Life has been proven omniperiodic. What next?

[hotcrystal0]

Interesting loop:

Code: Select all

x = 75, y = 61, rule = B3/S23
35bo$33b3o$32bo$17b2o13b2o$18bo$18bobo$19b2o$25bo$24bobo$23b2ob2o8bo$
24bo2bo9bo$24b2ob2o6b3o$25bobo$26bo$26bo$5b2o18bobo4b2o$6bo20bo4bo$5bo
7bo8b2obo7b3o$5b2o6bo8b3o10bo$2o19bo$o2b4o4b3o8b2o21bobo$bobo2bo3bob2o
3bobo2b2o22b2o$2o2b2o4b2o5bobo6bo19bo$2bobo14bo7b3o$2bo2bo21b2o$3b2o$
8b2o15bo$9bo14bobo$6b3o8b2o5b2o$6bo10bobo$17bo39bo$55bobo10bo$49b2o5b
2o8b3o$48bobo14bo$49bo15b2o$70b2o$46b2o21bo2bo$45b3o7bo14bobo$28bo19bo
6bobo5b2o4b2o2b2o$27b2o22b2o2bobo3b2obo3bo2bobo$27bobo21b2o8b3o4b4o2bo
$53bo19b2o$39bo10b3o8bo6b2o$39b3o7bob2o8bo7bo$42bo4bo20bo$41b2o4bobo
18b2o$48bo$48bo$47bobo$37b3o6b2ob2o$37bo9bo2bo$38bo8b2ob2o$48bobo$49bo
$54b2o$54bobo$56bo$41b2o13b2o$42bo$39b3o$39bo!

What's our next goal for oscillators? An engine for every period below 100? A goal even higher than that?

[hotdogPi]

Find the remaining gun periods.

[Chris857]

Glider syntheses for at least one interesting oscillator for every period up to some value like 100. For 1-100 we're pretty close. I think we're missing:
p41 Edit: completed
p65
p81
p95
p97

Somewhat boring syntheses:
p89 - timing independent glider loop
p93 - LCMs, and a B-R track
p98 - R49 loop, and a glider shuttle
p99 - an LCM

[snowman]

1. Write another NewLifeCA informing the broader community of the discovery
2. There's plenty of other challenges that are worth looking into. I think it's still worth searching for a smaller vex stabilization, for instance. Optimizing guns and glider syntheses still have a lot of unexplored territory. There are useful catalysts/conduits out there waiting to be found. Specialists could work on lowering the upper bound on things like RCT and quadratic growth patterns.

While one of the big focuses of the community's attention has finally been conquered, that doesn't mean Life is over.

[C28]

What's our next goal for oscillators? An engine for every period below 100? A goal even higher than that?

a sparker for every period below 200.

[Entity Valkyrie 2]

Glider gun omniperiodicity
p14/p15 LWSS guns
LWSS/MWSS/HWSS true-period guns
Small stable CC reflector
Small stable splitter
New spaceship speeds/periods
etc.

[GUYTU6J]

̶O̶n̶ ̶t̶h̶e̶ ̶o̶t̶h̶e̶r̶ ̶w̶a̶y̶ ̶o̶f̶ ̶s̶p̶e̶c̶t̶r̶u̶m̶,̶ ̶c̶a̶n̶ ̶w̶e̶ ̶m̶a̶k̶e̶ ̶a̶t̶t̶e̶m̶p̶t̶s̶ ̶t̶o̶ ̶m̶a̶k̶e̶ ̶C̶G̶o̶L̶ ̶m̶o̶r̶e̶ ̶n̶o̶v̶i̶c̶e̶-̶f̶r̶i̶e̶n̶d̶l̶y̶?̶ ̶
̶"̶N̶o̶v̶i̶c̶e̶"̶ ̶m̶e̶a̶n̶s̶ ̶b̶e̶g̶i̶n̶n̶e̶r̶ ̶t̶o̶ ̶m̶a̶t̶h̶e̶m̶a̶t̶i̶c̶s̶ ̶a̶n̶d̶ ̶c̶o̶m̶p̶u̶t̶e̶r̶ ̶p̶r̶o̶g̶r̶a̶m̶m̶i̶n̶g̶,̶ ̶w̶i̶t̶h̶ ̶p̶o̶s̶s̶i̶b̶l̶y̶ ̶a̶ ̶m̶i̶n̶i̶m̶u̶m̶ ̶e̶q̶u̶i̶p̶m̶e̶n̶t̶ ̶o̶f̶ ̶G̶o̶l̶l̶y̶ ̶w̶i̶t̶h̶ ̶s̶c̶r̶i̶p̶t̶s̶ ̶a̶v̶a̶i̶l̶a̶b̶l̶e̶.̶
̶"̶F̶r̶i̶e̶n̶d̶l̶y̶"̶ ̶m̶e̶a̶n̶s̶ ̶k̶i̶n̶d̶l̶y̶ ̶p̶r̶o̶v̶i̶d̶i̶n̶g̶ ̶o̶p̶p̶o̶r̶t̶u̶n̶i̶t̶i̶e̶s̶ ̶t̶o̶ ̶g̶e̶t̶ ̶L̶i̶f̶e̶W̶i̶k̶i̶ ̶p̶a̶g̶e̶s̶ ̶o̶r̶ ̶P̶O̶T̶Y̶ ̶e̶n̶t̶r̶i̶e̶s̶ ̶f̶o̶r̶ ̶n̶o̶t̶a̶b̶l̶e̶ ̶d̶i̶s̶c̶o̶v̶e̶r̶i̶e̶s̶

