through the edges/vertices of cells, these lower period cells would not occur.

Code: Select all

x = 29, y = 11, rule = B3/S23
11bo$2o8b2o15b2o$2o7b2o16b2o$10b2o2b2o4$10b2o2b2o$2o7b2o16b2o$2o8b2o
15b2o$11bo!

On {4,4}, gutteroids of an oscillator of period n can either be 0-dimensional with a max period of n/2, 0-dimensional with a max period of n/4 or 1-dimensional with a max period of n/2. Note how I said "max": indeed, a gutteroid cell can be even lower, and often can go effectively unnoticed if the oscillator doesn't "pass through" the affected region, for example a reflector less rotating oscillator that never touches the origin, or the origin is a stator cell.

Oscillators with the following kinetic symmetries will have gutteroids (you can check that they do using Identify):

n-f, 1D orthogonal, max n/2

Code: Select all

x = 29, y = 9, rule = B3-y/S23-k
2o2b2o4bo2b2o12b2o$2ob2o6b2obo12b2o$4bobo6bo$5b2o4b3o2$5b2o4b3o$4bobo6bo$3b2o
6b2obo$4b2o4bo2b2o!

n/, 1D diagonal, max n/2

Code: Select all

x = 3, y = 3, rule = B2-k3q4iy5ijr7c/S12k3ajr4it5ciqr6ae
obo$2bo$2bo!

n.f, 0D, max n/2

Code: Select all

x = 2, y = 5, rule = B2ack3ac4einr5jn6-kn/S01e2c3ijnq4ajkrw5k6ck7e
o2$bo2$bo!

-f+f, 1D orthogonal, max n/2

Code: Select all

x = 2, y = 3, rule = B3ai4a5aiy7e/S2-en3-ciky4i5i6i
bo$2o$bo!

-e+e, 1D orthogonal, max n/2

Code: Select all

x = 2, y = 4, rule = B2ei3aij4a/S2aek3ar
bo$2o$2o$bo!

/xf, 1D diagonal, max n/2

Code: Select all

x = 3, y = 3, rule = B3aijn4jt5k/S23ijn7c
2o$b2o$2bo!

/xv, 1D diagonal, max n/2

Code: Select all

x = 3, y = 3, rule = B2ekn3eiy4cw/S12ae3j4w
3o$obo$b2o!

.f+f, 1D 2x orthogonal, max n/2

Code: Select all

x = 7, y = 5, rule = B2n3aijnr/S2-c3-ceky
b2o$3o$bobobo$4b3o$4b2o!

.fxf, 1D 2x diagonal, max n/2

Code: Select all

x = 3, y = 5, rule = B2cek3ai4arz6n8/S02a3ijny4n5jny
o2$bo2$2bo!

.frf, 0D, max n/2

Code: Select all

x = 5, y = 5, rule = B2in3cekr4r5r6n/S012ai3r4ry5a
3bo$obo2$2bobo$bo!

.e+e, 1D orthogonal, max n/2

Code: Select all

x = 2, y = 5, rule = B2ac3nry4nt5er/S
o2$2o2$bo!

.vxv, 1D 2x diagonal, max n/2

Code: Select all

x = 2, y = 4, rule = B2ac3ej4jr5r6k/S2c4acjr
o$bo$o$bo!

+f*f, 1D 2x diagonal, max n/2

Code: Select all

x = 1, y = 3, rule = B2ai4eikr5i6i/S01e2i3ei5i6i7e
o2$o!

