Create your own terminology

[CARuler]

recently, I have been thinking about symmetries in the states of multi-state rules

this might seem redundant, but you can have more symmetries types with more states

for example, take a 3 state rule where state 1 can be swapped with state 2

this can be written:

Code: Select all

f1(s): 1 |-> 2, 2 |-> 1

using this ruletable as an example:

Code: Select all

@RULE 2stateCGOL-like
@TABLE
n_states:3
neighborhood:Moore
symmetries:permute
var a = {0,1,2}
var b = a
var c = a
var d = a
var e = a
var f = a
var g = a
var h = a
var i = {1,2}
var j = i
var k = i

k,i,j,a,0,0,0,0,0,1
0,1,1,1,0,0,0,0,0,2
0,1,1,2,0,0,0,0,0,2
0,2,2,2,0,0,0,0,0,1
0,2,2,1,0,0,0,0,0,1

0,1,1,1,1,2,2,0,0,2
0,2,2,2,2,1,1,0,0,1
#defaults
i,a,b,c,d,e,f,g,h,0

it has the additional symmetries:

Code: Select all

R2
{[a,b],f1([-a,-b])}

R4
{[a,b],f1([-b,a]),f1([b,-a]),[-a,-b]}

R8
{[a,b],f1([-a,b]),f1([b,a]),[-b,a],f1([-b,-a]),[-a,-b],[b,-a],f1([a,-b])}

F2|
{[a,b],f1([-a,b])}

F2/
{[a,b],f1([b,a])}

F2-
{[a,b],f1([a,-b])}

F2\
{[a,b],f1([-b,-a])}

F4+
{[a,b],f1([-a,b]),f1([a,-b]),[-a,-b]}

F4|
{[a,b],[a,-b],f1([-a,b]),f1([-a,-b])}

F4-
{[a,b],[-a,b],f1([a,-b]),f1([-a,-b])}

F4X
{[a,b],f1([b,a]),f1([-b,-a]),[-a,-b]}

F4/
{[a,b],f1([b,a]),[-b,-a],f1([-a,-b])}

F4\
{[a,b],[b,a],f1([-b,-a]),f1([-a,-b])}

F8+
{[a,b],[-a,b],f1([-b,a]),f1([-b,-a]),[-a,-b],[a,-b],f1([b,-a]),f1([b,a])}

F8X
{[a,b],[b,a],f1([b,-a]),f1([a,-b]),[-a,-b],[-b,-a],f1([-b,a]),f1([-a,b])}

notation:
{[p1],[p2],...,[pn]} means that the points [p1],[p2],...,[pn] have all the same states
(note: f1([pn]) means the state of [pn] (s) is prosected as f1(s) in order to fit with the other states

[confocaloid]

recently, I have been thinking about symmetries in the states of multi-state rules

this might seem redundant, but you can have more symmetries types with more states

for example, take a 3 state rule where state 1 can be swapped with state 2
[...]

Prior art:

• Self-complementary
• viewtopic.php?f=11&t=4611 Multistate cyclical rules, a notation

(note: f1([pn]) means the state of [pn] (s) is prosected as f1(s) in order to fit with the other states

I'm not sure whether I understand the idea, can you explain in more details how it is intended to work?

added later:

[...] using this ruletable as an example:

Code: Select all

@RULE 2stateCGOL-like

it has the additional symmetries: [...]

That example ruletable doesn't appear to have any "permutation of cellstates" symmetries, here are several examples where a state-1 seed evolves differently from the state-2 version of the same seed:

Code: Select all

x = 17, y = 23, rule = 2stateCGOL-like
2A8.2B$2A2.3A3.2B2.3B9$.A10.B$2.A10.B$3A8.3B8$.A9.B$.2A8.2B$2A8.2B!

@RULE 2stateCGOL-like

Source: https://conwaylife.com/forums/viewtopic.php?p=202001#p202001

@TABLE
n_states:3
neighborhood:Moore
symmetries:permute
var a = {0,1,2}
var b = a
var c = a
var d = a
var e = a
var f = a
var g = a
var h = a
var i = {1,2}
var j = i
var k = i

k,i,j,a,0,0,0,0,0,1
0,1,1,1,0,0,0,0,0,2
0,1,1,2,0,0,0,0,0,2
0,2,2,2,0,0,0,0,0,1
0,2,2,1,0,0,0,0,0,1

0,1,1,1,1,2,2,0,0,2
0,2,2,2,2,1,1,0,0,1
#defaults
i,a,b,c,d,e,f,g,h,0

[PiSpaceships]

A repli-object is a pattern that shows a some sort of self-replicating behaviour. This concept is important because there is a lot of objects that show such behaviour but are not replicators.
A repliship is an object that creates copies of itself while moving.
A repligun is an object than shoots spaceships while replicating.
A repli-object is chaotic if its copies/created objects collide with each other, creating chaos that doesn't affect all copies.

An oscillatorstretcher is an object which would be an oscillator if its stretching part were deleted. (one was posted in the Day&Night topic.)

[CARuler]

Code: Select all

x = 17, y = 23, rule = 2stateCGOL-like
2A8.2B$2A2.3A3.2B2.3B9$.A10.B$2.A10.B$3A8.3B8$.A9.B$.2A8.2B$2A8.2B!

@RULE 2stateCGOL-like

Source: https://conwaylife.com/forums/viewtopic.php?p=202001#p202001

@TABLE
n_states:3
neighborhood:Moore
symmetries:permute
var a = {0,1,2}
var b = a
var c = a
var d = a
var e = a
var f = a
var g = a
var h = a
var i = {1,2}
var j = i
var k = i

k,i,j,a,0,0,0,0,0,1
0,1,1,1,0,0,0,0,0,2
0,1,1,2,0,0,0,0,0,2
0,2,2,2,0,0,0,0,0,1
0,2,2,1,0,0,0,0,0,1

0,1,1,1,1,2,2,0,0,2
0,2,2,2,2,1,1,0,0,1
#defaults
i,a,b,c,d,e,f,g,h,0

oops
this is what i meant:

Code: Select all

x = 17, y = 23, rule = 2stateCGOL-like
2A8.2B$2A2.3A3.2B2.3B9$.A10.B$2.A10.B$3A8.3B8$.A9.B$.2A8.2B$2A8.2B!

