Thread for basic questions

[confocaloid]

Is it possible to construct some sort of reflector that, when a glider goes through it, bounces back towards it (using a 180-degree reflector), and comes out on the input side? In other words, is it possible to make a reversible reflector?

What about the Jubjub reflector?

As I understood the question, the problem was to make a reflector where the output path is different from the input lane (e.g. a 90-degree reflector), but the output and the input can be exchanged and the device will still work. The Jubjub reflector is "trivially reversible", because the output path coincides with the input path -- reversing it is a do-nothing operation.

[qqd]

As I understood the question, the problem was to make a reflector where the output path is different from the input lane (e.g. a 90-degree reflector), but the output and the input can be exchanged and the device will still work. The Jubjub reflector is "trivially reversible", because the output path coincides with the input path -- reversing it is a do-nothing operation.

I was thinking more on the lines of a symmetric reflector that reflects a glider on the axis of symmetry, since that kind of reflector would automatically be reversible because symmetry demands it. Besides, your example is still trivial in the sense that no components are used both in the original and reversed reflecting reactions. In other words, both reactions are completely separated, which isn't really a solution for a non-trivial reversible reflector.
EDIT: This would have worked if the beehive was transparent (uses RNW3T46):

Code: Select all

x = 21, y = 27, rule = B3/S23
9b2o$8bo2bo$8bo2bo$9b2o3$2b2o$bobo$bo$2o3$12b2o$11bo2bo$12b2o3$2o$bo$b
obo$2b2o$18b3o$18bo$9b2o8bo$8bo2bo$8bo2bo$9b2o!

[dingxutong]

Is there an eater that can eat a single glider wherever it comes from?
For example, Eater 1 can eat the glider in the left picture, but not in the right one, so it's not a solution.

Code: Select all

x = 18, y = 9, rule = B3/S23
11bo$bo10bo$2bo7b3o$3o2$4b2o8b2o$4bobo7bobo$6bo9bo$6b2o8b2o!

[squareroot12621]

Is there an eater that can eat a single glider wherever it comes from?
For example, Eater 1 can eat the glider in the left picture, but not in the right one, so it's not a solution.

Code: Select all

x = 18, y = 9, rule = B3/S23
11bo$bo10bo$2bo7b3o$3o2$4b2o8b2o$4bobo7bobo$6bo9bo$6b2o8b2o!

I assume the glider has to come inside the range of the eater, and that the eater is finite and stable.
If we use those assumptions, it's almost certainly impossible. First, we'd have to engineer the maximum-clearance eater mentioned in Highway robber. Then, we'd have to cover it in eaters so it doesn't get destroyed by a glider coming anywhere except the intended lane. However, to make sure those eaters don't get destroyed by a glider 1hd inward from the original intended lane, we have to use more maximum-clearance eaters. Big problem. We're going to have to use an infinite pile of them to guard the eaters inside, and, since eaters can't have 0 cells, the mega-eater will have to be infinite, and we already assumed that it would be finite! Therefore, unless we engineer a stable giga-eater that can miraculously eat all lanes of gliders inside its reach, this is impossible.
Also, oscillating eaters have been explored in some thread that I can't find the link to.
Edit: Here it is!

[confocaloid]

Is there an eater that can eat a single glider wherever it comes from?
For example, Eater 1 can eat the glider in the left picture, but not in the right one, so it's not a solution.

Code: Select all

x = 18, y = 9, rule = B3/S23
11bo$bo10bo$2bo7b3o$3o2$4b2o8b2o$4bobo7bobo$6bo9bo$6b2o8b2o!

Conjecture: Every pattern has a glider destruction. This might be easy to prove, but I'm not sure if a pattern can survive all kinds of collisions with a glider, and with anything else.