Dropping a little wishlist:
p149096 - Complete stable Bandersnatch splitter
p153129 - Build 2~3 gliders + object → pattern database for syntheses
p154671 - Make a bootstrapping almost-stable single-engine Cordership
p155067 - Synthesize all 10×10 54-cell still lives

[confocaloid]

Might be somewhat "out of line", but one thing that's missing are accessible expository explanations of some of "large" and "very large" engineered patterns that already exist.

Some write-ups that could help an outsider to understand "how this thing works" -- written in a smooth unobtrusive way, but still "mathematically honest".

Obviously mathematical exposition is hard. But maybe this could be done for some of already completed patterns/challenges.

See also
viewtopic.php?p=4397#p4397
viewtopic.php?p=128861#p128861
viewtopic.php?f=9&t=6044

[Haycat2009]

Extend the omniperidicity to
Guns: (A glider loop and duplicator will make an adjustable one)
Spaceships: (Much harder, I want to see a 7c/19 soon)

[pzq_alex]

̶O̶n̶ ̶t̶h̶e̶ ̶o̶t̶h̶e̶r̶ ̶w̶a̶y̶ ̶o̶f̶ ̶s̶p̶e̶c̶t̶r̶u̶m̶,̶ ̶c̶a̶n̶ ̶w̶e̶ ̶m̶a̶k̶e̶ ̶a̶t̶t̶e̶m̶p̶t̶s̶ ̶t̶o̶ ̶m̶a̶k̶e̶ ̶C̶G̶o̶L̶ ̶m̶o̶r̶e̶ ̶n̶o̶v̶i̶c̶e̶-̶f̶r̶i̶e̶n̶d̶l̶y̶?̶ ̶
̶"̶N̶o̶v̶i̶c̶e̶"̶ ̶m̶e̶a̶n̶s̶ ̶b̶e̶g̶i̶n̶n̶e̶r̶ ̶t̶o̶ ̶m̶a̶t̶h̶e̶m̶a̶t̶i̶c̶s̶ ̶a̶n̶d̶ ̶c̶o̶m̶p̶u̶t̶e̶r̶ ̶p̶r̶o̶g̶r̶a̶m̶m̶i̶n̶g̶,̶ ̶w̶i̶t̶h̶ ̶p̶o̶s̶s̶i̶b̶l̶y̶ ̶a̶ ̶m̶i̶n̶i̶m̶u̶m̶ ̶e̶q̶u̶i̶p̶m̶e̶n̶t̶ ̶o̶f̶ ̶G̶o̶l̶l̶y̶ ̶w̶i̶t̶h̶ ̶s̶c̶r̶i̶p̶t̶s̶ ̶a̶v̶a̶i̶l̶a̶b̶l̶e̶.̶
̶"̶F̶r̶i̶e̶n̶d̶l̶y̶"̶ ̶m̶e̶a̶n̶s̶ ̶k̶i̶n̶d̶l̶y̶ ̶p̶r̶o̶v̶i̶d̶i̶n̶g̶ ̶o̶p̶p̶o̶r̶t̶u̶n̶i̶t̶i̶e̶s̶ ̶t̶o̶ ̶g̶e̶t̶ ̶L̶i̶f̶e̶W̶i̶k̶i̶ ̶p̶a̶g̶e̶s̶ ̶o̶r̶ ̶P̶O̶T̶Y̶ ̶e̶n̶t̶r̶i̶e̶s̶ ̶f̶o̶r̶ ̶n̶o̶t̶a̶b̶l̶e̶ ̶d̶i̶s̶c̶o̶v̶e̶r̶i̶e̶s̶

Some thoughts:

• Since the Great Oscillator Discovery Project is nearly complete (at least it has accomplished its initial goal), we should tidy up the current search tools (mainly hotdogPi's script and CatForce) to put them in a more accessible/usable format. This includes porting to other rules and tidying up the input file format for CatForce (it's been a mess to figure out everything), perhaps creating a script that generates the catalyst format from a more accessible format (LifeHistory patterns and list-of-interactions have been proposed).
• Making an pattern editor that allows manipulating patterns in terms of components instead of on a cell level. This makes it easier to align outputs to inputs for circuitry and manage timing, among many other things. This sounds like a grand project, but currently the experience of just "building a larger pattern from smaller building blocks" is a pain in Golly.
• Making running Python scripts in Golly less painful. As of now, every other day someone asks "how do I run Python scripts in Golly? It complains dll-not-found/symbol-py-init-module-not-found/etc." Maybe the brute-force approach is to just grab a random Python installation from PATH.

There are probably many, many more ideas I'm just having trouble recalling.

[get_Snacked]

stable bumper

[Period1GliderGun]

a stable, fast glider splitter

[Entity Valkyrie 2]

a stable, fast glider splitter

best if:
- outputs have different colors
- both outputs are at different directions, and
- neither output is 180 degrees.

Here is a StateInvestigator example of such an "ideal splitter":

Code: Select all

x = 27, y = 27, rule = StateInvestigator
A$.2A$2A2$3.A.A$4.2A$4.A16.C$7.A8.2DE$8.2A6.EA3.E$7.2A6.ED$14.ED10.E$
13.ED9.D.E2$10.E.2ED9.E$10.CD.DED7.E$9.ED3.DED$7.DED5.DED$7.DA7.D2EDE
$7.E9.E$17.D$17.E$6.C.E2$14.E$11.D.E2$10.2E!

[Macbi]

I keep a little file of open problems. Sorry if some of them aren't self-explanatory.

Spaceships of all speeds (and periods)
Still life finitization problem
16x16 quadratic-growth
One-cell thick UC (ships, oscs, etc.)
90-degree 2c/3 wire elbow.
Any glider-constructible Life pattern can be constructed with less than N gliders. Find N
There exists a Garden of Eden inside a 4xN bounding box.
Any rectangular repetition of any 3x3 pattern can be shown to have at least one parent pattern -- i.e. such a pattern is not a Garden of Eden.
do all MxN arrays of adjacent blocks have glider syntheses?
c/2 against-the-grain agar ship
The eventual fate of an infinite universe with random starting state (In particular, limiting density?)
Is block the only finite strict still life where each living cell has exactly 3 neighbours
diagonal lightspeed telegraph
colour-changing reflector
elementary replicators
true period-14 glider gun
What's the thinest width cylinder on which Life is Turing Complete?
Is Life an explosive rule?
Phoenix of period > 2
Which periods have Phoenix agars?
Spaceship of speed (n,m)/2(n+m) for all n,m.
Is there a convoy of >4 ships such that no nontrivial subset gives a smaller convoy?
Can every spaceship synthesise a glider?
Does every spaceship have an eater? (At its minimum repeat time?)
Does every spaceship have an gun? (At its minimum repeat time?)
Can we get minimum period LWSS guns?
Can every finite population pattern be deleted by gliders?
Is there a still life that eats every glider that collides with it? (Is there a completely indestructible pattern?)
Is there a pattern robust to any 1 cell change?
Does any non-vanishing pattern exist where any pattern formed by flipping the state of a single cell will evolve convergently with the unmodified pattern after a finite number of ticks?
do strictly volatile oscillators exist at all periods for which oscillators exist?
What is the smallest still life without a two-glider destruction?
Given an n*n torus, what's the largest number of predecessors any pattern on that torus can have as a function of n?
How much can the population grow in n generations? I.e. if generation 0 has population P and generation n has population Q, how large can Q/P be? For n=1, Q/P can be arbitrarily close to, but not equal to, 3. Unknown for any larger n.
Consider a particular cell within a pattern, and look at the sequence of its states in gen 0, gen 1, ... Can every finite sequence of bits occur as such a sequence?
Is there a still-life which is annihilated by any single glider which hits it?
Create a compiler for apgsembly
How does behavior of random soups depend on initial density?
How much entropy per cell does the GoL universe store?
A ship in the 2x1 chicken wire agar? (A knightship?)
What's the average number of cells affected by toggling a single cell in a infinite soup? Is the distribution of such cells L2 circular?
Starting with cells only in one quadrant, can each cell be reached in the number of generations suggested by the empty space speed limit?
For any stable finite CGoL pattern, there is at least one cell, live or dead within its environment, for which a change in state results in a lower population once the stability of the new pattern is reached.
Stable small direct G-to-2G
Stable small direct two-state G-to-G switch (alternate output gliders sent in different directions)
quadratic-growth pattern with fewer than 23 cells
stable glider storage unit
Is 'Zone of influence' a useful concept? What's a good definition?
Agar with average density over 1/2
What is the probability of getting a Garden of Eden from a random soup of size n×n? What's the smallest orphan?
Smallest pattern that grows at 1 cell per generation
I wonder if there is a nice 3D embedding that is reversible and preserves the count of live cells.
The empty space speed limit is c/2. Can a ship go a little bit faster if it's not in empty space but rather an extremely sparse grid of blocks?
Does there exist an unstoppable space ship?
In a random initial starting configuration, does 'every cell eventually becomes periodic' have probability 1?
Do long 1xn lines of live cells generate novel behaviour as they get longer?
Is there a finite pattern such that every cell in every pattern containing it eventually dies?
Is it decidable whether a finite population pattern has a finite population predecessor?
Is it decidable whether a partial pattern can extend to a still life?
Does Sparse Life or Dense Life ever reach a positive density?
Can we build a border from which no information can escape?

