ConwayLife.com

I was thinking about indexing these, but the very premise raises some interesting questions.

There is no real way to distinguish between an "unnatural" spaceship and one that does occur naturally, but supremely rarely. We know from Life that rare spaceships are definitely observable: gliders are abundant, LWSSs are occasional, MWSSs a little less so, HWSSs rarer yet, switch engines occur once in a blue moon but occur regardless.

Considering additionally all the oscillators that have been observed naturally, the lesson seems to be that we could well assume that any random spaceship in Life — Schick engines, weekenders, lobsters, goddamn caterpillars — is capable of emerging from random soup or random seed starting conditions, if we could run and analyse a couple googolplex cases. And nothing seems to prohibit this being the case for other spaceships in other rules either.

So, "naturally occurring spaceship" is not really a yes/no question. Questions that can be asked are
1) are any spaceships (or similar structures; do we have a common hypernym for SS/puffer/shoot/wickstretcher/wickbeam/replicator?) known in the rule to begin with? This is already being worked on.
2) how frequently do the known ones occur?

The latter question is additionally going to require some new metrics for various rules. In Life and other ultimately stabilizing rules, we can simply measure spaceships per soup area (in some that stabilize fast but densely, the bare spaceship creation rate may be easier to determine than their escape rate), but in exploding rules something else is needed.

Spaceship output as a function of time seems easily quantifiable, but how to turn that into a "frequency" compatible with stabilizing rules I don't see immediately: this seems to be a function of soup perimeter rather than area.

Tropylium wrote:Spaceship output as a function of time seems easily quantifiable, but how to turn that into a "frequency" compatible with stabilizing rules I don't see immediately: this seems to be a function of soup perimeter rather than area.

…on closer thought, the number of spaceships escaping from a stabilizing soup is a function of perimeter as well: SSs born deep inside a soup will likely run into ash and fail to escape. Presumably the escape probability's an exponential decay of the distance of their birth location from the edge. (Though there are "kinetic" rules, typically Generations, that leave such sparse ash versus a decent amount of ships, that sample size needs to be huuuuge for this to actually matter.)

Spaceships emitted by explosiv rules can also emerge from "inside" soup (e.g. DryLife), so this seems quite compareable after all: calculate the explosion rate, which yields the perimeter growth rate, which can be compared with the SS output rate. That leaves only the issue of chaos catching up with a ship.

Actually I'm also not sure if ship collisions should be accounted for or not. In rules like Star Wars they can be the main limiting factor of the ship escape rate.

Each of my Java CA Simulators implement a process which generates and tests a New Rule by first generating random parameters in a selected Rule Family, then setting the world to random states and finally running the simulation. This process is initiated by a New Rule button click. Most of the rules featured in "Java CA Programs.zip" here:

http://bprentice.webenet.net/Java%20Square%20Cell/

were found by repeatedly clicking this New Rule button until something interesting turned up. Something interesting being defined as ships, puffers, oscillators, guns or replicators. The three CA simulators that I use most often are Square Cell, Hexagonal Cell and Triangular Cell. These three programs are included in "Java CA Programs.zip" together with the Java source code.

Brian Prentice

Tropylium wrote:I was thinking about indexing these, but the very premise raises some interesting questions.

There is no real way to distinguish between an "unnatural" spaceship and one that does occur naturally, but supremely rarely. We know from Life that rare spaceships are definitely observable: gliders are abundant, LWSSs are occasional, MWSSs a little less so, HWSSs rarer yet, switch engines occur once in a blue moon but occur regardless.

Considering additionally all the oscillators that have been observed naturally, the lesson seems to be that we could well assume that any random spaceship in Life — Schick engines, weekenders, lobsters, goddamn caterpillars — is capable of emerging from random soup or random seed starting conditions, if we could run and analyse a couple googolplex cases. And nothing seems to prohibit this being the case for other spaceships in other rules either.