These are open problems; see for example a forum thread:
"Structures resistant to attack" viewtopic.php?f=2&t=5296

In some rules other than Conway's Game of Life, there are indestructible patterns. For example, blocks should be indestructible in the rule shown below -- but only because the rule was designed to prevent births of dead cells adjacent to a block.
A further question is whether there are examples where a finite region can be significantly modified from outside (e.g. the state of every single cell in the region can be influenced), but cannot be cleanly destroyed (i.e. always transforms into some other non-removable pattern). This might be limited to attacks by single "slow" gliders, or attacks by any glider fleets, or by an arbitrary interaction from outside.

Code: Select all

x = 142, y = 82, rule = B2ei3aeij4aejrtw5-ejkr6-e78/S2ck3a
2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o
3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o$2o3b2o3b2o3b2o3b2o3b2o3b
2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o
3b2o3b2o3b2o3b2o3b2o4$2o68b2o68b2o$2o68b2o68b2o4$2o68b2o68b2o$2o68b2o
68b2o4$2o68b2o68b2o$2o68b2o68b2o4$2o68b2o68b2o$2o68b2o68b2o4$2o68b2o
68b2o$2o68b2o68b2o4$2o68b2o68b2o$2o68b2o68b2o4$2o138b2o$2o138b2o4$2o
138b2o$2o89b2o47b2o$91b2o3$2o138b2o$2o20b10o108b2o$32b2o$21bobobobobob
o$21b2obobobobobo$2o19bobobo7bo2bo33b2o68b2o$2o18b3obobobobob2o8bo27b
2o68b2o$19bobobobobobobobobob3ob2o$20b3obobobobobobobobobobo$21bobobob
obobobobobobo$2o19b2obobobobobobobobo31b2o68b2o$2o19bobobobobobobobobo
bo2bo27b2o68b2o$22bobobobobobobobobo2bo$21bobobobobobobobobo2bo$26bobo
b3obobo$2o23b3obobobobob2o31b2o68b2o$2o26b3obobobobo31b2o68b2o$29bobob
obobo$32bobobo2$2o68b2o68b2o$2o68b2o68b2o4$2o68b2o68b2o$2o68b2o68b2o4$
2o68b2o68b2o$2o68b2o68b2o4$2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o
3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b
2o$2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o
3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o!

[qqd]

This tub and glider collision almost restores the tub at generation 70 while creating some debris, but the tub gets 'stretched' into a beehive. Is it possible to perturb the beehive or the generations before it so that it restores the tub?

Code: Select all

x = 13, y = 12, rule = B3/S23
bo$obo$bo7$10b3o$10bo$11bo!

I tried a banana spark at generation 67, which almost works:

Code: Select all

x = 8, y = 21, rule = B3/S23
3bo$3bo$2bobo$3bo$3bo2$3bo$b3o$2o$o2bo$b2o$bobo$2b2ob2o$b3ob3o$2b2ob2o
$2b2ob2o$3bobo$4bo2$2b2o$bo!

But it turns into a barge due to what happens 3 generations later:

Code: Select all

x = 27, y = 19, rule = B3/S23
22bo2$22bo2$22bo2$22bo$18bo7bo$22bo$20bo3bo2$22bo3$2bo19bo$bobo17bobo$
o2bo16bo2bo2$20b2o!

[bluemanofgrapes]

Is there a pattern in B3/S23 of which the pattern oscillates but the period of the oscillator goes up infinitely?

[confocaloid]

Is there a pattern in B3/S23 of which the pattern oscillates but the period of the oscillator goes up infinitely?

Possibly relevant examples: sqrtgun, Sawtooth 177.
The terms oscillator and period are reserved for patterns with a specific non-changing period. If the number of ticks (to complete one cycle) changes non-periodically, then it's not an oscillator.

[mniemiec]

Is there a pattern in B3/S23 of which the pattern oscillates but the period of the oscillator goes up infinitely?

Possibly relevant examples: sqrtgun, Sawtooth 177.
The terms oscillator and period are reserved for patterns with a specific non-changing period. If the number of ticks (to complete one cycle) changes non-periodically, then it's not an oscillator.