@RULE 2stateCGOL-like

Source: https://conwaylife.com/forums/viewtopic.php?p=202001#p202001

@TABLE
n_states:3
neighborhood:Moore
symmetries:permute
var a = {0,1,2}
var b = a
var c = a
var d = a
var e = a
var f = a
var g = a
var h = a
var i = {1,2}
var j = i
var k = i

k,i,j,a,0,0,0,0,0,k
0,1,1,1,0,0,0,0,0,2
0,1,1,2,0,0,0,0,0,2
0,2,2,2,0,0,0,0,0,1
0,2,2,1,0,0,0,0,0,1

0,1,1,1,1,2,2,0,0,2
0,2,2,2,2,1,1,0,0,1
#defaults
i,a,b,c,d,e,f,g,h,0

[confocaloid]

[...] Prior art:

• Self-complementary
• viewtopic.php?f=11&t=4611 Multistate cyclical rules, a notation

(note: f1([pn]) means the state of [pn] (s) is prosected as f1(s) in order to fit with the other states

I'm not sure whether I understand the idea, can you explain in more details how it is intended to work?
[...]

[...]
oops
this is what i meant:
[...]

Here is a version with comments explaining (what appears to be) each rule, because you didn't yourself explain how it works.

Note that I changed the name (and fixed the link in the comments to point to the actual source of this set of rules), both because .rule filenames must begin with an uppercase letter, and because it is one of several "testing" modifications and it makes sense to use different names for different modifications.

There are two nonzero cellstates (1 and 2). This version is symmetric w.r.t. exchange of cellstates 1 and 2, by definition, because each commented set of rules has this property when viewed as an implementation of the rule stated in the comments:

• "if the cell is currently nonzero and has between two and three nonzero neighbours, then it stays in the same state in the next generation"
  This rule doesn't refer at all to any specific nonzero cellstates, and is therefore symmetric w.r.t. exchange of nonzero cellstates.
• "if the cell is currently zero and has precisely three nonzero neighbours, then in the next generation the cell becomes nonzero with the nonzero cellstate that isn't the majority nonzero cellstate"
  This rule doesn't refer at all to any specific nonzero cellstates, and is therefore symmetric w.r.t. exchange of nonzero cellstates.
• "if the cell is currently zero and has precisely six nonzero neighbours, with four neighbours of a single nonzero cellstate and two neighbours of the other nonzero cellstate, then in the next generation the cell becomes nonzero with the minority nonzero cellstate"
  This rule doesn't refer at all to any specific nonzero cellstates, and is therefore symmetric w.r.t. exchange of nonzero cellstates.
• "defaults"
  This rule doesn't refer at all to any specific nonzero cellstates, and is therefore symmetric w.r.t. exchange of nonzero cellstates.

Note the important difference between "the nonzero cellstate that isn't the majority nonzero cellstate" and "the minority nonzero cellstate". In a configuration where there are only state-0 and state-1 neighbours (i.e. no state-2 neighbours at all), the former would refer to the cellstate 2 while the latter would refer to the cellstate 1.

Note that since I did not understand your proposal for an alternative notation and there was no further explanation of it yet, I cannot tell whether this particular set of rules can be notated in the way you are imagining and if so how that could be done.

Code: Select all

x = 17, y = 23, rule = Temp_post202070
2A8.2B$2A2.3A3.2B2.3B9$.A10.B$2.A10.B$3A8.3B8$.A9.B$.2A8.2B$2A8.2B!

@RULE Temp_post202070

Source: https://conwaylife.com/forums/viewtopic.php?p=202070#p202070

@TABLE
n_states:3
neighborhood:Moore
symmetries:permute
var a = {0,1,2}
var b = a
var c = a
var d = a
var e = a
var f = a
var g = a
var h = a
var i = {1,2}
var j = i
var k = i

# if the cell is currently nonzero and has between two and three nonzero neighbours,
# then it stays in the same state in the next generation:
k,i,j,a,0,0,0,0,0,k

# if the cell is currently zero and has precisely three nonzero neighbours,
# then in the next generation the cell becomes nonzero with the nonzero cellstate
# that isn't the majority nonzero cellstate:
0,1,1,1,0,0,0,0,0,2
0,1,1,2,0,0,0,0,0,2
0,2,2,2,0,0,0,0,0,1
0,2,2,1,0,0,0,0,0,1

# if the cell is currently zero and has precisely six nonzero neighbours,
# with four neighbours of one nonzero cellstate and two neighbours of the other nonzero cellstate,
# then in the next generation the cell becomes nonzero with the minority nonzero cellstate:
0,1,1,1,1,2,2,0,0,2
0,2,2,2,2,1,1,0,0,1

#defaults
i,a,b,c,d,e,f,g,h,0

[hotcrystal0]

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.

Are there any other examples of strictly omniperiodic rules?
Edit: I think my rule LifeWithoutHF3 might be a good candidate. Here’s examples of state 1 and 2 still lives, and how states can change from any state to any other state:

Code: Select all

x = 8, y = 12, rule = LifeWithoutHF3
2.A4.B4$.2A3.B$.2A2.B.B$6.B3$A5.BA$6.2A$A.A!

Edit 2: nevermind. There’s no way for state 1 to become state 2.

[erictom333]

Wazirship, ferzship, dababbaship, alfilship: Ships with displacements of exactly (1, 0), (1, 1), (2, 0), and (2, 2) respectively, based on the respective fairy chess pieces.

[confocaloid]

Should there be a terminological distinction for different displacements with the same slope, or merely for different slopes?
How would one distinguish between a (2,1)c/n spaceship and a (2k,1k)c/n spaceship for k > 1?

[b-engine]

Should there be a terminological distinction for different displacements with the same slope, or merely for different slopes?
How would one distinguish between a (2,1)c/n spaceship and a (2k,1k)c/n spaceship for k > 1?

There's no need for such distinction: N is the period of the spaceship, and is enough for the purpose.

One could differentiate between (2,1)c/6 and (4,2)c/12 spaceships.

[confocaloid]

Should there be a terminological distinction for different displacements with the same slope, or merely for different slopes?
How would one distinguish between a (2,1)c/n spaceship and a (2k,1k)c/n spaceship for k > 1?

There's no need for such distinction: N is the period of the spaceship, and is enough for the purpose.

One could differentiate between (2,1)c/6 and (4,2)c/12 spaceships.

There is certainly a need for conceptual distinction.

For example, if you have an orthogonal c/7 spaceship (such as the loafer), then you have just one spaceship lane per path. A loafer on a specific path will eventually visit infinitely many of the same locations, regardless of where you put the loafer on that path initially. Shift a loafer backwards by one cell, and it will evolve to visit the original location.

In contrast, an orthogonal 2c/7 spaceship or an orthogonal 3c/7 spaceship will only visit some of possible locations on a path (but not all of them). For a 2c/7o spaceship, there are two lanes per path. For a 3c/7o spaceship, there are three lanes per path. Shift a 2c/7o spaceship backwards by one cell, and it will never visit the original location again simply by evolving.

Here is another example: the two LWSSes on the top are on the same lane; however, the two LWSSes on the bottom are on different lanes:

Code: Select all

x = 26, y = 30, rule = B3/S23
bo2bo16bo2bo$5bo19bo$bo3bo15bo3bo$2b4o16b4o23$o2bo17bo2bo$4bo20bo$o3bo
16bo3bo$b4o17b4o!