This is a very valid question. I mean after all, the switch engines are considered the only known naturally ocuring infinitely growing patterns, but the key is that they are the only ones ever observed. Others may and probably have formed, like say the recently discovered 20 cell or so "loafer." With that relatively small cell size I find it hard to believe that it can never occur naturally. In fact it probably does. But let's just say it occurs once per every 1,000 occurances of the block laying switch engine. And let's just say that 99.9% of the time, it occurs too deep within the chaos and dies. Unless someone was paying close attention to the right spot at the right time period, they would never know it ever arose. And that's assuming they recognized it as a spaceship. Since it has a c/7 velocity, unless it remained untouched for seven generations even the most observant person would probably miss it. And even if it did last 7 generations, people make human errors. The could be looking right at it and still miss it if they were daydreaming at the time.

Take this pattern for example A switch engine arises on generation 311 and gets fatally disrupted on generation 316. Now because I happened to pay attention to that part of the patter at the time, and knew what a switch engine looks like, I was able to attack that pattern with three more specifically placed gliders and geta glider-producing switch engine. But had any one of those things gone wrong (ie I wasn't looking there, I was spacing out, I didn't know what a switch engine looks like, or even I was too zoomed out to see enough detail to identify the pattern as a switch engine), that would certainly not be the case.

In factthis makes me wonder if it may not be nessary to undertake the painstaking process of expirimenting on all possible reasonably small patterns, find all the spaceships, and develope a complex computer algorithm to get an even reasonably accurate judgement on how often certain patterns show up.

LumpsOfMuck wrote:(…) say the recently discovered 20 cell or so "loafer." With that relatively small cell size I find it hard to believe that it can never occur naturally. In fact it probably does. But let's just say it occurs once per every 1,000 occurances of the block laying switch engine. And let's just say that 99.9% of the time, it occurs too deep within the chaos and dies.

(…) this makes me wonder if it may not be nessary to undertake the painstaking process of expirimenting on all possible reasonably small patterns, find all the spaceships, and develope a complex computer algorithm to get an even reasonably accurate judgement on how often certain patterns show up.

I think we can well get a ballpark approximation on how often soups might produce loafers. Consider these cell counts and bounding boxes:
• Glider: 5 cells, 3×3
• LWSS hull: 8 cells, 4×5
• MWSS hull: 9 cells, 4×6
• HWSS hull: 10 cells, 4×7
• Switch engine: 8 cells, 4×6
The SE is thus in a sense smaller than the MWSS (it has some much larger phases, but these are unlikely to arise from anything else than the small ones). It seems reasonable to assume that temporary SEs arise more often than temporary MWSSs, they just fail to escape.

One part of this discrepancy is obviously due to the need to stabilize, but if you throw some random stable junk behind a SE, you'll find that the odds of stabilization are clearly better than the about 1 : 70 ratio in their natural occurrence. (It's more like 1 : 3 really.) The remaining difference is probably due to (1) needing a wider escape path (37 lanes versus 7!), and (2) activity being more likely to catch up with them from the rear (c/12 versus c/2).

As for accounting for size in cell counts, the LWSS/MWSS ratio is a bit under 1 : 4, and the MWSS/HWSS ratio is a bit over 1 : 5. Ie. it seems like larger patterns get rarer at a somewhat faster than exponential rate. Still lifes tell a similar story: e.g. the boat/longboat ratio (5 → 7) is about 1 : 15, the ship/longship ratio (6 → 8) about 1 : 182, the longboat/vlongboat ratio (7 → 9) about 1 : 460 (though with the longboat being the 2ndmost common 7-cell still life, this particular number may be overly drastic). For a first approximation, let's say the occurrence ratio of a random M-cell pattern versus a random N-cell pattern is M!/N!. If we additionally were to assume the loafer to be of equal width and speed to the standard *WSSs (ie. equally likely to escape), with 20 cells it would still end up at 20!/10! ≈ 6·10¹¹ times rarer than a HWSS (10 orders of magnitude behind switch engines as well). I do not wonder the least that one has not been seen yet in the wild.