0E0P constructions

For discussion of specific patterns or specific families of patterns, both newly-discovered and well-known.
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dvgrn
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0E0P constructions

Post by dvgrn » February 23rd, 2019, 1:08 pm

in the thread for basic questions, Macbi wrote:I thought it might be interesting to have a thread where we try to work out minimal SMOSes, RROs and quadratic replicators based on the 0E0P metacell. Of course we wouldn't be able to run them in Golly, but we could calculate their bounding box and population. It would be a fun synthesis of OCA and Life since we would have to think of other rules in which there were small such patterns.
I'd like to see some more testing done on the 0E0P metacell, too, just to make sure there are no subtle bugs in it that only show up in rules with specific isotropic bits set, or something like that.

For 0E0P constructions based on simulating some non-CGoL rule, there are some aggregration threads already out there:

SMOS thread (with some SMOSMOSes, too!)
RRO thread
a replicator thread (is there a better one for small replicators?)

A simple 0E0P-based replicator only needs one properly programmed cell, e.g.,

Code: Select all

x = 1, y = 1, rule = B123/S45678
o!
or something a little more replicator-looking like

Code: Select all

x = 1, y = 1, rule = B12/S345678
o!
But that won't actually be the simplest 0E0P-based replicator construction. As the discussion page for the 0E0P article mentions, the period p2^36 metacell can "only" be programmed to simulate 2^511 rules -- but it does it by using just a small subset of the possible ways to program an underlying p2^35 BCC metacell that actually supports 8^4095 different rules.

So... abandon the Moore-neighborhood emulation and just program the p2^35 metacell directly, and I think you can get a quadratic-growth replicator that's twice as fast. With eight states, it should be possible to make a one-cell RRO also, and maybe a two-cell SMOS (?).

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Re: 0E0P constructions

Post by Moosey » February 23rd, 2019, 3:01 pm

Can the 0E0P metacell run nonisotropic rules? Judging by your post, I'm assuming yes.
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Re: 0E0P constructions

Post by Macbi » February 23rd, 2019, 3:42 pm

First I'd like to work out what the available rules are. Calcyman has said that the cells have eight states, the neighbourhood is the four orthogonally (which is actually diagonally, with respect to the small grid) adjacent cells, and that the rulespace has 8^4095 rules. We know that vacuum has to go to vacuum, so that suggests there 4095 + 1 = 4096 possible neighbourhoods. But this is only 8^4, not 8^5. Does the future value of the cell not depend on its current value, but only on that of its neighbours? That would effectively mean we were looking at the anisotropic Margolus rules, right? I can't even quite see how that lets you simulate Life, but it should be enough for our current purposes.
dvgrn wrote:quadratic-growth replicator
One cell should definitely be enough. The simplest rule would be to just use one nonvacuum state and say that a cell becomes live if it's touching any live cell. But it would be interesting to try to minimise population. How is the rule lookup table stored?
dvgrn wrote:one-cell RRO
I can imagine a pattern which is a one metacell RRO in the following senses
  • It uses one metacell
  • It's a volatility 1 oscillator
  • Four copies of it can occupy the same space, offset by a quarter of a period, such that the overall period is one quarter of the original
but I would say that it's not an RRO since it's not rotating. Indeed no metacell pattern can be, since the metacell doesn't rotate its own orientation. Instead I think we need four metacells on four separate grids, like this:

Code: Select all

x = 132, y = 132, rule = LifeHistory
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dvgrn wrote:two-cell SMOS
Consider the following rule
  • A state-1 cell in a vacuum travels one cell east every generation
  • A state-2 cell in a vacuum travels one cell south every generation
  • If a vacuum has a state-1 cell to its west and a state-2 cell to its north then it becomes state-3
  • If a vacuum has a state-3 cell to its west it becomes state-2
  • If a vacuum has a state-3 cell to its north it becomes state-1
  • Every cell dies every generation
Then a state-3 cell is a one-cell SMOS (of course it's two cells in the generation in which it's made of spaceships).

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calcyman
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Re: 0E0P constructions

Post by calcyman » February 23rd, 2019, 4:18 pm

Macbi wrote:Does the future value of the cell not depend on its current value, but only on that of its neighbours?
A cell (x, y) can be live at time t only if x + y + t is even. Inter alia, this means that live cells always die immediately.

If you imagine time as a third axis, the cellular automaton can be viewed as running on either a face-centred cubic lattice (w.r.t the norm x^2 + y^2 + t^2) or a body-centred cubic lattice (w.r.t. the norm 2x^2 + 2y^2 + t^2). I recall that my original mental picture of this was with the latter norm, which is why these are referred to as BCC cellular automata.
I can't even quite see how that lets you simulate Life, but it should be enough for our current purposes.
If you take the square of the rule (i.e. consider the effect of two successive timesteps), the neighbourhood is now the Moore neighbourhood. It should be clear that we can emulate Life with a 17-state rule (using two states for the usual Life states, and another 15 intermediate mid-generation states -- one for each non-empty 2x2 square of cells).

This can be reduced to 8 states, using {0, 7} for the Life states and {0, 1, 2, 3, 4, 5, 6} for the intermediate mid-generation states. I wasn't sure either whether it would let you simulate Life, but an exhaustive search found a way to associate 7 colours with each of the 2x2 binary matrices such that all 512 3x3 matrices are uniquely determined by the 4-tuple of colours of the four (overlapping) 2x2 corners.
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Macbi
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Re: 0E0P constructions

Post by Macbi » February 24th, 2019, 2:21 am

calcyman wrote:
Macbi wrote:Does the future value of the cell not depend on its current value, but only on that of its neighbours?
A cell (x, y) can be live at time t only if x + y + t is even. Inter alia, this means that live cells always die immediately.
i see. You could view this as evolving on a square grid and its dual in alternate generations. The state of a cell is determined by the states of the four cells corresponding to its vertices in the previous generation. I thought these rules were called "Margolus", but according to Wikipedia that's actually something different.

EDIT: Luckily the SMOS rule I suggested above is already of this form!
calcyman wrote:This can be reduced to 8 states, using {0, 7} for the Life states and {0, 1, 2, 3, 4, 5, 6} for the intermediate mid-generation states. I wasn't sure either whether it would let you simulate Life, but an exhaustive search found a way to associate 7 colours with each of the 2x2 binary matrices such that all 512 3x3 matrices are uniquely determined by the 4-tuple of colours of the four (overlapping) 2x2 corners.
Beatiful!