+v*v, 1D 2x diagonal, max n/2

Code: Select all

x = 4, y = 4, rule = B2ck3iq4iw5r6k/S2k3a4ar6a
o2bo$o2bo$o2bo$o2bo!

xf*f, 1D 2x orthogonal, max n/2

Code: Select all

x = 5, y = 5, rule = B2en8/S01c5a
o2$2bo2$4bo!

rf*f, 1D 2x orthogonal + 2x diagonal, max n/2

Code: Select all

x = 15, y = 15, rule = B3/S23
7b3o$6bo2bo$7bo3bo$2bo5b3o$3bo5bo$2ob2o$o2bo9bo$obo9bobo$bo9bo2bo$10b2ob2o$5b
o5bo$4b3o5bo$3bo3bo$5bo2bo$5b3o!

rv*v, 1D 2x diagonal, max n/2

Code: Select all

x = 8, y = 8, rule = B2n3/S2-ei3-cqy4q
bobo$3b2o2bo$4bo$b2o3b2o$2o3b2o$3bo$o2b2o$4bobo!

nrf, 0D, max n/4

Code: Select all

x = 2, y = 4, rule = B2eik3ijqr4knqrtz5ijkn6-ci7e/S02aei3cijqy4aknq5c6e
bo$o2$bo!

[Gamer729]

Robin Removal: any salvo that erases Sir Robin, like this one.

Code: Select all

x = 31, y = 87, rule = B3/S23
27bo$25bobo$26b2o6$25b2o$23bo2bo$22bo3bo$22b3o$17b4o6b2o$17b4o4b2obo$
15b3o6bo4bo$15bo3b2o4b4o$19b2o9bo$25bo3bo$15bo2b2o2b3o$14bo4bo7b2o$14b
2obo$12bo6b2o$12bob3ob2o$12bo2bo3b2o$14b2o2bobo$13bobobo2bo$11bo6b3o$
11bo3bobobo$11bobob2o$10b3o6bo2$9bo9bo$8bo6bo3bo$8b5o5bo$16b3o$13b2o$
12bo2b3o$13bob3obo$13bo2bo3bo$9b3ob2o4bo$6b2o4bob4o$6b2o4b4obo$11bo$6b
2o2bo$9b2o$5b5o$4b2o$2bo6b3o$2bobo3bobo$3bo3bo3bo$6b2o3bo$b3obo6bo$b2o
3bo3b2o$bo2bo2b4o$3bo3b2o$9bo$6bob2o$10bo$7b5o$6bo4bo$6b3ob3o$6b5obo$
12bo$10bo$6b4o4bo$4b2ob4o$6bo4b3o$4bobo$2bo$2b2o2bo$3b3o$7b2o$bo5b3o$
obo2b2o$obob3o2bo$2bo2bob2o$2o2bobo$3b2o$bo4b3o$bo4b3o$3o3b2o$2b2ob2o
$4b2o$5bo2$5b2o$4bo!

Could add extra cleanup gliders.

[Overweight spaceship]

Constricted diehard: a diehard that does not exceed its initial bounding box
Extinct methuselah: a methuselah with a relatively low initial population, a large peak population and a final population of 0
(i.e. a diehard that seems to have infinite growth)

[Gamer729]

Spontaneous/ incremental symmetry breaking:
Spontaneous: no part of pattern has symmetry but in 1 generation it has symmetry.

Code: Select all

x=2, y=3, rule=B3S23
ob$2b$2o!

Incremental: part of pattern was symmetrical, but part of both halves are not yet symmetrical, but will be in a generation.

Code: Select all

x=9, y=5, rule=B3S23
2b3ob3o$9b$o8b$9b$2b3ob3o!

This can also happen over multiple stages, hence ‘incremental’.

[confocaloid]

Constricted diehard: a diehard that does not exceed its initial bounding box
Extinct methuselah: a methuselah with a relatively low initial population, a large peak population and a final population of 0
(i.e. a diehard that seems to have infinite growth)

Every diehard can be modified into a constricted diehard by adding isolated dot sparks sufficiently far away. So for any diehard, one could look for a smallest-bounding-box "equivalent" constricted diehard (where "equivalent" could mean "evolves to the same pattern after 1 tick").

[atavoidirc]

In elementary conduits, Have the letter Z (for Zilch) represent nothing. E.g. an eater1 would be G*4Z. (the star is there because nothingness
only exists in one orientation)
In addition, other inputs and outputs without abbreviations shall be referred to by apgcode (no prefix) e.g.

