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Is anyone studying the active part of soups?

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Is anyone studying the active part of soups?

Postby pcallahan » March 9th, 2019, 2:25 pm

I can't find an existing topic, at least scanning over anything recent. One thing that has piqued my curiosity off and on is what we can say about the part of the Life pattern that is acting like a "Wolfram class 3" CA locally before it settles down into oscillators and spaceships. I don't think we can say very much, but there might be some interesting statistical analyses looking at cell state as a time signal.

I once added a custom hack (since lost) to either Xlife or something I had written that could store and match "time signatures", which were 32-bit sequences of consecutive live/dead values of a given cell position. It is a quick and dirty way to find things like gliders, pulsars, stabilized shuttles, etc. False positives can happen, but generally with a specific enough sequence, you get what you're looking for. The nice thing about this is you don't have to worry about all the symmetries. A passing glider is going to assign cells a certain way (after the leading 1) no matter what direction it's coming from.

With longer sequences, you might be able to make a qualitative judgments. Clearly, if something is settled and periodic, it is recognizable, likewise if it is empty space with an occasional passing glider. Intuitively, some regions look hot or cold depending on activity level (and that can be captured in graphics). Actually, though, a p46 shuttle is much "colder" than it looks in the sense that all of the activity is repeated. The active part of a methuselah will produce many more distinct time signals over thousands of steps.

I see a lot of interest in soup experiments, mostly (I think), in the interest of classifying identifiable patterns. My question is whether anyone is trying to analyze something like the "thermodynamics" of the hot part of the soup. It's unclear where this will go except for a fairly arbitrary classification of regions of a pattern, but it is more a question of how to nail down an intuitive notion of "active part." I am also a little curious what these signals look like. I imagine they could be modeled (approximately) as a markov process with just a small amount of previous history.

ADDED: one thing we will find besides the statistics is recurring "motifs", with b-heptomino and pi-heptomino predominating I think. So another question is with all the interest in tracking the stable components, is anyone tracking the frequency of these short-lived but often useful sequences?
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Re: Is anyone studying the active part of soups?

Postby pcallahan » March 10th, 2019, 1:06 pm

I'm posting one new reply to myself just to make the topic show up as active (the problem, I think with just editing a post is the thread looks untouched). But should I assume the answer to the subject line is "no" or "not many" or "nobody here"?

The sort of specific question that could be answered is "How frequently does the b-heptomino show up in soups?" "How long (on average) does it evolve before crashing into something else?" I have never heard of that being answered, but it's possible I missed it. There might also be reactions that show up repeatedly but not often enough to have been noticed. We should see a time series in which the cell is empty for a while, then changes according to a pseudorandom sequence, but prefixes of this exact sequence show up much more often than predicted by chance. Is there anything new to be found here? I may investigate it but I'd like to avoid repeating work.
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Re: Is anyone studying the active part of soups?

Postby testitemqlstudop » March 10th, 2019, 1:23 pm

I was thinking of something along the lines, modify apgsearch so that it also catagolues constellations. I think it's possible, keeping track of Herschel/B-hept/R-pent/switch occurrences.
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Re: Is anyone studying the active part of soups?

Postby Rhombic » March 10th, 2019, 7:03 pm

I am not aware of any recent research in that line. It would surely be interesting especially if applied to an arbitrarily low starting density.
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Re: Is anyone studying the active part of soups?

Postby Rhombic » March 18th, 2019, 3:39 pm

Bump. Now I am. To some extent.
I am trying to draw some general parallels between evolution dynamics and partitioning of activity in soups, but it looks quite complicated. Currently analysing some large 3% density soups to understand what the initial steps in growth would be in an aperiodic, arbitrarily low-density infinite plane.
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Re: Is anyone studying the active part of soups?

Postby pcallahan » March 20th, 2019, 12:57 am

Rhombic wrote:Bump. Now I am. To some extent.

I'm interested in hearing what you find, though I think I have the higher density cases in mind. Here was an idea I had a really long time ago that didn't pan out (over 25 years ago), but I didn't understand Life well enough at the time (ADDED also, I lacked the CPU, sparse algorithm implementations, and disk space for output; I think I hacked XLife and then put it aside):

If you only know the last n values of a single cell, can you say anything interesting about the next value? The final cell value is a function of a 2n+1 x 2n+1 neighborhood around the cell, but not all these neighborhoods are equally likely in a typical soup, so that history may contain a lot of information about the surroundings. Let n=10. There are 1024 possible cell histories, but the ones that appear in a b-heptomino evolution occur at more than uniform probability, so you will probably predict with better than 50% success if you assume you are seeing a b-heptomino (of course you can extend this to surroundings and do even better, probably even with just one adjacent history, or three in a triangle and actually infer the orientation of the b-heptomino if it is one). (Or in a simpler case, if you have ten 0s in a row, you will mostly likely get another 0).

But let's assume some of those histories are not especially predictive. You still might do better than 50% if the next cell is just always more likely to be one state than another (clearly true in stable ash, but I don't know about the explosive part). So this immediately gives a way of clustering history strings. Given a particular series of n cell values, what is the probability that the next is 0 or 1. What does this distribution look like? I would guess it should be distributed around a fixed density value, with some spikes for special cases like a passing glider or part of the b-heptomino or pi heptomino. Maybe it has more than one mode. Maybe my intuition is just totally off here. Has anyone compiled such statistics? (And seriously, this is a lot easier than most of the things we're working on.)

ADDED: And what is this good for besides making histograms? Well (and this was probably my idea at the time), if you do identify time series that are unusually predictive, you can set alarms for them in a long-running soup, and possibly find reactions that are more common than usual and might come up in syntheses. I'm a little less optimistic now than I was at one time, but b and pi heptominoes will show up in a search like this (potentially with false positives). If there are any small active patterns we haven't classified, they may also show up.
Last edited by pcallahan on March 20th, 2019, 12:35 pm, edited 2 times in total.
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Re: Is anyone studying the active part of soups?

Postby Macbi » March 20th, 2019, 4:57 am

It sounds like you might be trying to calculate the correlation functions.
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Re: Is anyone studying the active part of soups?

Postby pcallahan » March 20th, 2019, 12:40 pm

Macbi wrote:It sounds like you might be trying to calculate the correlation functions.

Maybe. I would start with much simpler analysis though, really just counting frequencies in a histogram. Now that I think about this more, I had more ambitious ideas at the time of trying to correlate time series of neighboring cells.

You are probably correct that it falls in the broad category of statistical mechanics. Does anyone know some results on this? The active, non-periodic, unstructured part of patterns is the one we talk about the least, and are usually just very happy when it disappears and leaves something nice behind. What can we say about it?
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Re: Is anyone studying the active part of soups?

Postby NickGotts » June 8th, 2019, 11:44 am

Rhombic wrote:
Currently analysing some large 3% density soups to understand what the initial steps in growth would be in an aperiodic, arbitrarily low-density infinite plane.


I don't think looking at 3% soups will get you far in understanding the arbitrarily low-density infinite plane ("Sparse Life"), although I'm sure they'd be interesting in their own right. I've done quite a bit of work on Sparse Life, including some published papers, and am currently returning to it. The "Systematic Survey of Small Patterns" thread reports on one aspect of this. If you're interested, send me an email (you can find a list of my publications, and a contact page on my website, nickgotts.weebly.com).
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