I'm not sure whether this distinction requires multiple different terms, though, or all orthogonal spaceships can simply be described as orthogonal spaceships, without needing terms like 'wazirship' or 'dababbaship'.

Similarly, there is a distinction between (2,1)c/n spaceships and (4,2)c/n spaceships due to different set of locations they will eventually visit starting from a given location. I'm not sure whether that distinction requires different terms, though, or all slope-2 oblique spaceships can simply be described as knightships.

[hth3]

Super bun:

Code: Select all

x = 6, y = 5, rule = B3/S23
2b3o$bo3bo$ob2obo$bo2bo$2b2o!

[d/dx]

A gnomonic rule is any two-state rule in which the birth transitions are a subset of the survival transitions.

Edit: By "transition" I mean "state of cell's neighborhood" and not "state of cell and cell's neighborhood". By this logic, B4t and S4t are equivalent. Also, "gnomonic" is a random word that entered my mind once and I just had to use it somewhere hehe sorry

[unname4798]

A gnomonic rule is any two-state rule in which the birth transitions are a subset of the survival transitions.

B3/S23 is an example of a gnomonic rule.

[PiSpaceships]

A non-explosive rule is a rule in which random soups do not tend to increase their population infinitely.

[confocaloid]

A gnomonic rule is any two-state rule in which the birth transitions are a subset of the survival transitions.

One problem with this is that it's unclear whether the word 'gnomonic' is intended to suggest some relevant helpful idea. Why this particular choice of the term? Why "gnomonic"?

The other problem is that the given definition doesn't make much sense, as far as I can tell. It is impossible for birth transitions to be a subset of survival transitions, for all plausible interpretations I can see.

• If by 'transition' you mean the same thing as very many existing Life/CA-related sources outside the local community and part of sources in the local community (i.e. a state-to-state transition, like 0 -> 1, 1 -> 0 and so on) then obviously birth transitions cannot be a subset of survival transitions, because every birth transition is of the form 0 -> x (where x is nonzero) and every survival transition is of the form x -> y (where x is nonzero).
  https://web.archive.org/web/20230928182 ... ary_03.htm
  https://web.archive.org/web/20040323172 ... ndixA.html
  https://conwaylife.com/w/index.php?titl ... 314#Page_2
• If by "transition" you mean the local jargon (where it's commonly and incorrectly shortened from the longer correct phrase 'transition rule'), then again, it is impossible for such birth "transitions" (transition rules prescribing births) to be a subset of survival "transitions" (transition rules prescribing survivals), because every rule prescribing birth specifies (in its condition part) that the current state of the cell must be zero, while every rule prescribing survival specifies (in its condition part) that the current state of the cell must be nonzero.
  A nonempty set whose elements all have property P cannot be a subset of a set neither of whose elements has the property P. Here the property P is "the condition part of the rule specifies that the current state of the cell is zero".

The only way out of this impossibility would be to have no births at all (so that cells are never born) which is usually an uninteresting degenerate case. Was your definition intended to refer to those degenerate cases without any rules prescribing births at all? If not, then it needs to be fixed (and any intended meaning behind the word 'gnomonic' needs to be clarified).

[hotdogPi]

"If a cell would turn on, a cell that is already on with nothing else different is guaranteed to stay on." (There's probably a better wording, and I'm aware my definition is only clearly defined for two-state rules.)

[confocaloid]

"If a cell would turn on, a cell that is already on with nothing else different is guaranteed to stay on." (There's probably a better wording, and I'm aware my definition is only clearly defined for two-state rules.)

I think one can simply say that the birth conditions must be a subset of the survival conditions.
The birth conditions are (a set of) conditions on states of neighbours of a currently-dead cell, for that cell to become alive in the next generation.
The survival conditions are (a set of) conditions on states of neighbours of a currently-alive cell, for that cell to remain alive in the next generation.

Compare with the following examples (quotes from Life/CA-related sources), which also use the same wording with the same meaning:

[...] While the birth conditions are totalistic (and, in fact, the same as Life's), the survival conditions are not totalistic - i.e. they depend not only on the number of neighbors, but also their relative positions. Birth occurs on any 3 neighbors, while survival occurs on 2-4 neighbors that are orthogonally connected to the original cell (i.e. diagonal neighbors are allowed only if they are themselves adjacent to one or two orthogonal neighbors). Most common patterns are shared by all variants. The variants arise by tweaking three of the survival conditions: [...]

[...] More succinctly, a Life-like cellular automaton emulates a Margolus block cellular automaton if and only if, in its rulestring, B3 = S5, B4 = S4, B5 = S6 = S7, and B1 = B2 = S3. 2x2 can be seen to satisfy these conditions because 4 is neither a birth condition nor a survival condition, 5 is not a birth condition and 6 and 7 are not survival conditions, 3 is a birth condition and 5 is a survival condition, and 3 is not a survival condition and 1 and 2 are not birth conditions. There are 2^12 = 4096 Life-like cellular automata that emulate 2^6 = 64 different Margolus block cellular automata. [...]

edit: fixed superscripts that were broken due to copy/pasting a quote.

---

Edit: By "transition" I mean "state of cell's neighborhood" and not "state of cell and cell's neighborhood". By this logic, B4t and S4t are equivalent. Also, "gnomonic" is a random word that entered my mind once and I just had to use it somewhere hehe sorry

When I read 'gnomonic' I think of the gnomonic projection, but unfortunately it doesn't seem relevant here.

I think any new terminology needs to be reasonably helpful and reasonably self-explanatory.

Your choice of the word 'transition' to mean "state of cell's neighborhood" (as you seem to claim) strikes me as counterintuitive and confusing. Are there any real "transitions" in this situation? What is "transitioning" here? Can this choice of wording be explained to someone who is familiar with the common English meanings of the word 'transition'?

[d/dx]

I believe hotdogPi already explained what I meant clearly.

[Aleph]

To hack a replicator is to modify the rule that it is in, so that it replicates "substantially differently" (informal+subjective). I do genuinely find this term useful.

[confocaloid]

To hack a replicator is to modify the rule that it is in, so that it replicates "substantially differently" (informal+subjective). I do genuinely find this term useful.

How about other types of objects (e.g. puffers)? There are many known examples where changing the rules can transform a puffer engine into a different-but-related puffer engine (often but not necessarily with a different period).

How about perturbing a replicator into (a substantially different but still related) another replicator, without changing the rules? Are there known examples of this?