And there's another open problem that occurs to me now that omnipediodicity is solved, which is to look at the group of symmetries of Life (including time-shift symmetries) and classify exactly which subgroups are achieved by some pattern. For example, is there a pattern that rotates by 90 degrees every 100 generations? Is there an agar with 17 by 20 repeating cells that translates itself 3 cells to the left every 7 generations?

[hotdogPi]

Is block the only finite strict still life where each living cell has exactly 3 neighbours

This search should take less than a second.

[dvgrn]

There exists a Garden of Eden inside a 4xN bounding box.

Isn't this one pretty well closed now? Or should we wait for some kind of independent verification?

[confocaloid]

There exists a Garden of Eden inside a 4xN bounding box.

Isn't this one pretty well closed now? Or should we wait for some kind of independent verification?

I think the linked post specifically clarifies that existence of four-row Gardens of Eden is still open:

I should probably call out a distinction between live cells and specified cells. I haven't quite disproved Gardens of Eden where the live cells are restricted to four (consecutive) rows. But when the specified cells in the target generation, both alive and dead, are restricted to four consecutive rows, there will always be a parent pattern.

[Period1GliderGun]

I'd like to see engine-based oscillators for all periods under 100 (and possibly 200).

[dvgrn]

I think the linked post specifically clarifies that existence of four-row Gardens of Eden is still open...

Seems like there's probably fairly broad agreement that a '"four-row Garden of Eden" implies that all required cells fit in four rows. The main thing that leaves the question still open is the lack of any independent review or verification.

EDIT 9/22/2023: See below -- confocaloid is completely correct on this. Looking back at the exchange today, I see that I added a "like" to that post when it was made. Just adding this note now to make sure the resolution was clear.

[confocaloid]

I think the linked post specifically clarifies that existence of four-row Gardens of Eden is still open...

Seems like there's probably fairly broad agreement that a '"four-row Garden of Eden" implies that all required cells fit in four rows. The main thing that leaves the question still open is the lack of any independent review or verification.

Unfortunately, I cannot see how such "fairly broad agreement" could possibly exist, given that in a Garden of Eden, every cell in the Life universe is specified (finitely many cells are required to be alive, and all the rest are required to be dead).

Quoting from the CGoLM&C textbook (page 22):

The pattern that we have constructed is interesting for the fact that it is not only a Garden of Eden, but it remains a Garden of Eden regardless of which live and dead cells we place outside of the central 266-cell spiral. Patterns like this one that cannot be any part of the evolution of another pattern (equivalently, they are still a Garden of Eden no matter what other cells are placed around them) are called orphans.

When specifying a Garden of Eden, one specifies the state of every cell in the plane.
When specifying an orphan, one specifies only finitely many cells.
A four-row Garden of Eden would be a Garden of Eden where all alive cells are in a 4xN rectangle, and all other cells are dead.

Based on the post by mscibing quoted above, I take it that existence of four-row Gardens of Eden is an open question.

What was resolved is the existence of four-row orphans. According to the title of that thread,

There Are No 4 Row High Orphans in Conway's Game of Life

[confocaloid]

What's our next goal for oscillators?

Honey farm predecessor hasslers of every period?

p19 by mvr:

p47 honey farm, which makes the lowest period for which we know an oscillator (i.e. not 19 or 41) but no honey farm hassler now 49

The honey farm has been a great tool for constructing low-period oscillators:

[hotcrystal0]

Shouldn’t this thread be locked?

[AlbertArmStain]

Shouldn’t this thread be locked?

You can simply ignore it or it could be moved to the sandbox.

[carsoncheng]

The omniperiodicity paper has been published on arxiv:
https://arxiv.org/abs/2312.02799

[Haycat2009]

I would love to see omniperiodicity of guns