Code: Select all

 x = 12, y = 13, rule = B3/S23
2o$bo5b2o$2bo4b2o$b2o2$8b2o$8bo$9b3o$11bo$3b2o$3bo$4b3o$6bo!

would be 1bcFx22R.
Finally some two letter abbreviations:
Hf - Honey farm
Hw - HWSS
Rt - R-turner
Se - Switch engine
Tl - Traffic light

[hotdogPi]

That makes sense. While I've seen (and used) Z for the Z-hexomino occasionally, it's not really worth tracking except for its conversion to a LWSS, and it was never intended as a conduit letter.

[Haycat2009]

In elementary conduits, Have the letter Z (for Zilch) represent nothing. E.g. an eater1 would be G*4Z. (the star is there because nothingness
only exists in one orientation)
In addition, other inputs and outputs without abbreviations shall be referred to by apgcode (no prefix) e.g.

Code: Select all

 x = 12, y = 13, rule = B3/S23
2o$bo5b2o$2bo4b2o$b2o2$8b2o$8bo$9b3o$11bo$3b2o$3bo$4b3o$6bo!

would be 1bcFx22R.
Finally some two letter abbreviations:
Hf - Honey farm
Hw - HWSS
Rt - R-turner
Se - Switch engine
Tl - Traffic light

Using a letter for nothing is confusing...

[hotdogPi]

I prefer Я for the R-turner.

[erictom333]

Here are my proposals for methuselah symbols:

Code: Select all

-  Nothing
Ac Acorn
An Angel
B  B-heptomino/C-heptomino
Bf Butterfly
Bk Bakery
C  Century
D  Dove
Dh Diehard
E  E-heptomino
F  F-heptomino
Ft Fleet
G  Glider
Gd Gliders by the dozen
H  Herschel
H' Herschel descendnt
H* Herschel predecessor
Hf Bun
Hw HWSS
I  I-heptomino/H-heptomino
Ia Iwona active region
Ic Interchange
J  Blonk-tie
La Lidka active region
Lb Long bun
Lw LWSS
Mp Multum in parvo
Mw MWSS
O  Two-glider octomino
Ob Octomino II
P  Pi heptomino
Ph Phi spark
Pp Prepulsar
Qb Queen bee
R  R-pemmtomino
Rt R-turner
S  LOM
Sa 2c/3 signal
Sb 5c/9 signal
Se Switch engine
T  Traffic light
Tb Thunderbird
Td Teardrop
Te Table
Tg TL + glider
Tm Two glider mess
U  U-turner
W  Wing
Z  Z-hexomino

[May13]

A cellular automaton is said to be omniperiodic if it has oscillators of all periods.

When this term is applied to multi-state cellular automata, it ceases to be interesting.
Consider, for example, a 5-state CA where state 1 emulates B3/S35, and states 2 (alive), 3 and 4 (dying) emulates StarWars (4-state rule 345/2/4). This CA is omniperiodic, although neither B3/S35* nor StarWars are omniperiodic (p1-p3 from B3/S35, p4+ from StarWars).
*There is no proof that B3/S35 is not omniperiodic, but there are currently no known oscillators with odd periods other than 1 or 3.
Therefore, I propose a more strict definition.
A cellular automaton is strictly omniperiodic if:

1. A cell of any state can be part of a still life;
2. For any pair of different states, there are oscillators of all periods (not counting 1) such that at least one cell oscillates with the same period as the oscillator itself, and is set to each of the selected states at different generations.

General facts related to this definition:

1. An omniperiodic two-state rule is strictly omniperiodic because:
   1. Each still life contains state 0 and state 1 cells;
   2. Only one pair of states (0 and 1) can be selected, while any rotor cell becomes alive and dead at different generations.
   Note: in the above statement, infinite periodic patterns (not counting the background with state 0 cells) are not considered oscillators or still lifes.
2. A strictly omniperiodic rule is omniperiodic because:
   1. There is at least one still life;
   2. There are oscillators with all periods.