There was earlier discussion of puffer orbits that looks related:

A puffer/spaceship has a volatile period if its period can be changed by perturbing it. Period multiplication does not count.
Surprisingly, a lot of puffers don't have a volatile period. For example, the Schick engine has a non-volatile period. No matter what you do, it'll always have a period of 12n. The Coe ship's period is slightly more volatile. There are a few rakes that rephase the Coe ship, but it's not easy.
EDIT: As dvgrn points out, technically everything is a multiple of 4 or 2. So I'll try something else.
A puffer spits out exhaust at some base period. Its total period is then some multiple of this base period. A puffer displays period volatility when its exhaust is perturbed in such a way that changes the base period.

The best example of this is this p270 puffer by David Bell (2002), where a pair of p90 rakes transform a base spaceship (found by Paul Tooke earlier in 2002) between p3, p6, and p21 orbits:

Code: Select all

x = 155, y = 196, rule = B3/S23
34bo85bo$33b3o83b3o$14bob2o14bo3bo14b2obo45bob2o14bo3bo14b2obo$13b2ob
2ob2obo10b3o10bob2ob2ob2o43b2ob2ob2obo10b3o10bob2ob2ob2o$12bo2bobob2ob
2o8b5o8b2ob2obobo2bo41bo2bobob2ob2o8b5o8b2ob2obobo2bo$13bo6bo5bo4b2o3b
2o4bo5bo6bo43bo6bo5bo4b2o3b2o4bo5bo6bo$21bo3b4obo7bob4o3bo59bo3b4obo7b
ob4o3bo$25bo3b3obobob3o3bo67bo3b3obobob3o3bo$20b2obo2bo3b2o5b2o3bo2bob
2o57b2obo2bo3b2o5b2o3bo2bob2o$19bo4bo2bobo2b2ob2o2bobo2bo4bo55bo4bo2bo
bo2b2ob2o2bobo2bo4bo$18b2obobo6b2o5b2o6bobob2o53b2obobo6b2o5b2o6bobob
2o$16b2obobo6b2obobobobob2o6bobob2o49b2obobo6b2obobobobob2o6bobob2o$
14b2obo9bo3bo2bo2bo3bo9bob2o45b2obo9bo3bo2bo2bo3bo9bob2o$13bo3bo9bobob
2o3b2obobo9bo3bo43bo3bo9bobob2o3b2obobo9bo3bo$14bobo11bobobo3bobobo11b
obo45bobo11bobobo3bobobo11bobo$31bobobobo79bobobobo$28bo11bo73bo11bo$
26b2obo3bobo3bob2o69b2obo3bobo3bob2o$29bo4bo4bo75bo4bo4bo$29bob2obob2o
bo75bob2obob2obo$28b2obo5bob2o73b2obo5bob2o$27bobobo5bobobo71bobobo5bo
bobo$26b2obobob3obobob2o69b2obobob3obobob2o$29bobo5bobo75bobo5bobo$26b
2obob2o3b2obob2o69b2obob2o3b2obob2o$5bob2o24b3o24b2obo27bob2o24b3o24b
2obo$b3ob2obob2o18b9o18b2obob2ob3o19b3ob2obob2o18b9o18b2obob2ob3o$o6b
2o2b4o15b2o5b2o15b4o2b2o6bo17bo6b2o2b4o15b2o5b2o15b4o2b2o6bo$b2o3bo3bo
4bo12b2o9b2o12bo4bo3bo3b2o19b2o3bo3bo4bo12b2o9b2o12bo4bo3bo3b2o$13b3o
5b2o9bobobo9b2o5b3o43b3o5b2o9bobobo9b2o5b3o$19bob2o5bo2b2o3b2o2bo5b2ob
o55bob2o5bo2b2o3b2o2bo5b2obo$16bob2o3b2o19b2o3b2obo49bob2o3b2o19b2o3b
2obo$15b2ob2obobobo4bob5obo4bobobob2ob2o47b2ob2obobobo4bob5obo4bobobob
2ob2o$15b2obo4bob3ob11ob3obo4bob2o47b2obo4bob3ob11ob3obo4bob2o$19b2obo
3bob13obo3bob2o55b2obo3bob13obo3bob2o$26bo15bo69bo15bo$27bo13bo71bo13b
o$29bo3b3o3bo75bo3b3o3bo$31bo5bo79bo5bo$29bobo2bo2bobo75bobo2bo2bobo$
28bo2b2obob2o2bo10bo51bo10bo2b2obob2o2bo$30bo3bo3bo8b3ob2o49b2ob3o8bo
3bo3bo$46bo5b3o45b3o5bo$26bob2o9b2obo4b2o7b2o39b2o7b2o4bob2o9b2obo$26b
obo11bobo8bo4b2o39b2o4bo8bobo11bobo$27b3o9b3o8bo4b3o39b3o4bo8b3o9b3o$
29bo9bo9b2o3b2o5b3o5bo15bo5b3o5b2o3b2o9bo9bo$27b2o11b2o5b2o2b2o2b3o2bo
6b3ob3o7b3ob3o6bo2b3o2b2o2b2o5b2o11b2o$27b2o11b2o5b3ob2o6b2o5b2o6bo5bo
6b2o5b2o6b2ob3o5b2o11b2o$48b2ob2o2b2o3b4obo2bo3b2o7b2o3bo2bob4o3b2o2b
2ob2o$30bo2bobo2bo77bo2bobo2bo$30bo7bo24bo27bo24bo7bo$30bo7bo24bobo23b
obo24bo7bo$32bo3bo81bo3bo$33b3o83b3o$25b3o99b3o$25b3o99b3o$23bo4bo97bo
4bo$24b3o4b2o3b2o79b2o3b2o4b3o$24b3o4b2o3b2o4b2o67b2o4b2o3b2o4b3o$42b
3o65b3o$42bo69bo$43b2o65b2o3$31b2o3b2o79b2o3b2o$31b2o3b2o79b2o3b2o2$
31b2o3b2o79b2o3b2o$31b2o3b2o79b2o3b2o5$36b3o77b3o$36b3o77b3o$37bobo75b
obo$36b2obo75bob2o$31b2o3b3o77b3o3b2o$30bo6bo79bo6bo$30bob3o85b3obo$
29bo5bo83bo5bo$29bo3b2o85b2o3bo$30bo8b3o71b3o8bo$32bo6bobo71bobo6bo$
39b3o71b3o8$28bo15b2o63b2o15bo$27bobo13bo2bo61bo2bo13bobo$7b2ob3o13bo
2b2o10bo71bo10b2o2bo13b3ob2o$7b2o4b2o11bo4b2ob5ob5obo61bob5ob5ob2o4bo
11b2o4b2o$6bo2bobo3bo10bo2bob6o4bo3b2o61b2o3bo4b6obo2bo10bo3bobo2bo$
13b3o2b3o11b3o3bo2bo3b2o61b2o3bo2bo3b3o11b3o2b3o$15b3obobo6b3o2b2o85b
2o2b3o6bobob3o$15bo4bo9b4o5bobo71bobo5b4o9bo4bo$16b2o13b3o7bo71bo7b3o
13b2o$41b3o67b3o$41b3o67b3o$31bo10bo69bo10bo$32bobobo81bobobo$28bo3b2o
2b2o79b2o2b2o3bo$28bobob2ob2o28b2ob2o15b2ob2o28b2ob2obobo$30bo4b2o26b
2obob2ob2o9b2ob2obob2o26b2o4bo$30b3o27b3obo2b3o2b4o3b4o2b3o2bob3o27b3o
$31bo24b3o4b3o5bo4bobo4bo5b3o4b3o24bo$32bo22bobobob3obo8b2o3b2o8bob3ob
obobo22bo$34bo20bobobob4o25b4obobobo20bo$33bo22bobo4bo2bo21bo2bo4bobo
22bo$33bo31bo23bo31bo$57bo39bo$57bo39bo7$66b3ob2o11b2ob3o$64b2o4b2o11b
2o4b2o$63bo3bobo2bo9bo2bobo3bo$58b3o2b3o23b3o2b3o$57bobob3o27b3obobo$
48b2o8bo4bo7b2o9b2o7bo4bo8b2o$48b2ob2o8b2o5b2ob2o9b2ob2o5b2o8b2ob2o$
42b2o4b2o2b4o9b4o2bobo7bobo2b4o9b4o2b2o4b2o$42b2ob2o4bo4bo7bo4bo4bo5bo
4bo4bo7bo4bo4b2ob2o$41bo3b2o7b2o9b2o7bo5bo7b2o9b2o7b2o3bo$45b2o27bo5bo
27b2o$70b3o9b3o$69bo15bo$70bob2o7b2obo$74bo5bo$70b2o11b2o$69bo3bo7bo3b
o$72bo9bo$70bo13bo$70bo13bo$76b3o$28b2o40b2o4b3o4b2o40b2o$27bobo45bo3b
o45bobo$69b3o11b3o$28bo42bo2bo5bo2bo42bo$26bo2bo40bo3b2o3b2o3bo40bo2bo
$27b4o45bobo45b4o$29b2o38b3o5bo5b3o38b2o$27bo41b4ob2obob2ob4o41bo$26b
2o43bo2b7o2bo43b2o$26bo2bo42b4o3b4o42bo2bo$27b3o41b3o7b3o41b3o$28bo41b
o4bo3bo4bo41bo$69bo3bo3bo3bo3bo$74bob3obo$69bob4o5b4obo$69bo4b3ob3o4bo
$72b2o3bo3b2o$75bo3bo$10bo60b2o2b2ob2o2b2o60bo$6b3ob3o57bobo2b2ob2o2bo
bo57b3ob3o$5bo6b2o56bo6bo6bo56b2o6bo$6b2o3bo2bo3bo50b2o6bo6b2o50bo3bo
2bo3b2o$16b4o49bob3o2bobo2b3obo49b4o$16bo3bo52bo7bo52bo3bo$14bo2bobo
52bobo5bobo52bobo2bo$15bo53b3o2bob3obo2b3o53bo$3b2ob3o32b2o25bobobob2o
3b2obobobo25b2o32b3ob2o$3b2o4b2o31b2o24bobobob2o3b2obobobo24b2o31b2o4b
2o$2bo2bobo3bo29bo27b2ob3obobob3ob2o27bo29bo3bobo2bo$9b3o2b3o53b2o3b2o
b2o3b2o53b3o2b3o$11b3obobo10b2o42b3obobob3o42b2o10bobob3o$11bo4bo11b2o
39bo4bobobobo4bo39b2o11bo4bo$12b2o60bobobobo60b2o$64bo7bobobobobobo7bo
$64b2o7bo2bobo2bo7b2o$63bobo7b3o3b3o7bobo$74bo5bo3$13b2ob3o20b3ob2o65b
2ob3o20b3ob2o$13b2o4b2o16b2o4b2o65b2o4b2o16b2o4b2o$12bo2bobo3bo14bo3bo
bo2bo63bo2bobo3bo14bo3bobo2bo$19b3o2b3o4b3o2b3o77b3o2b3o4b3o2b3o$21b3o
bobo2bobob3o81b3obobo2bobob3o$21bo4bo4bo4bo12bo55bo12bo4bo4bo4bo$22b2o
10b2o9b3ob3o51b3ob3o9b2o10b2o$44bo6b2o49b2o6bo$45b2o3bo2bo3bo39bo3bo2b
o3b2o$55b4o37b4o$55bo3bo35bo3bo$53bo2bobo37bobo2bo$54bo45bo!