So the Python script you provided for metafying a pattern in an isotropic rule could in theory be extended to the anisotropic (2-state, range-1 Moore neighbourhood) rules? So long as the vacuum is quiescent.

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calcyman
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Re: 0E0P constructions

Post by calcyman » February 24th, 2019, 7:51 am

Macbi wrote:So the Python script you provided for metafying a pattern in an isotropic rule could in theory be extended to the anisotropic (2-state, range-1 Moore neighbourhood) rules? So long as the vacuum is quiescent.
Yes, it could indeed. The reason I stayed with isotropic rules is that I don't need to carefully track orientations and ensure that the orientations of the individual metacells match the orientation of the metafied pattern.
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simsim314
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Re: 0E0P constructions

Post by simsim314 » February 24th, 2019, 12:10 pm

@calcyman Does the computer that calculates the rule there is turing complete? Not the metacell turing complete buy the rule table - it could be considered like an input to a tape of turing machine. And I've created a script that converts turing machine table into some stable pattern in CGOL. Maybe we can put my turing machine inside there, instead of the circuitry you have now? Or your circuitry is even better than mine and I said something embarrassing? We could basically place there the computer that made the calculation of pi. Anyway just a stupid question from the audience.

EDIT Do we have a competition for minimal turing complete computer in CGOL? Maybe we should. Someone created 8 bit computer, I've created turing machine, you've created pi calculator. There are different computational design there, maybe there is something which works simplest and fastest?

EDIT2 I know it's not the standard CA approach to use inside a cell Turing machine instead of a simple Hash table of rules. But if you think of complex systems, and you want to explore them, they more like some very complex function of their environment, not simple hash table. And this can be expressed in the metacell.

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Macbi
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Re: 0E0P constructions

Post by Macbi » March 1st, 2019, 6:24 am

I had a go at creating rules for two of these patterns. I tried to minimise the population that the corresponding metacells would have. In the metacell the rule is stored as a lookup table on a glider tape where each possible neighbourhood corresponds to a location on the tape and there are n gliders in that location if the metacell should go to state n. So we should try to use as few transitions as possible and try to prefer low numbered states.

Of course this is just scraping a few cells off a population of millions, but it's still satisfying.

Calcyman, do you know approximately at which point a metacell would achieve its minimum population? Presumably the population is always changing slightly as the tape runs through its snark loop. Would it be practical to run a metacell over the possible time interval in which the minimum population might be achieved in order to calculate its exact minimum population? (On the other hand we could say that we only care about bounding box rather than population, since the reverse caber-tosser gives us quadratic replicators, RROs and SMOSes with population 143. What's the minimal bounding box of the metacell? Does it depend on the rule?)

Quadratic replicator

Code: Select all

x = 1, y = 1, rule = MAPACAAAIAAAAAAAAAAAAAAAIAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
o!
I think this (or one of its rotations) is the minimum population quadratic replicator. The rule says that you become live if you have a cell to your north only, a cell to your west only, or cells to your south and east only. It only uses one state and three transitions. You need at least three transitions to produce quadratic growth, and this is the only choice of three transitions that does so (the other possibility is the rule where a cell becomes live if it has one cell to its west, north or east, but this rule sierpinskis in such a way that its population returns infinitely often to three cells, meaning I'm not sure if it counts as a quadratic replicator).

SMOS

Code: Select all

@RULE metacell-SMOS0

@TABLE
n_states:4
neighborhood:vonNeumann
symmetries:none

var a={0,1,2,3}
var b={0,1,2,3}
var c={0,1,2,3}
var d={0,1,2,3}
var e={0,1,2,3}
var f={1,2,3}

f,a,b,c,d,0
0,2,0,0,1,3
0,3,0,0,0,1
0,0,0,0,3,2
0,2,0,0,0,2
0,0,0,0,1,1
a,b,c,d,e,0

Code: Select all

x = 5, y = 5, rule = metacell-SMOS0
4.B4$A!
This is a one-cell SMOS using only five transitions. I suspect this is minimal but I can't prove it. I'm also not quite sure if this is the minimum-population way to number the states in this rule. I have the one-cell state being state 3 and the two ships being states 1 and 2, which only puts 9 gliders on the rule tape. But the metacell must store its own state somewhere. Depending on how efficient this storage is it might be better to have the one-cell state be state 1 and the other two states be 2 and 3, even though this would put 11 gliders on the tape.

RRO
This seems really tricky, I'm stumped. I can't even write down a super inefficient one using one of 2718281828's isotropic RROs, because I can't get four (or even two) of those to orbit together in the way I described above.

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Re: 0E0P constructions

Post by Hunting » March 1st, 2019, 7:58 am

Hey, I have problem understanding these. Why can't we just use this as a quadratic replicator?

Code: Select all

x = 0, y = 0, rule = B1c/S
o!
Is the point that 0E0P uses a strange rule-representing system so the strange looking MAP rule will use less populations than B1c/S?
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LeapLife - DirtyLife - LispLife

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Macbi
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Re: 0E0P constructions

Post by Macbi » March 1st, 2019, 8:37 am

Hunting wrote:Is the point that 0E0P uses a strange rule-representing system so the strange looking MAP rule will use less populations than B1c/S?
Yes exactly. Only by about 5 cells in 20000000 though!

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Re: 0E0P constructions

Post by dvgrn » March 1st, 2019, 8:51 am

Macbi wrote:
Hunting wrote:Is the point that 0E0P uses a strange rule-representing system so the strange looking MAP rule will use less populations than B1c/S?
Yes exactly. Only by about 5 cells in 20000000 though!
More specifically, B1c/S is really four transitions from a MAP-rule point of view, one for each intercardinal direction. The 0E0P metacell needs a glider for each transition. Macbi's rule only needs three transitions, so one less glider in the rule-table part of the glider stream.

