ConwayLife.com

A rule is pseudo-omniperiodic if it has an oscillator for every period that is not ruled out by the following simple constraints:
An oscillator's period must be a multiple of the background period (this rules out odd-period oscillators in B0 rules)
An oscillator's period must be a period in which ...

Did anyone tried glider synthesis of spark for LCM guns before?

x = 67, y = 45, rule = LifeHistory
11.2A4.2A$11.A.A2.A.A$13.A2BA12.2A$11.B2A2B2AB2.A2.A4.A$11.3A2B3A2.4A
5.A$12.BA2BAB7.2A2.2A$6.2A6.2B4.A.2A.A.A3.2A$4.A2.A6.B5.2A.ABA.2A.A2.
A$4.2A.A.AB2.2B9.BA2B3.3A28.2A$6.A.2AB.4BA7.2AB4A31.A.A$6 ...

The p28 block puffer allows for a weird HWSS supported interchange-tagalong. (but does not turn it into a ship)
x = 42, y = 103, rule = B3/S23
5$5bo45$16bo5bo$6b3o6b3o3b3o6b3o$6bo2bo4b2o2bobo2b2o4bo2bo$6bo7bo3bobo
3bo7bo$6bo3bo2b2obobobobob2o2bo3bo$6bo7bobobobobobo7bo$7bobo4b3obobob
3o4bobo ...

AsyncLife: Life except each cell only gets updated every second generation (odd cells on odd generations, even cells on even generations). Explosive.
x = 5, y = 4, rule = AsyncLife
3.A$.BABA$B$AB!
@RULE AsyncLife
@TABLE
n_states:3
neighborhood:Moore
symmetries:rotate4reflect
var a=0,1,2
var b=0,1,2 ...

A rule R has a generalised gutter symmetry if there is a set of cells G (the generalised gutter ) and a symmetry S of the plane except for G such that if at t=0 G is empty and the remainder of the plane has the symmetry S, then at t=1 (and hence for all t) G is empty and the remainder of the plane ...

I call these rules linear rules , *snip*


Very nice work!

Does this idea generalize in more than one way (other than addition modulo state count) to multistate grids?

Yes, actually: I believe any kind of addition that forms a group can be used. (I'm not sure if it has to be a field, or if ...

NNlk05 wrote: September 13th, 2026, 10:57 pm

erictom333 wrote: September 13th, 2026, 10:53 pm I call these rules linear rules, *snip*

Parity rules

I use the term "linear rule" since the property R(a) + R(b) = R(a + b) is called linearity, and because it generalises to more than two states by replacing bitwise XOR with addition modulo n.

And finally a side note on replicators. Notice that for B1357/S1357 the rule is its own XOR symmetries, this is also true for the von Neumann replicator rules:

Screenshot 2026-09-07 141313.png

Therefore, the rules are also maximally XOR symmetric, because in MAP a rule cannot have more than 512 ...

Regarding the idea of soup-searching as a gacha game, I believe the necessary element to get non-Lifenthusiasts interested would be anime waifus. Every pattern would have an anime girl counterpart which could be unlocked by discovering the object in a soup, and if a player discovers a certain amount ...

I would like a script to analyse infinite growth patterns (specifically guns, puffers, and rakes) similarly to how it is possible to analyse oscillators and spaceships. I would like to extract the following information:
Period, displacement, and velocity
Minimum and maximum population ignoring ash ...

*discussion*

I disagree. I believe that Spartan shouldn't include anything rarer than an eater 1, sticking with the 2006 set of {blinker, block, tub, boat, beehive, ship, toad, beacon, loaf, eater 1, long boat, pond}. I coined the term "Athenian" for what is currently referred to as ...

I feel like Eonian is more restrictive than other types of restrictive circuitry like thessalonic, because Eonian circuitry is missing one crucial component: the eater 1. Should we invent the term Eonian* for Eonian + eater 1 circuitry?


I think that just becomes spartan.


I think that ...

Can we add Entity Valkyrie's yearly oscillator stamp collections?
Makes sense to me!

There's definitely some work to do, hopefully sometime in 2026, to rework Golly's pattern collection so that there are fewer authoritative stamp collections (since these inevitably get out of date) and more ...

Personally I would like to see the ConwayLife Skyscraper return, as I have been fairly active there. However, I do think that discussion and forum games in the Sandbox should be at least somewhat CA-related.
One other potential change would be to make forum games their own subforum of the Sandbox ...

I think I've cracked unknown-constant-width-growth.rle's growth constant. I believe that the constant 1.945 in the growth rate is actually the real root of x⁵ = x⁴ + x³ + x² + x + 1, which is closer to 1.966. My reasoning is that for cell n to be born, all of cells n-1, n-2, n-3, n-4, n-5 must be ...

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.

Floor NyaN is the same as floor NaN, but everything is cats.
Floors 148+26i through 148+87i contain a multidimensional video store sellive every single piece of media from every possible universe .
Floor ∞ contains my analysis teacher telling me that infinity isn't a number and shouldn't be treated ...

The following 14-cell alien still life in ruels with S4z should be called a zeppelin, as it occurs in rules with S4z from the Z-hexomino, and it kind of looks like one.
x = 6, y = 5, rule = B3/S234z
3bo$b5o$o4bo$5o$2bo!

Also, the following motif should be called a book, as it fits between two ...

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Here's a potential start, with two intersecting but noninteracting oscillators:
x = 39, y = 39, rule = LifeSuper
14.A$14.3A$17.A$16.2A$16.4B$18.3B$18.3B$17.5B$17.5B$16.7B$16.7B$16.7B
$16.7B$16.2A3B2A$16.2B3A2B14.2I$17.A3BA15.I$9.JI4J2.BABAB2.4JIJ4.JI.I
$7.JIJI6J.BAB.6JIJIJ2.J2I$5.2JIJI9JB9JIJI3J$4 ...

Can a quintuple (or higher) psuedo oscillator exist? It would require two noninteracting oscillators that cross each other, which can (boringly) be achieved with pairs of glider guns pointed at each other.

Floor 1296 contain Tinker's Construct smelteries and fluid tanks containing every single real and fictional metal and alloy, and facilities for casting them into tools.
Floor NaR contains a single person ranting about the benefits of unums.

What is this, a customised chatbot for some character?

Floor 1 (since nobody has actually done it) is the reception. It is staffed by spiders in inflatable anime girl mechs that mostly redirect people who confuse Conway's Game of Life with the board game.
Floor 10i contains your ideal (as determined by an onmiscient group of Alien Space Bats) boyfriend ...

tommyaweosme wrote: May 26th, 2024, 10:08 pm even my spam fonts on fonstruction?

yes