Thread for advanced questions

[otismo]

Two schools of thought regarding CA

Generative

AND

Emergent

It seems that a Generative Singularity requires its Own Universe

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#C [[ AUTOSTART AUTOHIDEGUI ZOOM 5 GPS 34 NEIGHBOR LOOP 5500 TITLE "Generative Singularity" ]]
x = 3, y = 3, rule = B35cj6ce7/S34-cry5-jnr6ci78
bo$3o$bo!

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#N novelty-cross.rle
#O toroidalet, December 18 2017
#C
#C     A tiny X-pentomino in this non-totalisic rule is a long-lived,
#C prolific hotspring, spawning a cross-shaped configuration with a
#C scattering of objects everywhere. 
#C     At T=868, four X-pentominoes 37 cells away from center forms,
#C later disrupted to give sixteen of these seeds at T=1221. From
#C their interaction arises several transient 6-cell c/2o spaceships.
#C     At T=2252, four triangular 9-cell c/3o spaceships appears,
#C travelling backward to be consumed at the center.
#C     At T=3160, sixteen seeds begin to expand perpendicularly,
#C creating 9-cell 8c/76o spaceships towards the axes.
#C     At T=3781, the first four escaping c/3o spaceships emerges. 
#C Later, if removing the debris 140 cells away from the center, the
#C pattern would converge to a massive four-barrelled period-5040 gun.
#C     At T=16758, a c/3o spaceship catches up with a 8c/76o one along
#C the axis, dropping a seed at a whopping 908 cells away from the 
#C center. But multiple spaceship collisions terminate its activity
#C at T=28433. Similar events will happen a lot of times soon.
#C     Sometimes the center may temporarily settle into a simple still
#C life or an oscillator, but after a while it will be re-ignited by
#C spaceships from four directions. The generation counts are listed
#C below:
#C 1755681 4bo$2b5o$b7o$b2obob2o$9o$b2obob2o$b7o$2b5o$4bo! 1760440 
#C 2444797 2obob2o$7o$bobobo$7o$bobobo$7o$2obob2o! 2719552 
#C 2822812 3bo3bo$2b2o3b2o$bob5obo$3o5b3o$2bob3obo$2bob3obo$2bob3obo$3o5b3o$bob5obo$2b2o3b2o$3bo3bo! 2875606 
#C 3210741 b2obob2o$ob5obo$2o5b2o$bob3obo$2ob3ob2o$bob3obo$2o5b2o$ob5obo$b2obob2o! 4092264 
#C 4274117 b2obob2o$ob5obo$2o5b2o$bob3obo$2ob3ob2o$bob3obo$2o5b2o$ob5obo$b2obob2o! 4275201 
#C 5353175 4bo$2b5o$b7o$b2obob2o$9o$b2obob2o$b7o$2b5o$4bo! /
#C     Eventually the center is extinguished at T=5353175, and soon no
#C further interesting events will take place.
#C 
#C Reference:
#C https://conwaylife.com/forums/viewtopic.php?p=53857#p53857
#C A screenshot for the settled pattern at generation 2^24 is available:
#C https://conwaylife.com/forums/download/file.php?id=5000
x = 3, y = 3, rule = B35cj6ce7/S34-cry5-jnr6ci78
bo$3o$bo!

Furthermore

it also seems that "Generative" can come from the RULEspace ( outside the Universe )

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x = 1, y = 1, rule = BLAHMONALISA2
A!

or any Universal Construction which also originates from outside the universe

<code />

@ rowett

ruleBLAHMONALISA2 not working in LV

A Generative Singularity

may not quite be a periodic pattern

( StillLife-Oscillator-SpaceShip

Spark/Fire/Plasma/FireCloud )

but may be Infinite depending on

RULE and Initial Pattern

[PK22]

Is there a known universal toolkit using binary slow salvos that uses a block as the elbow, and if so, what is the most efficient such toolkit, in terms of the number of slow gliders needed for each operation?
EDIT: Found one, but it seems quite inefficient.
EDIT 2: The initial intent of this question was to find a toolkit for use with a Thessalonic spaceship, but after figuring out a working design with single-channel construction, it is no longer necessary.

[muzik]

Is it technically correct to state that a still life has a volatility of 0, but a strict volatility of 1?