Also the B1c/S replicator keeps returning to a four-cell population, which is slightly annoying if you want your replicator to, you know, take over the universe. It still counts as a replicator by most people's definitions, but it's a lousy model of a replicator -- we wouldn't want to send a real-life von Neumann machine version of it into space to turn the Moon's surface into solar panels. Macbi's version isn't all _that_ much better -- the old machines stop working too soon -- but at least the population keeps growing nicely.
Macbi wrote:Presumably the population is always changing slightly as the tape runs through its snark loop. Would it be practical to run a metacell over the possible time interval in which the minimum population might be achieved in order to calculate its exact minimum population?
It's strangely time-consuming to collect a definite minimum population even for Gemini variants, which is presumably why nobody has done it for Gemini 2 yet. For the 0E0P it seems like it would take something like a CPU-month to get a definite number, and then the number is slightly different for different rules of course.

I was thinking that at least the task is massively parallelizable, but I guess that's only for rules where a programmed 0E0P has already been run and has saved checkpoints available to start from.
Macbi wrote:(On the other hand we could say that we only care about bounding box rather than population, since the reverse caber-tosser gives us quadratic replicators, RROs and SMOSes with population 143. What's the minimal bounding box of the metacell? Does it depend on the rule?)
The bounding box seems to stay fairly stable at 261841x261841 -- it only starts getting smaller when it's self-destructing.

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Macbi
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Re: 0E0P constructions

Post by Macbi » March 1st, 2019, 9:56 am

dvgrn wrote:
Macbi wrote:Presumably the population is always changing slightly as the tape runs through its snark loop. Would it be practical to run a metacell over the possible time interval in which the minimum population might be achieved in order to calculate its exact minimum population?
It's strangely time-consuming to collect a definite minimum population even for Gemini variants, which is presumably why nobody has done it for Gemini 2 yet. For the 0E0P it seems like it would take something like a CPU-month to get a definite number, and then the number is slightly different for different rules of course.
I was hoping that Calyman might be able to narrow down the search range considerably. There much be some point at which the metacell begins to construct things whose population is larger than any possible dip in population that occurs as the gliders run through the snark loop. So we might only have to run through some tiny initial portion of the metacell's period (although of course that will be very slow since we're going one generation at a time).

It just occured to me that the minimum population metacell might not be the one with the least transitions. It could be that there's a rule with more transitions but for which the gliders happen to be timed just right so that a lower population is reached as they travel through snarks. The population of a snark decreases by two at some points as a glider travels through it. So it would be worthwhile to add one transition to the rule if it allowed us to arrange timings such that three gliders travelled through snarks simultaneously. Sadly this means that we might not ever know for sure whether we have found the smallest 0E0P-based quadratic replicator, SMOS and RRO.

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Re: 0E0P constructions

Post by dvgrn » March 1st, 2019, 3:07 pm

Macbi wrote:It just occured to me that the minimum population metacell might not be the one with the least transitions. It could be that there's a rule with more transitions but for which the gliders happen to be timed just right so that a lower population is reached as they travel through snarks... Sadly this means that we might not ever know for sure whether we have found the smallest 0E0P-based quadratic replicator, SMOS and RRO.
It may be a bit worse than that. I haven't tried to track exactly how incoming gliders from neighbors (encoding the state in unary) interact with the glider stream that encodes the rule. But a large part of the 0E0P metacell is made out of single-use circuitry, including a lot of the switching system:
calcyman wrote:The same tape is essentially executed 8 times:

1. Construct SE
2. Copy tape to SE

3. Construct NE
4. Copy tape to NE

5. Construct NW
6. Copy tape to NW

7. Construct SW
8. Copy tape to SW

To move to constructing the next neighbour, an internal Snark is destroyed
to cause the glider stream to be re-routed. The transition between building
a neighbour and copying the tape is invisible to the parent.

The children are only launched later in the life-cycle, when the parent
broadcasts its state (a number n between 1 and 7, encoded in unary as
n+1 gliders). The '+1' is tapped off to tell the child to commence; the
other n gliders are stored in the one-time memory units for indexing the
rule table.
I don't know if the one-time memory units have a lower population after they store the incoming bits, but I kind of expect they do -- "one-time" probably means a lot of boat turners got burned up getting the signals to their storage location.

I think that means that means it's possible for higher state numbers to result in a lower population at some point in the cycle... but again I'm not absolutely sure.

The following isn't entirely relevant, because it's the self-destruct system rather than the switching system. But there's a lot of similarity -- and in particular any one-time circuits that may or may not get used, have to be able to self-destruct reliably no matter what state they're left in. There would be a lot of cleverness to marvel at in the 0E0P metacell, if only someone would label all the pieces clearly enough that all the cleverness can even be understood --!

Anyway, here's a tiny sample piece of the metacell -- center of the NW edge -- with a self-destruct glider added. If you wait long enough, all that's left is an output glider:

Code: Select all

x = 3296, y = 2980, rule = B3/S23
2465bo$2464bobo$2464b2o5$2519bo$2518bobo$2519b2o294$2013b2o$2004b2o7b
2o$2005bo$2005bobo$1999bo6b2o$1999b3o81bo$2002bo79bobo$2001b2o79b2o3$
2002b2o$2002b2o$2019b2o$2019bobo$1996b2o23bo$1995bobo23b2o$1996bo4$
2030bo$2029bobo$2015b2o12bo2bo$2015bo9b2o3b2o$2016b3o5bo2bo$2018bo5bob
o$2025bo3$1999b2o$1998bobo$1998bo$1997b2o2$2029bo$2028bobo$2028b2o3$
2007b2o$2007b2o7b2o$2016bo$2014bobo36bo$2014b2o36bobo$2053b2o$2022bo$
1996b2o23bobo$1988b2o7bo24b2o$1988b2o7bobo$1998b2o154b2o$2154b2o2$
1983bo28b2o$1982bobo27bobo$1982bobo7bo21bo28b2o$1983bo7bobo20b2o7bo20b
o125b2o$1991b2o29bobo16b3o105b2o19b2o$2022bobo16bo107b2o$2023bo110b2o$
2134b2o3$2009b2o$2009bo$2010b3o$2012bo4$1977b2o14b2o$1977b2o13bobo$
1992bo$1991b2o2$2128b2o$2128b2o$1983b2o$1975bo7b2o$1974bobo$1973bo2bo
24b2o132b2o$1974b2o25b2o7b2o123b2o$2010bo$1980b2o26bobo$1979bobo26b2o$
1975bo4bo38b2o$1974bobo41bo2bo$1974bo2bo16b2o22bobo$1975b2o16bobo23bo$
1993bo$1992b2o4$1971bo$1969b3o$1968bo$1968b2o$1953b2o$1954bo202bo$
1954bob2o198bobo$1955bo2bo197b2o$1956b2o$1971b2o13b2o$1971b2o13b2o3$
2017b2o$2017bo$2010b2o6b3o28b2o$2010b2o8bo28b2o168b2o$1974b2obo6b2o
233bobo$1974b2ob3o3bobo234bo$1980bo2bo$1974b2ob3o2b2o26b2o$1975bobo32b
2o$1963b2o10bobo18b2o$1963b2o11bo18bobo$1995bo$1994b2o8b2o$2004bo$
2005b3o$2007bo2$2110b2o$1969bo73b2o65b2o$1968bobo72b2o$1967bo2bo$1968b
2o$2013b2o$2004b2o7b2o35b2o$2005bo44b2o$2005bobo$1999bo6b2o$1999b3o$
2002bo$2001b2o3$2002b2o$2002b2o100b2o$2019b2o83b2o$2019bobo$1996b2o23b
o$1995bobo23b2o$1996bo114b2o$2111b2o3$2030bo$2029bobo$2015b2o12bo2bo$
2015bo9b2o3b2o$2016b3o5bo2bo$2018bo5bobo$2025bo3$1999b2o$1998bobo$
1998bo$1997b2o2$2029bo$2028bobo$2028b2o3$2007b2o$2007b2o7b2o$2016bo$
2014bobo$2014b2o2$2022bo$1996b2o23bobo$1988b2o7bo24b2o$1988b2o7bobo$
1998b2o261bo$2260bobo$2261b2o$1983bo28b2o$1982bobo27bobo$1982bobo7bo
21bo$1983bo7bobo20b2o7bo$1991b2o29bobo$2022bobo$2023bo4$2009b2o$2009bo
$2010b3o$2012bo3$2131b2o$1977b2o14b2o136b2o$1977b2o13bobo$1992bo$1991b
2o4$1983b2o$1975bo7b2o$1974bobo$1973bo2bo24b2o$1974b2o25b2o7b2o273bo$
2010bo273bobo$1980b2o26bobo273b2o$1979bobo26b2o$1975bo4bo38b2o116b2o$
1974bobo41bo2bo115b2o$1974bo2bo16b2o22bobo$1975b2o16bobo23bo$1993bo$
1992b2o136b2o$2130b2o3$1971bo$1969b3o$1968bo$1968b2o$1953b2o$1954bo
1249bo$1954bob2o1245bobo$1955bo2bo1244b2o$1956b2o$1971b2o13b2o$1971b2o
13b2o3$2017b2o$2017bo$2010b2o6b3o$2010b2o8bo$1974b2obo6b2o$1974b2ob3o
3bobo$1980bo2bo$1974b2ob3o2b2o26b2o$1975bobo32b2o$1963b2o10bobo18b2o$
1963b2o11bo18bobo$1995bo$1994b2o8b2o$2004bo$2005b3o$2007bo3$1969bo$
1968bobo$1967bo2bo$1968b2o$2013b2o$2004b2o7b2o$2005bo$2005bobo$1999bo
6b2o65b2o$1999b3o71b2o1091bo$2002bo1161b3o$2001b2o1160bo$3163b2o2$
2002b2o$2002b2o1167b2o$2019b2o1151bo$2019bobo1150bob2o$1996b2o23bo
1142b2o4b3o2bo$1995bobo23b2o1141b2o3bo3b2o$1996bo1172b4o$3155b2o15bo$
3154bobo12b3o$3154bo13bo$2030bo36b2o1084b2o14b5o$2029bobo35b2o1104bo
87b2o$2015b2o12bo2bo1138bo89bobo$2015bo9b2o3b2o1139b2o89bo$2016b3o5bo
2bo$2018bo5bobo47b2o$2025bo48b2o3$1999b2o$1998bobo$1998bo$1997b2o2$
2029bo$2028bobo$2028b2o3$2007b2o$2007b2o7b2o$2016bo$2014bobo$2014b2o2$
2022bo$1996b2o23bobo$1988b2o7bo24b2o$1988b2o7bobo$1998b2o3$1983bo28b2o
$1982bobo27bobo$1982bobo7bo21bo$1983bo7bobo20b2o7bo1177b2o$1991b2o29bo
bo1176b2o$2022bobo$2023bo2$2123b2o1083b2o$2123b2o1083b2o$2009b2o$2009b
o$2010b3o$2012bo4$1977b2o14b2o$1977b2o13bobo$1992bo$1991b2o4$1983b2o
144b2o1071b2o$1975bo7b2o144b2o1071b2o$1974bobo$1973bo2bo24b2o$1974b2o
25b2o7b2o$2010bo111b2o$1980b2o26bobo111b2o1084b2o$1979bobo26b2o1197bob
o$1975bo4bo38b2o1187bo$1974bobo41bo2bo$1974bo2bo16b2o22bobo$1975b2o16b
obo23bo$1993bo$1992b2o4$1971bo$1969b3o$1968bo$1968b2o$1953b2o$1954bo$
1954bob2o$1955bo2bo$1956b2o$1971b2o13b2o$1971b2o13b2o3$2017b2o1148b2o$
2017bo1148bobo$2010b2o6b3o1146bo$2010b2o8bo$1974b2obo6b2o$1974b2ob3o3b
obo$1980bo2bo$1974b2ob3o2b2o26b2o$1975bobo32b2o$1963b2o10bobo18b2o$
1963b2o11bo18bobo$1995bo$1994b2o8b2o$2004bo$2005b3o$2007bo3$1969bo95b
2o$1968bobo94b2o$1967bo2bo$1968b2o$2013b2o$2004b2o7b2o$2005bo$2005bobo
$1999bo6b2o$1999b3o$2002bo$2001b2o3$2002b2o$2002b2o$2019b2o38b2o$2019b
obo37b2o$1996b2o23bo$1995bobo23b2o$1996bo$2066b2o$2066b2o2$2030bo$
2029bobo$2015b2o12bo2bo$2015bo9b2o3b2o$2016b3o5bo2bo$2018bo5bobo$2025b
o3$1999b2o$1998bobo$1998bo$1997b2o2$2029bo$2028bobo$2028b2o3$2007b2o$
2007b2o7b2o$2016bo$2014bobo77bo$2014b2o77bobo$2093b2o$2022bo$1996b2o
23bobo$1988b2o7bo24b2o$1988b2o7bobo$1998b2o3$1983bo28b2o$1982bobo27bob
o$1982bobo7bo21bo$1983bo7bobo20b2o7bo$1991b2o29bobo$2022bobo$2023bo4$
2009b2o$2009bo$2010b3o$2012bo4$1977b2o14b2o$1977b2o13bobo$1992bo$1991b
2o4$1983b2o$1975bo7b2o$1974bobo$1973bo2bo24b2o$1974b2o25b2o7b2o$2010bo
$1980b2o26bobo$1979bobo26b2o$1975bo4bo38b2o$1974bobo41bo2bo$1974bo2bo
16b2o22bobo$1975b2o16bobo23bo$1993bo$1992b2o4$1971bo$1969b3o$1968bo$
1968b2o$1953b2o$1954bo75b2o$1954bob2o72bobo$1955bo2bo72bo$1956b2o$
1971b2o13b2o$1971b2o13b2o520bo$2507bobo$2507b2o$2017b2o$2017bo$2010b2o
6b3o$2010b2o8bo$1974b2obo6b2o478bo$1974b2ob3o3bobo477bobo$1980bo2bo
