ConwayLife.com

Ah ok.

Is there a specific name for non-stilllife wicks, then?

Is there a name for patterns that would be spaceships, but require an infinite linear chain (not 2d tiling) of repeats to work? Think of it as a subclass of a linear agar, or a generalization of a wick to allow non-stilllife. For instance: x = 4, y = 5, rule = B3/S23:T0,5 o2bo$o2bo$b2o$b2o! May be e...

Thanks for the responses!

Food for thought.

Hence why I asked...

It's an interesting question.

Personally, I'm in the "it's possible but good luck finding a pattern that works" camp.

Good answer, thanks.

On a related note: is there an upper bound on the depth required to support an arbitrary row of still-life with only dead cells on the other side, assuming there is a way to support said row?

So, "pattern" here means both alive and dead cells, as is the case with some Garden of Eden patterns. With that in mind, two patterns being "indistinguishable" means that for every possible pattern P (or P') that contains one of the two patterns (C and C') embedded at (0,0), run for an arbitrary num...

I'm looking for an upper bound on the lower bound . In other words, a minimum size such that "assuming there is a pN oscillator, there is guaranteed to be one that fits in an NxM box, where N and M are defined as follows...". The concrete example works, but I'm specifically looking at the remaining ...

Things like garden-of-eden problems are rather difficult to express cleanly as a SAT problem - given they are more alone the lines of "find a pattern such that there does not exist a precursor", and it's hard to map that easily. The paper you linked did warm-start based QSAT; I'd be shocked if it wa...

Is there an upper bound to the size of the bounding-box of the minimum-sized-bounding-box-period-N-oscillator?

Whoops, you're right.

And you'll have to be careful to ensure that the corner tiles ensure the mirrored configuration cannot happen. I think that's true as-is, though.

Also there's only 6 corner tiles, which is nice. (0 live, 1 live, 2 adjacent live, 2 diagonal live, 3 live, 4 live). So yeah, you should be able to do it with <= 38 unique tiles. As you say, splitting the 4 / 5 / 6 into 2/3 half tiles would reduce it further: index center #neighbors #neighborhood 1 ...

Bravo. One obvious issue is that your "no-neighbors" corner piece (the diamond) tiles the plane on its own - but that's simple to fix. I suspect that you can actually go for a straight "square" tiling from this. My thought process: First, shift from using the octagons for the cells and the diamonds ...

(Note: this was pulled away from the "basic questions" thread here .) x = 64, y = 64, rule = LifeHistory 3D2C3D3.2A3.2D2CDC2D3.2A3.3D2C3D3.2A3.2D2CDC2D3.2A$8D8.8D8.8D8.8D$DC 6D.A6.2D2CDC2D8.DC6D.A6.2D2CDC2D$CDC5DA.A5.DCDCD3C4.2A2.CDC5DA.A5.DCD CD3C4.2A$DC3D2CD.A3.2A.C2DC4DA2.A2.A.DC3D2CD.A3.2A.C2DC4...

Let's move that aspect to a new thread about SAT solvers, then?

I'll make one.

First, thank you again. This is rather interesting. With the restriction that the 16 corner cells are blank and everything is still life, I have an 8x8 set of tiles, and 7x7 or smaller is not allowed (assuming my code was correct): x = 32, y = 32, rule = B3/S23:T32,32 3.2A6.2A5.2A.A5.2A3.$32.$.A7.A8...

Do we know that bounded-periodic oscillatory patterns have an upper-bound 1/2 density limit on average, at least? Seems easier to prove than the aperiodic case. Although still way above my pay grade. Hasn't been proven yet, as far as I can recall. I think everyone suspects that 1/2 is in fact the h...

Do we know that bounded-periodic oscillatory patterns have an upper-bound 1/2 density limit on average, at least? Seems easier to prove than the aperiodic case. Although still way above my pay grade. Also I'm interested by the aperiodic tiling suggestion. If I'm reading correctly, basically set up e...

So... In normal Life an agar cannot have an average density (over space and time) above 1/2, if I read correctly.

What about patterns that are aperiodic, be it in space, time, or both? Does this still hold?

Also: is there an equivalent to Penrose tilings for Life?

Is there such a thing as the following? Two finite and stable patterns that are both constructible but that are indistinguishable from each other by the outside world. (Simple definition of constructible as I am thinking: able to be constructed via glider synthesis.) (Stable: returning to its origin...