[WhiteHawk]

What is the lowest oscillator period in life with an endemic example? (preferrably nontrivial - interacting rotors)

[PK22]

What is the lowest oscillator period in life with an endemic example? (preferrably nontrivial)

Less than or equal to 20:

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x = 78, y = 47, rule = B3/S23
22bo$22b3o$25bo$24b2o2$54bo6b2o$39b2o4b2o6bobo4bo2bo2bo4b2o$29b2o8bob
o2bobo5bo2bo4bobo3b3o2bobo2b2o$15b2o6bo4b2o11bo2bo7b4ob2obo2b3o3bobo2b
o2bo$5b2o4bo2bo2bo4bobo5bo9bo4bo11bobobobo2bob2ob2obobo$2o2bobo2b3o3b
obo4bo2bo14bo4bo8b3o2bobo4b3o5bob2o$o2bo2bobo3b3o2bob2ob4o14bo4bo7bo2b
2ob2o6bo2bo3bo$bobobo2bo2bo2bobobobo13b2o6b2o7bo2b2o2bob3ob2obobo4bo$
2obo2bobo2b2obobo4bobo9b2o15bo3bobob2o2bobob2ob5o$3bob2ob2o2b2obo6bob
o10bo14b3o3bobob2o2bo3bo$3bo4bobo2bob2o3bobo22b2o2b2o2b2obobobo3bo3bo
2bo$4b5ob2obobo2bo6b2o17bobob3o2bo2b2obo2bob2o3b3o$9bo3bo2b2obobo3b2o
12b2o3bo3b3o2b3o3bob2o$6bo2bo3bo3bobobobo2bo11b2o4bobob3o2bo2b2obo2bo
b2o3b3o$6b3o3b2obo2bob2o4bo3b3o7bo4b2o2b2o2b2obobobo3bo3bo2bo$15b2obo
3bobo2bo3b2o17b3o3bobob2o2bo3bo$6b3o3b2obo2bob2o4bo3b3o17bo3bobob2o2b
obob2ob5o$6bo2bo3bo3bobobobo2bo24bo2b2o2bob3ob2obobo4bo$9bo3bo2b2obob
o3b2o11bo3b2obo7bo2b2ob2o6bo2bo3bo$4b5ob2obobo2bo6b2o10bobo6bo7b3o2bo
bo4b3o5bob2o$3bo4bobo2bob2o3bobo12b2o5bo4bo9bobobobo2bob2ob2obobo$3bo
b2ob2o2b2obo6bobo9b2o7b2ob2o4b4ob2obo2b3o3bobo2bo2bo$2obo2bobo2b2obob
o4bobo11bob2o9b2o2bo3bo3bobo3b3o2bobo2b2o$bobobo2bo2bo2bobobobo14bobo
8bobobobobobo3bo2bo2bo4b2o$o2bo2bobo3b3o2bob2ob4o6b5o7bo5bobob2o5b2o$
2o2bobo2b3o3bobo4bo2bo4b3obo8b2o5b2o$5b2o4bo2bo2bo4bobo4bo6bo8b2o$15b
2o6bo4bob3o4bo7bo2bo$28bo4b2ob2o7bo2bo$26b2obo2bo12bob2o$26bo2bo22bo$
28b2ob2o15b2o2b3o$30b2ob2o12b3o5bo$30bo2b3o11b3o2b2obo$27b2ob2o3bo2b2o
7b3o3bob2o$26bobobo2b2o4bo7b3o3bo$26bobobo5b3o9b2o2b2o$27bo2bob4o13bo
4b2o$30bobobob3o8bobob2obo$29b2obobobo2bo7b2o2bo2bo$33b2obobo12bobo$37b
o14bo!

I assume that the rotors are required to interact to be non-trivial. There is probably an endemic p2, but it would have non-interacting rotors.

[hotcrystal0]

What is the decimal number, that when converted to binary and 1s are interpreted as on cells and 0s off cells, results in the 1 cell thick phase of the unidimensional spaceship?

[b-engine]

Is it possible to build a macro-spaceship with conduits (whose output is same as input but will extra glider) replacing a crawler mechanism?

Such design builds the conduit track instead of supporting a crawler, and destruct the track at backend instead of ash.

[PK22]

Is it possible to build a macro-spaceship with conduits (whose output is same as input but will extra glider) replacing a crawler mechanism?

Such design builds the conduit track instead of supporting a crawler, and destruct the track at backend instead of ash.

There is a thread for the construction of a 50c/154 'Condupillar', which uses Fx77s. It's certainly possible, but work on it stopped over a year and a half ago.

[77551enpassant]

Where is the list of all unique 10-cell infinite growth patterns? Is there also a list of unique patterns <=15 cells that produce switch engines? I want it to do some experiments with beating the 20-cell quadratic growth record.