479b2o$1974b2ob3o2b2o26b2o$1975bobo32b2o$1963b2o10bobo18b2o$1963b2o11b
o18bobo$1995bo$1994b2o8b2o$2004bo$2005b3o$2007bo3$1969bo$1968bobo$
1967bo2bo$1968b2o6$3292bo$3291bobo$3292b2o3$3294b2o$3293bobo$3292bobo$
3293bo289$2345b2o$2345bobo$2346bobo$2347bo28$2186b2o$2187bo$2185bo$
2185b5o14b2o$2190bo13bo$2187b3o12bobo$2186bo15b2o$2186b4o$2184b2o3bo3b
2o$2183bo2b3o4b2o$2183b2obo$2186bo118b2o4b2o$2186b2o117bobo3bobo$2306b
obo3bobo$2307bo5bo$2194b2o$2195bo$2192b3o$2192bo22$2332b2o$2332b2o$
2061bo$2060bobo$2061b2o$2336b2o$2336b2o8$2153bo$2152bobo$2152b2o3$
2146b2o$2146bobo$2147bo3$2266b2o$2266bo$2268bo$2248b2o14b5o$2249bo13bo
$2131bo117bobo12b3o$2130bobo117b2o15bo$2129bo2bo131b4o$2129bobo127b2o
3bo3b2o$2130bo128b2o4b3o2bo$2267bob2o$2127b2o138bo$2127bobo136b2o$
2128b2o2$2258b2o$2258bo$2259b3o$2261bo55$2239bo$2238bobo$2239b2o3$
2241b2o$2240bobo$2239bobo$2240bo24$2209b2o$2209b2o15$2215b2o$2215b2o4$
2208b2o$2208b2o$2010b2o$2010bo$2012bo$1992b2o14b5o$1993bo13bo$1993bobo
12b3o$1994b2o15bo$2008b4o$2003b2o3bo3b2o$2003b2o4b3o2bo$2011bob2o$
2011bo$2010b2o3$2002b2o$2002bo$2003b3o$2005bo41$1857bo$1856bobo191bo$
1856b2o191bobo$2050b2o3$2056b2o$2055bobo$2056bo6$1868b2o$1868b2o19b2o$
1889b2o181bo$2037b2o32bobo$2037b2o32bo2bo$2072bobo$2073bo$1873b2o$
1873b2o158b2o40b2o$2033b2o39bobo$2074b2o4$1849bo$1848bobo$1849b2o10$
1916bo$1915bobo$1915b2o6$2066b2o$2066bobo$2062b2o3bobo$2061bobo4bo$
2062bo6$1874b2o$1874bobo$1804bo71bo4b2o$1803bobo66b4ob2o2bo2bo$1804b2o
66bo2bobobobob2o$1875bobobobo$1876b2obobo$1880bo2$1866b2o$1819b2o46bo
7b2o$1818bobo46bobo5b2o198bo$1819bo48b2o204bobo4bo$2075b2o3bobo$2079bo
bo$2079b2o4$1878b2o$1878bo$1879b3o$1881bo13$1918bo$1916b3o$1915bo$
1915b2o3$1923b2o$1924bo$1924bob2o$1916b2o4b3o2bo$1916b2o3bo3b2o$1921b
4o$1907b2o15bo$1906bobo12b3o$1906bo13bo$1905b2o14b5o$1925bo$1923bo$
1923b2o50$1964bo5bo$1963bobo3bobo$1962bobo3bobo$1962b2o4b2o49$2014bo$
2013bobo$2012bobo$2012b2o130$1660bo$1660b3o$1663bo$1662b2o3$1654b2o$
1654bo$1651b2obo$1651bo2b3o4b2o$1652b2o3bo3b2o$1654b4o$1654bo15b2o$
1655b3o12bobo$1658bo13bo$1653b5o14b2o$1653bo$1655bo$1654b2o12$1692bo$
1690b3o$1689bo$1689b2o7$1679b2o$1678bobo5b2o$1678bo7b2o$1677b2o2$1691b
o$1687b2obobo$1686bobobobo$1683bo2bobobobob2o$1683b4ob2o2bo2bo$1687bo
4b2o$1685bobo$1685b2o50$1552b2o$1552b2o3$1547b2o$1547b2o9$1545bo$1544b
obo$1544bo2bo$1545b2o7$1540b2o$1540bobo$1541bo4$1544bo5bo$1543bobo3bob
o$1544bobo3bobo$1545b2o4b2o3$1590b2o$1590bobo$1517bo68b2o3bobo$1516bob
o66bobo4bo$1517b2o67bo15$1639bo$1638bobo$1637bobo$1637b2o3$1639b2o$
1639bobo$1556bo83bo$1555bobo$1555b2o4$1551bo$1550bobo$1551b2o$1510bo$
1509bobo$1510bobo$1511b2o4$1620b2o$1620bobo$1621bo4$1540b2o$1539bo2bo$
1538bo2bo$1534b2o3b2o$1534bobo$1535b2o$1640bo$1638b3o$1637bo$1627b2o8b
2o$1628bo$1596b2o11bo18bobo$1596b2o10bobo18b2o$1608bobo32b2o$1607b2ob
3o2b2o26b2o$1613bo2bo$1607b2ob3o3bobo$1607b2obo6b2o$1643b2o$1643b2o5$
1604b2o13b2o$1604b2o13b2o$1589b2o$1588bo2bo$1587bob2o$1587bo$1586b2o$
1601b2o$1601bo$1602b3o$1604bo4$1596b2o7b2o18b2o$1595bo2bo5bo2bo18bo$
1595bobo7bobo18bobo$1596bo9bo20b2o$1618bo$1617bobo$1617bobo21b2o$1598b
o19bo22bobo$1597bobo43bo$1597bo2bo33b2o7b2o$1598b2o34b2o3$1651b2o$
1642b2o6bo2bo$1642b2o7bobo$1652bo$1624b2o$1625bo104bo$1534b2o89bobo
101bobo$1488bo34b2o8bo2bo70bo18b2o101b2o$1487bobo32bobo9bobo69bobo$
1488b2o33bo11bo70bo2bo$1515bo91b2o$1513b3o129bo$1512bo130b3o5b2o$1512b
2o128bo7bobo$1524b2o116b2o7bo$1524bo15bo27b2o3b2o$1522bobo9b2o4b3o25b
2o3b2o$1522b2o10b2o7bo$1500b2o40b2o$1500b2o78b2o$1580bo$1578bobo41bo
25b2o$1578b2o41bobo24bo$1622b2o22bobo$1539b2o105b2o$1503b2o34b2o88b2o$
1504bo124b2o$1501b3o$1501bo$1510b2o63b2o51b2o$1506b2o2b2o63bo53bo$
1505bobo38b2o28b3o47b3o$1505bo23b2o15bo31bo47bo6b2o$1504b2o23bo17b3o
82bobo$1530b3o16bo82bo$1532bo98b2o7b2o5b2o$1513b2o125b2o5bobo$1513bobo
133bo$1514bo134b2o$1562b2o$1543b2o17b2o$1542bo2bo24b2o$1543b2o25bo$
1571b3o$1573bo2$1572bo$1571bobo$1571bobo$1570b2ob3o$1527bo48bo$1526bob
o41b2ob3o$1526bo2bo17b2o21b2obo$1527b2o17bo2bo$1547bobo12b2o$1548bo4b
2o7b2o$1554bo$1554bobo110bo$1555b2o109bobo4bo$1540bo126b2o3bobo$1539bo
bo129bobo$1539bo2bo5bo122b2o$1540b2o5bobo25b2o$1546bo2bo25b2o$1547b2o
4$1560bo$1559bobo$1559bobo$1560bo$1557b3o$1557bo9$1643bo$1642bobo$
1643b2o59b2o$1704bobo$1705bo28$1682b2o$1681bobo$1682bo521$42bo$41bobo$
41b2o46$bo$obo$b2o7$97b2o$97b2o15$91b2o$91b2o4$98b2o$98b2o149$251bo$
250bobo$250b2o15$210b2o$210bobo$212bo4b2o$208b4ob2o2bo2bo$208bo2bobobo
bob2o$211bobobobo$212b2obobo$216bo2$202b2o$203bo7b2o$203bobo5b2o$204b
2o7$214b2o$214bo$215b3o$217bo90$1137b3o$1139bo$1138bo!
#C [[ STEP 50 ]]
The south corner is where a lot of the action happens. That's where the semi-Snark chain gun is, that gets turned on when the child metacells "go live". Once it counts out a large enough number of ticks, the population starts dropping steadily, as boats and other objects are burned up to send one-time signals to wherever they need to go. And certainly the "internal Snarks" mentioned above disappear and reduce the population at regular intervals.