EDIT by dvgrn: ... which is showcased in Golly's pattern collection with LifeViewer commands, edited in here so that they don't go to waste.

Code: Select all

#C p270-frothing-puffer-rake.rle
#C Period 270 forward rake using period tripling of p90 input streams.
#C In this rake, the base c/3 ship (found in Jan. 2002 by Paul Tooke)
#C cycles between all three possible frothing periods: 21, 12, and 6.
#C David Bell, 20 October 2002.
x = 249, y = 371, rule = B3/S23
72bo85bo$71b3o83b3o$52boboo14bo3bo14boobo45boboo14bo3bo14boobo$51boob
ooboobo10b3o10boboobooboo43boobooboobo10b3o10boboobooboo$50bobboboboob
oo8b5o8booboobobobbo41bobbobobooboo8b5o8booboobobobbo$51bo6bo5bo4boo3b
oo4bo5bo6bo43bo6bo5bo4boo3boo4bo5bo6bo$59bo3b4obo7bob4o3bo59bo3b4obo7b
ob4o3bo$63bo3b3obobob3o3bo67bo3b3obobob3o3bo$58boobobbo3boo5boo3bobbob
oo57boobobbo3boo5boo3bobboboo$57bo4bobbobobbooboobbobobbo4bo55bo4bobbo
bobbooboobbobobbo4bo$56boobobo6boo5boo6boboboo53boobobo6boo5boo6bobob
oo$54boobobo6booboboboboboo6boboboo49boobobo6booboboboboboo6boboboo$
52boobo9bo3bobbobbo3bo9boboo45boobo9bo3bobbobbo3bo9boboo$51bo3bo9bobob
oo3boobobo9bo3bo43bo3bo9boboboo3boobobo9bo3bo$52bobo11bobobo3bobobo11b
obo45bobo11bobobo3bobobo11bobo$69bobobobo79bobobobo$66bo11bo73bo11bo$
64boobo3bobo3boboo69boobo3bobo3boboo$67bo4bo4bo75bo4bo4bo$67bobooboboo
bo75bobooboboobo$66boobo5boboo73boobo5boboo$65bobobo5bobobo71bobobo5bo
bobo$64boobobob3oboboboo69boobobob3oboboboo$67bobo5bobo75bobo5bobo$64b
ooboboo3booboboo69booboboo3booboboo$43boboo24b3o24boobo27boboo24b3o24b
oobo$39b3obooboboo18b9o18booboboob3o19b3obooboboo18b9o18booboboob3o$
38bo6boobb4o15boo5boo15b4obboo6bo17bo6boobb4o15boo5boo15b4obboo6bo$39b
oo3bo3bo4bo12boo9boo12bo4bo3bo3boo19boo3bo3bo4bo12boo9boo12bo4bo3bo3b
oo$51b3o5boo9bobobo9boo5b3o43b3o5boo9bobobo9boo5b3o$57boboo5bobboo3boo
bbo5boobo55boboo5bobboo3boobbo5boobo$54boboo3boo19boo3boobo49boboo3boo
19boo3boobo$53booboobobobo4bob5obo4bobobobooboo47booboobobobo4bob5obo
4bobobobooboo$53boobo4bob3ob11ob3obo4boboo47boobo4bob3ob11ob3obo4boboo
$57boobo3bob13obo3boboo55boobo3bob13obo3boboo$64bo15bo69bo15bo$65bo13b
o71bo13bo$$68b9o77b9o$$69boo3boo13bo51bo13boo3boo$72bo12b3oboo49boob3o
12bo$67bo9bo6bo5b3o45b3o5bo6bo9bo$67bo9bo7boo7boo39boo7boo7bo9bo$66bo
3bobobo3bo10bo4boo39boo4bo10bo3bobobo3bo$66bo4bobo4bo9bo4b3o39b3o4bo9b
o4bobo4bo$65bo4bo3bo4bo7boo3boo5b3o5bo15bo5b3o5boo3boo7bo4bo3bo4bo$65b
5o5b5o5boobboobb3obbo6b3ob3o7b3ob3o6bobb3obboobboo5b5o5b5o$85b3oboo6b
oo5boo6bo5bo6boo5boo6boob3o$86booboobboo3b4obobbo3boo7boo3bobbob4o3boo
bbooboo$$64b3o11b3o20bo27bo20b3o11b3o$69bo5bo25bobo23bobo25bo5bo$68boo
5boo77boo5boo$66bo3bobobo3bo73bo3bobobo3bo$66bobbo5bobbo73bobbo5bobbo$
66bo3bobobo3bo73bo3bobobo3bo$67bobo5bobo75bobo5bobo$68boo5boo77boo5boo
3$69boo3boo79boo3boo$69boo3boo79boo3boo$$78bo73bo$78bobo69bobo$78boo
71boo$$69boo3boo79boo3boo$69boo3boo79boo3boo$$69boo3boo79boo3boo$69boo
3boo79boo3boo4$75boo77boo$74boboo75boobo$73boobb3o71b3obboo$73b3ob3o
71b3ob3o$73bobboboo71boobobbo$73bobbobo73bobobbo$73boobobo73boboboo$
71bobbobobo73bobobobbo$70bobo5boo71boo5bobo$$70b3o8bo67bo8b3o$81bo67bo
$81bo67bo$$77b3o71b3o5$45boob3o129b3oboo$45boo4boo125boo4boo$44bobbobo
3bo20bobo77bobo20bo3bobobbo$51b3obb3o3bobo9bobo77bobo9bobo3b3obb3o$53b
3obobobbooboo8bobbo73bobbo8booboobbobob3o$53bo4bo8bobo6b3o73b3o6bobo8b
o4bo$54boo7boboo3boo87boo3boobo7boo$64b3obo8boo73boo8bob3o$66boboo7b3o
71b3o7boobo$66bobo10bo71bo10bobo$67bo11boo69boo11bo$79bo71bo$70bo10bo
21booboo15booboo21bo10bo$70bo9bobo18boobobooboo9boobooboboo18bobo9bo$
69boo4boo3boo16b3obobb3obb4o3b4obb3obbob3o16boo3boo4boo$68boo5boo3bo
13b3o4b3o5bo4bobo4bo5b3o4b3o13bo3boo5boo$68bobobboboo16bobobob3obo8boo
3boo8bob3obobobo16boobobbobo$72bobbo17bobobob4o25b4obobobo17bobbo$72b