Several examples:

• DoubleB3S23 is strictly omniperiodic.
  From left to right: still lifes, then oscillators with selected pairs (0,1), (0,2), (0,3), (1,2), (1,3), (2,3):

  Code: Select all

  x = 232, y = 51, rule = DoubleB3S23
  2A8.2B8.2C$2A8.2B8.2C18$31.B9.B9.A$3A7.3B7.3C7.ACA7.AC8.BC$31.B8.AC8.
  BC9$4.2A38.2B38.2C38.2C38.2B38.2A$4.A39.B39.C39.C39.B39.A$.2A.A10.A
  25.2B.B10.B25.2C.C10.C25.2C.C10.C25.2B.B10.B25.2A.A10.A$.A2.2A9.3A23.
  B2.2B9.3B23.C2.2C9.3C23.C2.2C9.3C23.B2.2B9.3B23.A2.2A9.3A$3.A2.A11.A
  24.B2.B11.B24.C2.C11.C24.C2.C11.C24.B2.B11.B24.A2.A11.A$.A.3A.A9.2A
  22.B.3B.B9.2B22.C.3C.C9.2C22.C.3C.C9.2C22.B.3B.B9.2B22.A.3A.A9.2A$A.A
  4.A32.B.B4.B32.C.C4.C32.C.C4.A32.B.B4.B32.A.A4.A$A2.3A15.A18.B2.3B15.
  B18.C2.3C15.C18.C2.3CB13.BC18.B2.3B15.B18.A2.3A15.A$.2A2.A5.A8.2A7.2A
  10.2B2.B5.B8.2B7.2B10.2C2.C5.C8.2C7.2C10.2C2.C5.A8.2C7.2C10.2B2.B5.B
  8.2B7.2B10.2A2.A5.A8.2A7.2A$3.2A6.A16.A.A12.2B6.B16.B.B12.2C6.C16.C.C
  12.2C5.BCB7.2B6.C.C12.2B6.B3.2A11.B.B12.2A6.A3.2B11.A.A$3.A7.A8.A7.A
  14.B7.B8.B7.B14.C7.C8.C7.C14.C7.A8.A7.C14.B7.B2.A2.A2.B7.B14.A7.A2.B
  2.B2.A7.A$.A.A16.A6.2A12.B.B16.B6.2B12.C.C16.C6.2C12.C.C6.2B7.BCB5.2C
  12.B.B11.2A3.B6.2B12.A.A11.2B3.A6.2A$.2A7.2A8.A5.A2.2A10.2B7.2B8.B5.B
  2.2B10.2C7.2C8.C5.C2.2C10.2C7.2C8.A5.C2.2C10.2B7.2B8.B5.B2.2B10.2A7.
  2A8.A5.A2.2A$10.A15.3A2.A18.B15.3B2.B18.C15.3C2.C18.CB13.B3C2.C18.B
  15.3B2.B18.A15.3A2.A$24.A4.A.A32.B4.B.B32.C4.C.C32.A4.C.C32.B4.B.B32.
  A4.A.A$13.2A9.A.3A.A22.2B9.B.3B.B22.2C9.C.3C.C22.2C9.C.3C.C22.2B9.B.
  3B.B22.2A9.A.3A.A$13.A11.A2.A24.B11.B2.B24.C11.C2.C24.C11.C2.C24.B11.
  B2.B24.A11.A2.A$14.3A9.2A2.A23.3B9.2B2.B23.3C9.2C2.C23.3C9.2C2.C23.3B
  9.2B2.B23.3A9.2A2.A$16.A10.A.2A25.B10.B.2B25.C10.C.2C25.C10.C.2C25.B
  10.B.2B25.A10.A.2A$27.A39.B39.C39.C39.B39.A$26.2A38.2B38.2C38.2C38.2B
  38.2A!
  [[ ZOOM 2 ]]
  

• Wireworld5 is omniperiodic, but not strictly omniperiodic, because state 0 cells cannot be set to other states.
• Symbiosis is omniperiodic, but not strictly omniperiodic, because there is no period 2 rotor with at least one cell whose state alternates between 1 and 2.
• [R]History and [R]Super are omniperiodic, but not strictly omniperiodic due to state 6. For the same reason, StateInvestigator is not strictly omniperiodic too (state 6 from [R]History=state 3 from StateInvestigator).