TL;DR: Let's just work out the minimum population of a metacell programmed with S0, and call it good enough.

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Macbi
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Re: 0E0P constructions

Post by Macbi » March 1st, 2019, 3:59 pm

dvgrn wrote:TL;DR: Let's just work out the minimum population of a metacell programmed with S0, and call it good enough.
I agree that would be a great first step. Unfortunately that's not actually a rule we can simulate. (For some reason I find this really funny. Like, even after we resort to the most trivial thing there is, it's still impossible.) I suggest we pick one of the intercardinal directions and look at one period of the ship that travels that way. I think SW will be the best, since the one-time circuitry used for the other three directions will have already been destroyed.

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dvgrn
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Re: 0E0P constructions

Post by dvgrn » March 1st, 2019, 4:13 pm

Macbi wrote:
dvgrn wrote:TL;DR: Let's just work out the minimum population of a metacell programmed with S0, and call it good enough.
I agree that would be a great first step. Unfortunately that's not actually a rule we can simulate.
Why not? B0 is certainly impossible, but there shouldn't be anything wrong with a 0E0P metacell that just sits there and survives, but never causes any new births.

-- Except the twelve temporary stage-1 and stage-2 descendants, where the last eight stage-2 ones are in the cell's eight neighboring locations, but they all self-destruct just before the next metatick begins. (Here's hoping I have that right now.)

EDIT: Pretty close, I think. The center metacell self-destructs after it builds its four stage-1 children; it's rebuilt pretty much immediately by one of those children, along with eight other neighbor metacells. The four children self-destruct. Almost immediately after that, the eight neighbor metacells figure out that they're supposed to be state 0 for the next metatick, so they self-destruct also. The whole cycle for B/S0 should look exactly like calcyman's video -- that test metacell was actually running B2-an3-eiky4aiqw5ijnr6ak/S012ik3-acir4kqw5acq6ack7c8, but the only one of those MAP bits that mattered was the S0 one. (!)
Macbi wrote: I think SW will be the best, since the one-time circuitry used for the other three directions will have already been destroyed.
Let's see, though... by the time that one-time circuitry has been destroyed, the stage-1 child metacells will already have been built in those three directions, which means we're definitely out of the possible minimum-population zone -- right?

So really the only possible time slice where there might be a minimum population is the early stages of each metatick, starting just after all the surrounding metacells have self-destructed and ending when the metacell starts extending a construction arm to build its first child copy.