[Disaster16439]

I want a full list of house-shifting components in CGOL for my OCA synthesis (yes, I know this is for CGOL only, but I don’t think people would need OCA knowledge to answer this question, and I don’t know if the people who can answer this question check the OCA thread):

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 x = 251, y = 45, rule = B34q/S23-k
237b2o$237b3o$236bob2o$236b3o$54bo182bo$55b2o$54b2o3$bobo$2b2o$2bo$71b
o157bobo$69bobo158b2o$70b2o124bo33bo17bobo$188bobo5bobo38bo10b2o$77bo
39b2ob2o67b2o5b2o38bobo10bo$3o63bo10bobo37b2obobo46b3o17bo47b2o$2bo63b
o10b2o41bobo2b2o40b2o3bo$bo64bo50b2obobobobo39bo5bo$117b2ob2o2bo41bo5b
o63b2ob2o3b2o4bo$124bobo45bo63b2obobobobo2b2o$125b2o45bo17b2ob2o3b2o
39bobobo5b2o$18b2o151bo18b2obobobobo30b2o4b2obobobobo$18bobo30b2o24b2o
92bo21bobobo33b2o3b2ob2o3b2o$18bo33b2o23b2o91bo19b2obobobobo30bo$12b2o
37bo118bo19b2ob2o3b2o$11bobo156bo66b2o$13bo222bobo$237bo$230bo$169b2o
18bo40b2o$168bobo18b2o5b2o31bobo$168b3o17bobo5bobo$169b2o25bo6$237bo$
236b3o$236bob2o$237b3o$237b2o!

I can check if they work in my OCA myself


Also, I’ve generally found that while syntheses for base still lives are common on say, LifeWiki, components aren’t. Where can I find them?

Edit 1:

Oh, I forgot I posted a similar question a few months back. Oops.

[b-engine]

Is it possible to build a spaceship that consists of only helixes?

[I6_I6]

Is it possible to build a spaceship that consists of only helixes?

Well, I can't think of anything that prevents the existence of a spaceship consisting of multiple helices that synthesize each other.

[WhiteHawk]

Is it possible to build a spaceship that consists of only helixes?

Well, I can't think of anything that prevents the existence of a spaceship consisting of multiple helices that synthesize each other.

I guess technically the new "adjustable" giraffeship is solely made of helices perturbing blocks to extract gliders that synthesize new helices.

[glider_rider]

Is it possible to build a spaceship that consists of only helixes?

It is! https://conwaylife.com/wiki/Caterloopillar

[Anivec]

Can Sharkovskii's/Sharkovsky's theorem be applied to oscillators in cellular automata, or is that only for iterated functions? Can we treat the cells on the board as matrices for CA if it must be a function to be applicable?

[vilc]

Can Sharkovskii's/Sharkovsky's theorem be applied to oscillators in cellular automata, or is that only for iterated functions? Can we treat the cells on the board as matrices for CA if it must be a function to be applicable?

I am not an expert of Sharkovsky's theorem, but I have some familiarity with broader dynamical systems. Here is what I found after some reading.

For a direct application, the answer is clearly no. CAs and the dynamical systems that are covered by Sharkovsky's theorem both belong to the class of discrete dynamical systems (systems that consist in successive iterations of a map over a given universe). However, Sharkovsky's theorem needs two key hypotheses that are not verified by CAs :
- the transition map has to be over an interval of the real numbers
- the transition map has to be continuous
Note that even if the second hypothesis can probably be made true for some well-chosen topology over P(Z^2) and for specific CAs, it would be -- if possible -- a highly nontrivial task to transpose the ideas from Sharkovsky's theorem to this setting.

There might be similar known theorems on CAs though. A quick search on Google Scholar yields some matches for "cellular automata Sharkovsky". Notably, I found this paper on rule 40 which proves near omniperiodicity https://content.wolfram.com/sites/13/2018/02/17-3-6.pdf. Unfortunately, the proof seems to rely on very specific preperties of rule 40 so this result is much more limited than Sharkowsky's theorem. There is an interesting remark at the end of the paper:

The left-shift dynamical system (g_40 , S) may be easily related to an
interval dynamical system. Because the proof of the chaotic properties
in Theorem 2 is similar to that of the chaotic left-shift dynamical system
(Σ_L, A), which is homeomorphic to a logistic map or triangular trans-
formation. Precise examination of the relationship between (g_40, S) and
an interval dynamical system will be presented in a forthcoming paper.

(where (g_40, S) denotes rule 40, and interval dynamical system are the systems covered by Sharkovsky's theorem)
I couldn't find the "forthcoming paper".

Edit: corrected the remark on topology.

[parrot]

How does LifeViewer’s ruletable format work?

[b-engine]

How does LifeViewer’s ruletable format work?

Also applies to Golly, as it's a "standard".