Maybe there is a better name than "strictly omniperiodic", but I haven't seen anywhere an idea to extend the concept of omniperiodicity to multi-state CA.

[confocaloid]

A cellular automaton is strictly omniperiodic if:

1. A cell of any state can be part of a still life;
2. For any pair of different states, there are oscillators of all periods (not counting 1) such that at least one cell oscillates with the same period as the oscillator itself, and is set to each of the selected states at different generations.

Maybe one could measure how far a given rule is from being strictly omniperiodic. If I understand correctly, Brew is omniperiodic (a pattern made entirely of blue cells follows Life, which is now known to be omniperiodic), but not strictly omniperiodic (there is no p2 rotor with a cell that alternates between "red" and "dead"). Still, there are p2 oscillators where a cell alternates between any two non-quiescent cellstates, a p3 oscillator where a cell cycles through all three non-quiescent cellstates, and a p4 oscillator where a cell cycles through all four cellstates; pentant is a p5 example and extremely impressive is a p6 example.

Code: Select all

x = 26, y = 27, rule = Brew
4.2A4.2B4.2C$4.2A4.2B4.2C5$4.2A4.2C4.2C$3.3BA2.3BC2.3AC$3.A3B2.C3B2.C
3A$4.2A4.2C4.2C4$20.A$5.A13.A.A$4.A.A12.A.A$4.A.A11.2A.2A$3.2A.2A9.A
2.B2.A$A.A2.B2.A.A5.A.5A.A$2A.5A.2A5.A.A3CA.A$3.A.A.A7.2A.A3CA.2A$3.A
.A.A7.A2.5A2.A$4.A.A10.A2.B2.A$5.A12.2A.2A$19.A.A$19.A.A$20.A!

Here are my proposals for methuselah symbols:

I would like to propose JJ for b3o$bo2bo$o2b2o$2o2bo! (the intermediate object that appears in the Jubjub reflector and the speed tunnel).

[C_R_116]

Detonator: A rule neighborhood that increases the rule's explosivity.

For example, in B3/S234i, 4i would be a detonator:

Code: Select all

x = 3, y = 3, rule = B3/S234i
bo$3o$o!

Defuser/Retardant: A rule neighborhood that decreases the rule's explosivity.

For example, in B3-a/S23, 3-a would be a defuser.

Code: Select all

x = 3, y = 3, rule = B3-a/S23
bo$3o$o!

[confocaloid]

Proposed name: Baitless G-to-Pi

Direct g-to-pi by Mvr with no bait objects:

Code: Select all

x = 13, y = 15, rule = B3/S23
6bo$7bo$5b3o3b2o$11b2o2$2o$o2bob2o$b3obo$5bo$b3ob3o$o2b2o3bo$bo4b2o$2b
3obo$4bobo$5bo!

G-to-hive with some kind of use:
...

p36 glider/pi hassler based on the new catalyst:
...

Reduced:
...

[AlbertArmStain]

Universal construction based replicators can be divided in to two classes, each with their own sub classes. The two classes of replicators are "tape based replicators" and "channel construction replicators". The sub classes for "tape based replicators" are "stable tape replicators" (e.g. William R. Buckley's replicators, NP-replicator, anything that has a static tape), and "moving tape replicators" (e.g. JVN loop replicator, rct (although I don't think the rct counts). The subclass for "channel construction replicators" are "single channel construction replicators" (e.g DOGun SaGaQR, 0E0P metacell(?)) and "multiple channel construction replicators" (e.g. Linear propagator). Additionally, replicators can be linear, super-linear, or quadratic.