The total number of possible states in an n*n square is 2^n^2, and given that most such states aren't parts of an oscillator, the number of states in any oscillator constrained within an n*n square must be considerably less than that. If you want an "oscillator" to have a period that grows without any finite limit, it must thus necessarily have a bounding box that similarly grows without limit (and, as confocaloid pointed out above, the term "oscillator" itself is no longer appropriate anyway.)

(This argument applies to all 2-state CAs, not only Life - and by changing the number 2 to k, also applies to all k-state CAs as well.)

[dvgrn]

If you want an "oscillator" to have a period that grows without any finite limit, it must thus necessarily have a bounding box that similarly grows without limit...

All of that said, we now have the tools in CGoL to fairly easily build an object that looks like an oscillator -- a large glider loop with Scorbie Splitters at the corners, let's say -- but actually grows very slowly in the manner described.

At each corner, the gliders circulating in the loop could execute a recipe that builds and triggers a seed constellation that moves the Scorbie Splitter outwards by (1,1). This is basically the same idea as the old self-constructing volatility-1 oscillator, but the technology has improved quite a bit since that pattern was completed.

[qqd]

This tub and glider collision almost restores the tub at generation 70 while creating some debris, but the tub gets 'stretched' into a beehive. Is it possible to perturb the beehive or the generations before it so that it restores the tub?

Code: Select all

x = 13, y = 12, rule = B3/S23
bo$obo$bo7$10b3o$10bo$11bo!

I tried a banana spark at generation 67, which almost works:

Code: Select all

x = 8, y = 21, rule = B3/S23
3bo$3bo$2bobo$3bo$3bo2$3bo$b3o$2o$o2bo$b2o$bobo$2b2ob2o$b3ob3o$2b2ob2o
$2b2ob2o$3bobo$4bo2$2b2o$bo!

But it turns into a barge due to what happens 3 generations later:

Code: Select all

x = 27, y = 19, rule = B3/S23
22bo2$22bo2$22bo2$22bo$18bo7bo$22bo$20bo3bo2$22bo3$2bo19bo$bobo17bobo$
o2bo16bo2bo2$20b2o!

It turns out the debris produced by the tub-glider collision is hard to use. I have tried almost 30 possible catalyses already, and all get destroyed some way or another, but that is by no means a reason to stop trying to modify the debris.

[confocaloid]

Would it be possible to track glider syntheses in non-B3/S23 rules such as tlife and DryLife?

I was thinking that rules would just be granted synthesis-recording privileges on a case-by-case basis. Only rules that support the glider would be granted this, since I'm sure most of the technology used for recording syntheses is optimised for them.

Is there a list of these somewhere? (It would be nice if Catagolue supported syntheses in non-CGoL rules...)

One idea that (maybe) would work reliably if implemented, is to create a (very simple to use, either integrated with Golly or standalone) software tool to maintain collections of syntheses in some way that would not depend on any single centralised location.

If a collection of syntheses is stored as a single file which can be easily browsed/updated/shared with others, and if there's a simple intuitive way to automatically merge different versions of the file into a single collection, that could provide a way to collect syntheses in some rule and share them, without needing an "official" version.
The drawback is that everyone interested would end up with a copy of the database. The advantage is that there would be no single point of failure.
The puzzle is to design and implement a convenient/intuitive to use toolkit to work with your local copy of collection/database (i.e. add, browse, find, export/import, etc.)

Maybe something like this could be done for collections of other patterns (in Life and/or in alien rules), where having an "official" online service is either impractical or unlikely?

[qqd]

Would it be possible to construct a metacell that can simulate Margolus rules? Metacells have been constructed for Life, Life-like, non-totalistic, and even non-isotropic rules, but a metacell has never been constructed in Life for reversible celluar automata.

[confocaloid]

Is the synthesis cost well-defined, when constructing the glider itself?

Catagolue definition:

A glider synthesis is a recipe for constructing an object by colliding multiple copies of the glider, the simplest moving configuration in the rule B3/S23. The cost of a synthesis is the number of gliders required.