A header defines "metadata":

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#R Testrule
!
@RULE Testrule
@TABLE
n_states:3
neighborhood:Moore
symmetries:rotate4reflect

You put transitions below the metadata:

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0,1,1,1,0,0,0,0,0,1
1,1,1,0,0,0,0,0,0,1

Bottom transitions override top transitions.

You can define variables:

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var a = {0,1,2}
var a1 = a
var a2 = a
var a3 = a
var a4 = a
var a5 = a
var a6 = a
var a7 = a
var a8 = a

a,a1,a2,a3,a4,a5,a6,a7,a8,0

[parrot]

But what does “symmetries:rotate4reflect” mean?

[b-engine]

But what does “symmetries:rotate4reflect” mean?

It means that it's isotropic non-totalistic.

Permute = outer totalistic
Rotate4 = INT, but reflections are distinct
None = nonisotropic

[muzik]

What is the largest strict still life predecessor that fits in a 16x16 box? Here is a lower bound from D2_x (not yet synthesized):

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x = 16, y = 16, rule = B3/S23
boobbbobobobbooo$
obobbboooboobbbo$
boobooooobooobbo$
oboobboobbbooobb$
bobobbbbbbobooob$
bbobbbboobbobooo$
ooooobooobbbbbbb$
boboobooboobbooo$
booboobbooobooob$
oobboboboobboooo$
bobbobbobbbbbobb$
obbooooooobbbobb$
bbooobbbooboobbb$
bboobbbobooboooo$
bbbbbooooobobobo$
obbbobobbobbobob!

[77551enpassant]

What is the largest strict still life predecessor that fits in a 16x16 box? Here is a lower bound from D2_x (not yet synthesized):

Code: Select all

x = 16, y = 16, rule = B3/S23
boobbbobobobbooo$
obobbboooboobbbo$
boobooooobooobbo$
oboobboobbbooobb$
bobobbbbbbobooob$
bbobbbboobbobooo$
ooooobooobbbbbbb$
boboobooboobbooo$
booboobbooobooob$
oobboboboobboooo$
bobbobbobbbbbobb$
obbooooooobbbobb$
bbooobbbooboobbb$
bboobbbobooboooo$
bbbbbooooobobobo$
obbbobobbobbobob!

I don't think that's strict, because the block doesn't interact with the rest of the still life.

[hotdogPi]

What is the largest strict still life predecessor that fits in a 16x16 box? Here is a lower bound from D2_x (not yet synthesized):

Code: Select all

x = 16, y = 16, rule = B3/S23
boobbbobobobbooo$
obobbboooboobbbo$
boobooooobooobbo$
oboobboobbbooobb$
bobobbbbbbobooob$
bbobbbboobbobooo$
ooooobooobbbbbbb$
boboobooboobbooo$
booboobbooobooob$
oobboboboobboooo$
bobbobbobbbbbobb$
obbooooooobbbobb$
bbooobbbooboobbb$
bboobbbobooboooo$
bbbbbooooobobobo$
obbbobobbobbobob!

I don't think that's strict, because the block doesn't interact with the rest of the still life.

You can just ignore the block and count the number of cells in the rest of it.

[LuveelVoom]

What is the largest strict still life predecessor that fits in a 16x16 box? Here is a lower bound from D2_x (not yet synthesized):

Code: Select all

x = 16, y = 16, rule = B3/S23
boobbbobobobbooo$
obobbboooboobbbo$
boobooooobooobbo$
oboobboobbbooobb$
bobobbbbbbobooob$
bbobbbboobbobooo$
ooooobooobbbbbbb$
boboobooboobbooo$
booboobbooobooob$
oobboboboobboooo$
bobbobbobbbbbobb$
obbooooooobbbobb$
bbooobbbooboobbb$
bboobbbobooboooo$
bbbbbooooobobobo$
obbbobobbobbobob!

Surely one can fit a tubstretcher predecessor and some delay mechanism to blow it up in a 16x16 box...

[vilc]

What is the largest strict still life predecessor that fits in a 16x16 box? Here is a lower bound from D2_x (not yet synthesized):

160-bit still-life with a 16x16 predecessor (found with LLS). Optimal for predecessors with D8 symmetry that stabilise within 6 generations.

Code: Select all

x = 16, y = 16, rule = B3/S23
4o3b2o3b4o$2ob2o6b2ob2o$o5b4o5bo$2ob3o4b3ob2o$bobo2b4o2bobo$3bobo4bobo
$2bobobo2bobobo$obobo2b2o2bobobo$obobo2b2o2bobobo$2bobobo2bobobo$3bobo
4bobo$bobo2b4o2bobo$2ob3o4b3ob2o$o5b4o5bo$2ob2o6b2ob2o$4o3b2o3b4o!