[hotcrystal0]

Free oscillator/spaceship: An oscillator/spaceship that requires support in Life, but doesn’t, or has much smaller supports, in another rule: Examples: worker bee and an unnamed P18

Code: Select all

 x = 44, y = 24, rule = Rainbow1TFL
6.2A12.2A$7.A12.A$7.A.A8.A.A$8.2A8.2A2$11.6A19.6U2$8.2A8.2A$7.A.A8.A.
A$7.A12.A$6.2A12.2A3$13.2A22.2X$13.2A7.A14.2X$3A15.7A.A15.2X$2A.A.A12.
3A3.3A15.2X$5.A9.A6.A3.A12.X$14.A.A6.3A12.X.X$5.2A7.A.A8.2A11.X.X$.A3.
3A2.2A3.A18.2X3.X$2.2A7.A15.3A4.2X$7.A.A5.2A22.2X$15.2A22.2X!

[MEisSCAMMER]

Free oscillator/spaceship: An oscillator/spaceship that requires support in Life, but doesn’t, or has much smaller supports, in another rule: Examples: worker bee and an unnamed P18

So would the pattern be called free regardless of rule, or is it only called free in the OCA?

[hotcrystal0]

Free oscillator/spaceship: An oscillator/spaceship that requires support in Life, but doesn’t, or has much smaller supports, in another rule: Examples: worker bee and an unnamed P18

So would the pattern be called free regardless of rule, or is it only called free in the OCA?

Only free in OCA

[SuperNerdUqau]

Recurrer: A pattern that recurs at some point in its evolution. The term is very broad, covering still lives, oscillators, spaceships, puffers, guns, and replicators.

[confocaloid]

Recurrer: A pattern that recurs at some point in its evolution. The term is very broad, covering still lives, oscillators, spaceships, puffers, guns, and replicators.

A semiinfinite diagonal line would count as a recurrer. Is the pi-heptomino a recurrer because of two copies visible at T = 26, or the copy needs to be isolated like the one-tick descendant reappearing at T = 30?

Code: Select all

x = 3, y = 3, rule = B3/S23
3o$obo$obo!
#C [[ ZOOM 16 STOP 26 ]]

[confocaloid]

Let Y stand for some set of active objects. A conduit is said to be elementary relative to the set Y, when the conduit is not composed of two or more conduits whose inputs and outputs all belong to the set Y. For example, F117 and Lx200 are elementary relative to the set { H }, but composite relative to the set { H, B }; R64 is elementary relative to the set { H, B }, but composite relative to the set { H, 2o$ob2o$3bo$bobo$b2o! }. Unlike the existing elementary/composite distinction (elementary conduit), this one cannot be affected by new discovered intermediate objects.

[haaaaaands]

square = cell because in most rules they're square
smol ship = glider because they're small xd
sandal = boat because it looks more like a sandal than a boat to me
octogonal = orthogonal because i make that "typo" a lot

[azulavoir]

Battleship: Any oscillator that involves one or more naval still lives (Ships, boats, barges, canoes, aircraft carriers). Could also be 29p9, specifically.

[C_R_116]

Fighter Jet: A puffer that gives off spaceships faster than its speed.

The Glider producing switch engine is an example of a fighter jet as the gliders are faster than the switch engine.

[confocaloid]

square = cell because in most rules they're square
smol ship = glider because they're small xd
sandal = boat because it looks more like a sandal than a boat to me
octogonal = orthogonal because i make that "typo" a lot

Constillation: a constellation of still lives.
"There are no sandals in a constillation where every alive square has exactly two other alive squares octogonally adjacent to it."

Code: Select all

x = 19, y = 15, rule = LifeHistory
5.2A$5.2A2$3.4A$3.A2.A10.D$2A.A2.A.2A6.D.D$2A.4A.2A7.2D2$2A.2A$2A.2A$
8.2A$8.2A2$.2A5.2A$.2A5.2A!