3o19bobo4bobbo21bobbo4bobo19b3o$74bo28bo23bo28bo$73bo21bo39bo21bo$70bo
bbo21bo39bo21bobbo7$104b3oboo11boob3o$102boo4boo11boo4boo$101bo3bobobb
o9bobbobo3bo$96b3obb3o23b3obb3o$95bobob3o27b3obobo$86boo8bo4bo7boo9boo
7bo4bo8boo$86booboo8boo5booboo9booboo5boo8booboo$80boo4boobb4o9b4obbob
o7bobobb4o9b4obboo4boo$80booboo4bo4bo7bo4bo4bo5bo4bo4bo7bo4bo4booboo$
79bo3boo7boo9boo7bo5bo7boo9boo7boo3bo$83boo27bo5bo27boo$108b3o9b3o$
107bo15bo$108boboo7boobo$112bo5bo$108boo11boo$107bo3bo7bo3bo$110bo9bo$
108bo13bo$108bo13bo$114b3o$108boo4b3o4boo$113bo3bo$107b3o11b3o$66boo
41bobbo5bobbo41boo$66boo40bo3boo3boo3bo40boo$114bobo$107b3o5bo5b3o$
107b4obooboboob4o$109bobb7obbo$110b4o3b4o$109b3o7b3o$108bo4bo3bo4bo$
107bo3bo3bo3bo3bo$65bo46bob3obo46bo$65boo40bob4o5b4obo40boo$64bo42bo4b
3ob3o4bo42bo$65b3o42boo3bo3boo42b3o$66bo46bo3bo46bo$48bo60boobbooboobb
oo60bo$44b3ob3o57bobobbooboobbobo57b3ob3o$43bo6boo56bo6bo6bo56boo6bo$
44boo3bobbo3bo50boo6bo6boo50bo3bobbo3boo$54b4o49bob3obbobobb3obo49b4o$
54bo3bo52bo7bo52bo3bo$52bobbobo52bobo5bobo52bobobbo$53bo53b3obbob3obo
bb3o53bo$41boob3o59boboboboo3boobobobo59b3oboo$41boo4boo32b3o22bobobob
oo3boobobobo22b3o32boo4boo$40bobbobo3bo33bo23boob3obobob3oboo23bo33bo
3bobobbo$47b3obb3o27bo25boo3booboo3boo25bo27b3obb3o$49b3obobo54b3obobo
b3o54bobob3o$49bo4bo52bo4bobobobo4bo52bo4bo$50boo60bobobobo60boo$66boo
46bobo46boo$66boo36boo8bobo8boo36boo$103bobo7booboo7bobo$105bo19bo$
113bo3bo$112bo5bo$51boob3o20b3oboo30bo3bo30boob3o20b3oboo$51boo4boo16b
oo4boo65boo4boo16boo4boo$50bobbobo3bo14bo3bobobbo63bobbobo3bo14bo3bobo
bbo$57b3obb3o4b3obb3o77b3obb3o4b3obb3o$59b3obobobbobob3o81b3obobobbobo
b3o$59bo4bo4bo4bo12bo55bo12bo4bo4bo4bo$60boo10boo9b3ob3o51b3ob3o9boo
10boo12bo$82bo6boo49boo6bo33bobo$83boo3bobbo3bo39bo3bobbo3boo18bo14bo
3bo14bo$93b4o37b4o24b3ob3o13b3o13b3ob3o$93bo3bo35bo3bo23bo6bob3o21b3ob
o6bo$46b3o42bobbobo37bobobbo22boo3bo5bo6boo3boo6bo5bo3boo$46b3o43bo45b
o31b7o3boo3boo3b7o$26boob3o13bo3bo13b3oboo99bobboo3boobb3ob3obboo3boo
bbo$26boo4booboo21booboo4boo100boobo4boo9boo4boboo$25bobbobo4boo7bo5bo
7boo4bobobbo105b4obbooboobb4o$32boobobboo4booboboo4boobboboo104boob4o
7booboo7b4oboo$38boboo11boobo109boboboo5boobob3oboboo5boobobo$33b3oboo
bbo3bo3bo3bobboob3o101boobo10boobo5boboo10boboo$33bo3b3obo4bobo4bob3o
3bo101boobo9bobobo5bobobo9boboo$31booboboo4bobbo3bobbo4booboboo99bobo
10bo3bo5bo3bo10bobo$30bobobbo8bobobobo8bobbobo117bobo$28b3obobbo5boobo
bbobboboo5bobbob3o109bo3b3ob3o3bo$27boobo9bobobob3obobobo9boboo108bob
5ob5obo$26bo3bo9bobobbooboobbobo9bo3bo107bobo9bobo$41b3obbobobb3o124bo
booboboobo$42boboo3boobo124boobob3oboboo$40boo3bo3bo3boo123bobob3obobo
$40bobo4bo4bobo120booboboo3booboboo$42bobbobobobbo122boobobo5boboboo$
42bob3ob3obo123bobobo5bobobo$42bobo5bobo104bo21boo5boo21bo$39boobobobb
obboboboo94boob3ob3o20b7o20b3ob3oboo$39boobobobbobboboboo94boo4bobboob
oo19bo19booboobbo4boo$42bobob3obobo96bobboboo3bobboo14bobobbobbobo14b
oobbo3boobobbo$41bobb7obbo107bobbo5bo6boobo5boboo6bo5bobbo$15boboob3o
49b3oboobo85bobb4o5boo3bobo3boo5b4obbo$14booboo4boobo16bo7bo16boboo4b
ooboo87bo3bo6boo5boo6bo3bo$13bobbobobbo3b3o18b3o18b3o3bobbobobbo81b3o
bboboboo5b9o5boobobobb3o$14bo5bo3bo3bo13b3o5b3o13bo3bo3bo5bo85bobboobo
boo15booboboobbo$27boo4b3o5boob3ob3oboo5b3o4boo100boobo3boboo9boobo3bo
boo$27boobboobo9b3ob3o9boboobboo107bobob9obobo13b3o$28boo4boboo9bo9boo
bo4boo109b15o13bo$33bobbobo3boo7boo3bobobbo116b11o14boo$28boobobbobobo
bo13bobobobobboboo130boboobboobb3o$24boo6bo8bo11bo8bo133boobooboo5bo4b
oo$23boobo12bob13obo122boo3bo3boo6bobboo3boboo4booboo$23boobo20bo129bo
booboboboobo11b4o6boo3bo$21b3oboo3bo16bo128boo11boo6boboboo8boo$16bo3b
o4bobb3ob3o10booboo127bobo7bobo9bo$15b4o4b3obboo5bo8bobobobo127boo7boo
7boo18bo$14bo3bo9boobobbo7bobooboboobo59bo5bo60bobo3bobo7boobbo4boobo