Life Lexicon:

:glider synthesis Construction of an object by means of glider collisions. It is generally assumed that the gliders should be arranged so that they could come from infinity. That is, gliders should not have had to pass through one another to achieve the initial arrangement.

Given the above, the idea of a glider synthesis depends on the idea of a collision between multiple copies of the glider.
Since a glider collision always takes at least two gliders (a single glider in an otherwise empty universe will never collide with anything), the cheapest synthesis of the glider should logically take two gliders -- i.e. either of two 2G collisions shown in Patterns/Life/Syntheses/two-glider-collisions.rle.

Before April 2023, Catagolue did actually give synthesis cost 2 for the glider -- see e.g. archived copy from 2023-03-27:
https://web.archive.org/web/20230327105 ... _153/b3s23
However, it was recently changed for some reason, to give cost 1 for the glider:
https://catagolue.hatsya.com/object/xq4_153/b3s23
I think that contradicts the above definitions -- the definition of "cost" depends on the definition of "synthesis", which in turn relies on the definition of "collision", and both Catagolue and Life Lexicon seem to be clear that there should be multiple colliding gliders.

Hence the question: is the glider synthesis cost for the glider equal to 2, or equal to 1, or it is not well-defined in the first place?

[mniemiec]

Hence the question: is the glider synthesis cost for the glider equal to 2, or equal to 1, or it is not well-defined in the first place?

It depends on how you define the metric. If it's "How many gliders does it take to produce object X", it's 1, because it's possible to input one glider into a box, and have exactly one glider and nothing else come out. If the word "collision" is used, the answer is 2. In practical terms, the former is likely more useful, but sometimes the latter can more illuminating, especially in rules where there is a very common natural spaceship that is used for syntheses, but that spaceship may be difficult to synthesize itself (e.g. in B2/S2, the rule is so explosive that it takes 4 gliders to synthesize 1 without leaving behind any explosive debris). In my own database, I use the latter definition.

[qqd]

Would it be possible to construct a metacell that can simulate Margolus rules? Metacells have been constructed for Life, Life-like, non-totalistic, and even non-isotropic rules, but a metacell has never been constructed in Life for reversible celluar automata.

Can someone answer this question?

[AlbertArmStain]

Is it possible to make a square free integer generator like primer?

[mniemiec]

Is it possible to make a square free integer generator like primer?

Since Life is computationally universal, if you can program any algorithm in any language on any platform, it can also be done in Life by emulation. That doesn't necessarily mean that a solution will be small, efficient, and/or elegant.

[ProfMonkey07]

Does there exist any structure that is basically indestructible meaning if any other patterns collide with it it either stays intact or repairs itself?

[hotdogPi]

Does there exist any structure that is basically indestructible meaning if any other patterns collide with it it either stays intact or repairs itself?

This is a very well-known open question. Most people think no, but it's difficult to prove such a thing.

[dvgrn]

Does there exist any structure that is basically indestructible meaning if any other patterns collide with it it either stays intact or repairs itself?

Moved to the "basic questions" thread, because as hotdogPi says, this question comes up fairly regularly -- most recently in May on this thread.

Here's a thread from a couple of years ago that covers the topic reasonably well:

Structures resistant to attack

[bibunsekibun]

Is there a pattern that completely destroys the pattern in all ways no matter where or when the glider hits it?

[dvgrn]

Is there a pattern that completely destroys the pattern in all ways no matter where or when the glider hits it?

... Possibly? But nobody has found a way yet. This is actually a minor corollary of the "universal eater" or "indestructible object" idea.

Assuming that there is a universal eater and it's some kind of engineered object, the odds seem pretty good that it will then be possible to add a self-destruct mechanism that triggers after the recovery process is complete.

[hotdogPi]

At least you're not the person on Discord who asked a similar question to the indestructible object question, except that it was that it recovers itself if any one cell was manually removed (rather than a glider hitting it). The person asking it was thinking of some large engineered pattern. However, this one definitely exists, and it's called a block.

[AlbertArmStain]

Has anyone built a gun where the period can be adjusted by input gliders?