3bo3boob3o$15bobobbo4boo4bo12bobobobo61bo5bo58boo9boo7b3oboobobooboob
oobob3obbo3b3o$19bo9bob3o8bo9bo59bo5bo58boo9boo3bobbo5boboo6bo9bobbobo
boo$14bo16bo3bo5boo9boo123bobooboboboobo4bob4obo3b3o3bobobbo3bobobbobo
3bo$14b3obbo6bo3bobobbo3bo15bo124bo5bo12b3obboo10bo4boobbobbobo$3boo4b
5o4bobob3ob3o6boo3bobo9bobo126bo3bo13boo4bo16b5o$ooboo3b3obbo4bobo3boo
bbo3booboo5bo9bo129b3o15boboobo17boo$oo3bo4b5obobo3boo12bo3bobo9bobo$o
bobbobbo3boo12bobboobobbo4boo11boo117bo28bobbo$3bob4o16boobboobbo137b
4o26bobbo$25boboo142boboo$30bo11b3o5b3o$26b4o14bo5bo129boo$27boo17b3o
10bo120boo$46b3o9bobo$47bo$177boo$176bobbo$49boo125bobo18b3ob3o$49boo
126bo16b4obo4boobo$190bo3boo3boobo3b3o$189b4o5boobo3bo3bo$28booboo19b
oo134bo3bobo3bo9bo$25boobooboboo16bobbo133bobobobo3bo$22b4obb3obbob3o
14bobo122bo5boo4b3o4bobo$21bo4bo5b3o4b3o11bo122boo4bobbo4bo13b3ob3o$
22boo8bob3obobobo133boo5b3o15b4obo4boobo$33b4obobobo154bo3boo3boobo3b
3o$31bobbo4bobo117bo36b4o5boobo3bo3bo$21booboo6bo122b3ob3o33bo3bobo3bo
9bo$18boobooboboo12bo4b3o106bo6boo14bo17bobobobo3bo$15b4obb3obbob3o9bo
3bo3bo106boo3bobbo3bo7booboo7boo7b3o4bobo$14bo4bo5b3o4b3o8bo5bo115b4o
6booboo6bobbo7bo$15boo8bob3obobobo8bo3bo21b3oboo89bo3bo5booboo6boob5o
15b3oboo$26b4obobobo9b3o4b3o13boo4boo87bobbobo8bo8boobb4o13boo4boo$24b
obbo4bobo16bo3bo11bo3bobobbo87bo24b3obboo10bo3bobobbo$25bo15bobo6bo5bo
5b3obb3o118b3obobbo5b3obb3o$17boboo12bo15bo3bo3bo3bobob3o116boo3boo4bo
4bobob3o$16boobooboo9bo10bo4bobbobobbo4bo4bo116b3obo4boo6bo4bo$15bobbo
bobbo12boo11bo3bo3bo7boo117boboo16boo$16bo5boo4boo13boobo3bo5bo128boo
bbo$25booboo3boobo3bobobo6bo3bo128bobb4o$25boo3bobbobboobobboobbo5b3o
124boo4bo5bo$25boo6bobbobboo5boo131boo5b5o$34bobobbo6bo140b3o4$50boo$
38boboo8boo$39b3o84bo26bo$40bo81b3ob3o11b4obo5b4o$121bo6bob3o7bobobboo
3boo3bo$122boo3bo5bobboobobbo4bo5boboo$130boobobbobobboobobbo3b3obobo
26b3o$76b3o6booboo13b3oboo23boobboboobbobbobbo4boboboboobo15b3o4boo$
77boboo3bo3boboo6booboo4boo23boo3b3obbooboobobbobobobobooboo14bobboobb
o$74boobo3bobo4bo4bo4boo4bobobbo25b3obbobbobo3bobobobobobo4bo13booboo
bboo$73bobobb5o3b3o3b3obboboboo30bobbo5bo3bo4bobobobo5b3o14boboboo12b
3oboo$71b3obobo3boobbobbo3bo4boo36bo17boboboboobb4o14b4o11boo4boo$67b
3obobobobobbo4b3o3bobbo60bo5b3obbo15boo11bo3bobobbo$45b3oboboobo11bo6b
obobob3o3bobo3bobbo3bo54bo7bo4bo23b3obb3o$28boboo13boo3bo3bo12booboobo
bobobo3bobobobo4bo3bo48boo4bo3b4obboboo22bobob3o$27boobooboo10b4o3bobo
9boo7bobobobo15boo37boboo8bobbooboobbobobobooboo23bo4bo$26bobbobobbo8b
oob6o12boobboobbooboo56boobooboo4bo3bobboobo8bo28boo$27bo5boo4boo4bo
20boobobboobo56bobbobobbo5b4o13boo$36booboo21bobb3oboboobb3o4bo50bo5b
oo4bobbobobboo$36boo3bo21bobo9b3o3boboo8bo48boobobbobobboo$36boo29bobb
obobbo3boboboo6b3ob3o44boo4bobo4bo$66bo10bo3boobbo4boo6bo45bobobobobob
o9boo$67bo12bo8bobbo3boo65boo$76boobbobobb3o77bo$75bob4ob4obo$76bobobo
bobobobbo62b3o$66b3o83bo$68bo84bo$67bo74bo$78bo62boo$78boo61bobo$77bob
o$130boo$89boo39bobo$88bobo39bo$90bo$119boo$100boo16boo$101boo17bo$
100bo$$111b3o$113bo$112bo20$179boo$178bobo$180bo21$246b3o$248bo$247bo!
#C Script commands for showinviewer.lua:
#C [[ THEME 6 LABELALPHA .5 COLOR LABEL LightBlue X -9 Y -24 Z 6 AUTOSTART TRACK 0 -1/3 GPS 12 ]]
#C [[ LABEL 87 153 4 "adjustable-period\nc/3 spaceship" ]]
#C [[ LABELSIZE 20 ]]
#C [[ LABEL 140 153 4 "(Paul Tooke,\nJanuary 2002)" ]]
#C [[ COLOR LABEL DarkRed ]]
#C [[ LABELT 20 115 5 ]]
#C [[ LABEL 115 187 4 "period 12" ]]
#C [[ LABELT 130 205 5 ]]
#C [[ LABEL 115 187 4 "period 6" ]]
#C [[ LABELT 210 285 5 ]]
#C [[ LABEL 115 187 4 "period 21" ]]
#C [[ LABELT 290 385 5 ]]
#C [[ LABEL 115 187 4 "period 12" ]]
#C [[ LABELT 400 475 5 ]]
#C [[ LABEL 115 187 4 "period 6" ]]
#C [[ LABELT 480 555 5 ]]
#C [[ LABEL 115 187 4 "period 21" ]]

[Aleph]

To hack a replicator is to modify the rule that it is in, so that it replicates "substantially differently" (informal+subjective). I do genuinely find this term useful.

How about other types of objects (e.g. puffers)? There are many known examples where changing the rules can transform a puffer engine into a different-but-related puffer engine (often but not necessarily with a different period).

How about perturbing a replicator into (a substantially different but still related) another replicator, without changing the rules? Are there known examples of this?

There was earlier discussion of puffer orbits that looks related:

<snip big quote>

The reason why I specifically mentioned replicators is because that was the context in which I originally came up with the term. I think that this term would easily extend to other cases.

[confocaloid]

To hack a replicator is to modify the rule that it is in, so that it replicates "substantially differently" (informal+subjective). I do genuinely find this term useful.

How about other types of objects (e.g. puffers)? [...]
How about perturbing a replicator into (a substantially different but still related) another replicator, without changing the rules? Are there known examples of this? [...][...]

The reason why I specifically mentioned replicators is because that was the context in which I originally came up with the term. I think that this term would easily extend to other cases.

I think it would be interesting to see in general, how much of the intuitive notion "substantially different, but nevertheless related" can be captured in an objective measurable way, when talking about Life/CA objects or reactions. I see the "(informal+subjective)" but there should be some set of tests/measurements that would let to avoid considering endless "boring variations" of "essentially the same" reaction, while still capturing all "interesting" unique reactions and interactions.

[apg]

How about perturbing a replicator into (a substantially different but still related) another replicator, without changing the rules? Are there known examples of this?

Have you seen the Basilisk gun (from January 2012) in B36/S23 (best watched at step size 8^4)? https://golly.sourceforge.io/patterns/basilisk-gun.mc

It converts a c/24 XOR-extensible spaceship into a replicator by uncapping the ends, allows it to reproduce naturally as a replicator, and then recaps the outputs to form spaceships again; by doing this, it is able to produce an infinite stream of Basilisks (pseudoperiod 1966080 and true period 5898240) without ever needing to glider-synthesise a Basilisk from scratch.

[squareroot12621]

Clarint spark: An obobo spark.
Etymology: Oboe - e = obo, Clarinet - e = clarint.

Code: Select all

x = 5, y = 1, rule = B3/S23
obobo!

[tommyaweosme]

Clarint spark: An obobo spark.
Etymology: Oboe - e = obo, Clarinet - e = clarint.

Code: Select all

x = 5, y = 1, rule = B3/S23
obobo!

the draft for a wiki article