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Re: 0E0P constructions

Post by Macbi » March 1st, 2019, 5:56 pm

Quoting your second section first:
dvgrn wrote:Let's see, though... by the time that one-time circuitry has been destroyed, the stage-1 child metacells will already have been built in those three directions, which means we're definitely out of the possible minimum-population zone -- right?
Ah! I hadn't quite realised how that aspect of the metacell worked yet. I thought the four cells surrounding an empty space discussed what state should go in that space, and then if the state was nonzero then one of them would build the metacell in that space. But after reading your comment and rereading the description on calcyman's blog I see that what actually happens is that each cell builds all four neighbours every time, and then the new cells look at what their neighbours are and commit suicide if they need to be in state 0.
So really the only possible time slice where there might be a minimum population is the early stages of each metatick, starting just after all the surrounding metacells have self-destructed and ending when the metacell starts extending a construction arm to build its first child copy.
Right, I see that now.
dvgrn wrote:
Macbi wrote:I agree that would be a great first step. Unfortunately that's not actually a rule we can simulate.
Why not? B0 is certainly impossible, but there shouldn't be anything wrong with a 0E0P metacell that just sits there and survives, but never causes any new births.

-- Except the twelve temporary stage-1 and stage-2 descendants, where the last eight stage-2 ones are in the cell's eight neighboring locations, but they all self-destruct just before the next metatick begins. (Here's hoping I have that right now.)
I suppose it depends on whether you think of the metacell running at p2^36 or p2^35. I was thinking in p2^35 terms, in which case every metacell dies every metageneration and so S0 is impossible. I think the simplest p2^35 pattern would be one of the ones I described, where a state-1 cell just moves itself one metacell in a fixed direction every 2^35 generations.

At p2^36 it is of course possible to simulate S0. But there are many rules of the p2^35 metacell that could be chosen to simulate S0 at p2^26. I think the simplest would be the one where every state-1 cell creates a state-2 cell to its SE and then every state-2 cell creates a state-1 cell to its NW. (As above the cell really creates all four of its neighbours and three commit suicide, and then the new cell creates all four of its neighbours and again three of them suicide.)

If instead we were to use calcyman's script to simulate S0, we would find that our live cells were being represented by state 7. Each state-7 cell creates around it cells in states 1, 2, 4 and 6. Then the nine cells around these ones are constructed, the outer ones in state 0 and the inner one in state 7. Then the state-0 cells suicide leaving us with the state-7 cell again.

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Re: 0E0P constructions

Post by dvgrn » March 1st, 2019, 7:12 pm

Macbi wrote:I suppose it depends on whether you think of the metacell running at p2^36 or p2^35.
Ah, got it. Of course I should have been thinking in p2^35 terms, not p2^36 terms.

So I guess one remaining question is what cell state corresponds to the lowest population. Maybe it's time to start obsessively labeling pieces of 0E0P metacell machinery until the one-time memory cells show up. There are a bunch of islands of still lifes constructed by the huge single-channel 0E0P recipe:

Code: Select all

x = 641, y = 642, rule = B3/S23
318b3o$318b4o$317b5o$317b6o$317b6o$317b6o$318b3o150$473b3o$473b3o$161b
2o310b3o$161b2o310b3o$160b5o310b3o$160b5o310b7o$158b7o311b6o$158b4o
315b5o$158b4o315b5o$155b2ob3o317b3o$155b3o$155b3o56$255b5o$255b5o$255b
5o$256b4o10$242b4o$241b5o$240b7o$240b7o$238b10o$237b13o$236b6o3b6o$
235b6o5b6o$235b6o5b6o$233b7o7b6o$232b6o10b7o$231b6o13b6o$230b6o15b6o$
230b6o15b6o$228b7o17b6o$227b6o20b7o$226b6o23b6o$225b6o25b6o$225b6o25b
6o$223b7o27b6o$222b6o30b7o$221b6o33b6o$220b6o35b6o$220b6o35b6o$218b7o
37b6o$217b6o40b7o$216b6o43b6o$215b6o45b6o$215b6o45b6o$213b7o47b6o$212b
6o50b7o$211b6o53b6o$210b6o55b6o$210b6o55b6o$208b7o57b6o$207b8o58b7o$
206b9o60b6o$205b6o4b3o58b6o$205b6o4b3o58b6o$203b7o5b5o57b6o$202b6o8b4o
58b7o$201b6o9b5o59b6o$200b6o11b6o58b6o$200b6o11b6o58b6o$198b7o15b3o59b
6o$197b9o15b5o57b7o$196b11o15b5o58b6o$195b13o15b4o59b6o$195b13o15b4o
59b6o$193b17o15b2o60b6o$192b19o16b4o57b7o$191b21o15b4o59b6o$190b23o15b
5o58b6o$190b23o15b5o58b6o$188b27o13b8o56b6o$187b29o15b6o56b7o$186b31o
15b5o58b6o$185b33o14b5o59b6o$185b33o14b5o59b6o$183b37o77b6o$182b39o77b
7o$181b41o16b4o58b6o$180b43o15b4o59b6o$180b43o15b4o59b6o$178b47o16b4o
57b6o$177b49o15b5o57b7o$176b51o14b6o58b6o$175b53o14b6o58b6o$175b53o14b
6o58b6o$173b57o13b7o57b6o$172b59o14b5o58b7o$171b61o14b6o58b6o$170b63o
15b4o59b6o$170b63o15b4o59b6o$168b67o16b2o59b6o$167b69o15b4o58b7o$166b
71o15b3o60b6o$165b73o78b6o$165b73o78b6o$163b77o15b3o59b6o$162b79o14b3o
60b7o$2b3o156b81o13b5o60b6o$5o155b83o14b6o58b6o308b5o$5o155b83o14b6o
58b6o308b5o$6o152b87o12b8o57b6o305b8o$6o151b89o12b8o57b7o303b8o$5o151b
91o13b6o59b6o304b5o$155b93o13b6o59b6o303b3o$155b93o13b6o59b6o303b3o$
153b97o12b5o60b6o$152b99o14b6o57b7o$151b101o13b6o59b6o$150b103o13b6o
59b6o$150b103o13b6o59b6o$148b107o13b4o60b6o$147b109o12b8o57b7o$146b
111o13b6o59b6o$145b113o13b5o60b6o$145b113o13b5o60b6o$143b117o12b5o60b
6o$142b119o12b8o57b7o$141b121o13b6o59b6o$140b123o13b5o60b6o$140b123o
13b5o60b6o$138b127o12b6o59b6o$137b129o12b7o58b7o$136b131o13b5o60b6o$
135b133o13b5o60b6o$135b133o13b5o60b6o$133b137o13b4o60b6o$132b139o12b5o
60b7o$131b141o13b5o60b6o$130b143o14b4o60b6o$130b143o14b4o60b6o$128b
147o12b5o60b6o$127b149o12b5o60b7o$126b151o14b4o60b6o$125b153o13b7o58b
6o$125b153o13b7o58b6o$123b157o13b5o59b6o$122b159o14b5o58b7o$121b161o
14b6o58b6o$120b163o13b7o58b6o$120b163o13b7o58b6o$118b167o12b6o59b6o$
117b169o14b5o58b7o$116b171o13b6o59b6o$115b173o13b6o59b6o$115b173o13b6o
59b6o$113b177o13b4o60b6o$112b179o12b8o57b7o$111b181o13b6o59b5o$110b
183o13b7o58b6o$110b183o13b7o58b6o$108b187o12b6o59b6o$107b189o12b5o60b
7o$106b191o14b4o60b6o44b3o$105b193o13b6o59b6o43b3o$105b193o13b6o59b6o
43b3o$103b197o12b5o60b6o42b3o$102b199o14b6o57b7o40b3o$101b201o13b6o59b
6o$100b203o13b7o58b6o$100b203o13b7o58b6o$98b207o12b6o59b6o$97b209o12b
5o60b7o$96b211o13b5o60b6o$95b213o13b6o59b6o$95b213o13b6o59b6o$93b217o
12b8o57b5o$92b219o14b6o57b7o$91b221o14b5o59b6o$90b223o14b5o59b6o$90b
223o14b5o59b6o$88b227o13b5o59b6o$87b229o14b6o57b7o$86b231o13b7o58b6o$
85b233o14b6o58b7o$85b233o14b6o58b7o$83b237o12b6o59b6o$82b239o14b6o57b
8o$81b241o13b6o59b6o$81b242o13b6o58b6o$81b242o13b6o58b6o$82b243o13b5o
55b7o$86b240o12b8o51b6o$87b240o13b7o49b6o$88b240o14b5o48b6o$88b240o14b
5o48b6o$90b240o12b5o46b7o$91b240o12b8o41b6o$92b240o13b7o39b6o$93b240o
13b7o37b6o$93b240o13b7o37b6o$95b240o12b6o35b7o$96b240o14b3o34b6o$97b
240o13b5o31b6o$98b240o13b5o29b6o$98b240o13b5o29b6o$100b240o13b7o23b7o$
101b240o12b8o21b6o$102b240o14b5o20b6o$103b240o13b6o18b6o$103b240o13b6o
18b6o$105b240o13b7o13b7o$106b240o12b7o12b6o$107b240o13b6o10b6o$108b
240o13b6o8b6o$108b240o13b6o8b6o$110b240o12b6o5b7o$111b240o12b5o4b6o$
112b240o13b12o$113b240o13b10o$113b240o13b10o$115b240o12b8o$116b240o11b
6o$117b240o9b6o$118b240o7b6o$118b240o7b6o$120b240o3b7o$121b240ob6o$
122b245o$123b243o$123b243o$125b240o$126b237o$127b235o$128b233o$128b
233o$130b230o$131b227o$132b225o$133b223o$133b223o$135b220o$136b217o$
137b215o$138b213o$138b213o$140b210o$141b207o$142b205o$143b203o$143b
203o$145b200o$146b197o$147b195o$148b193o$148b193o$150b190o$151b187o$
152b185o$153b183o$153b183o$155b180o$156b177o$157b175o$158b173o149b3o$
158b173o149b3o$160b170o150b5o$158b170o150b7o$157b170o150b4o$157b169o
151b4o$157b169o151b4o$157b168o150b6o$158b7ob157o152b6o$167b155o153b6o$
164b3ob153o$163b4ob153o$163b4o3b150o$171b147o$172b145o$173b143o$173b
143o$175b140o$176b137o$177b135o$178b133o$178b133o$180b130o$181b127o$
182b125o$183b123o$183b123o$185b120o$186b117o$187b115o$188b113o$188b
113o$190b110o$191b107o$192b105o$193b103o$193b103o$195b100o$196b97o$
197b95o$198b93o$198b93o$200b90o$201b87o$202b85o$203b83o$203b83o$205b
80o$206b77o$207b75o$207b75o$208b73o$210b70o$211b67o$212b65o$212b65o$
213b63o$215b60o$216b57o$217b55o$217b55o$218b53o$220b50o$221b47o$222b
45o$222b45o$223b43o$225b40o$226b37o$227b35o$227b35o$228b33o$230b30o$
231b27o$232b25o$232b25o$233b23o$235b20o$236b17o$236b16o$236b16o$238b
13o$240b10o$241b7o$241b6o$241b6o$241b5o$242b3o72$317b4o$317b4o$316b7o$
316b7o$316b7o$316b6o$316b6o$316b6o$318b4o$318b4o!
#C [[ Z -2 WIDTH 480 HEIGHT 480 VIEWONLY ]]
#C [[ LABEL 320 -40 -2 "N" ]]
#C [[ LABEL 120 120 -2 "NW" ]]
#C [[ LABEL 500 120 -2 "NE" ]]
#C [[ LABEL 250 200 -2 "C1" ]]
#C [[ LABEL 425 340 -2 "C2" ]]
#C [[ LABEL -30 320 -2 "W" ]]
#C [[ LABEL 670 320 -2 "E" ]]
#C [[ LABEL 130 500 -2 "SW" ]]
#C [[ LABEL 520 500 -2 "SE" ]]
#C [[ LABEL 320 660 -2 "S" ]]
#C [[ COLOR LABEL Red ]]
#C [[ LABEL 190 230 -2 "mN" ]]
#C [[ LABEL 400 427 -2 "mE" ]]
#C [[ LABEL 240 580 -2 "mS" ]]
#C [[ LABEL 35 395 -2 "mW" ]]
A good goal might be a LifeHistory blueprint of the 0E0P with all the major pieces labeled, and state-2 history tracks showing everywhere that gliders go -- just during the switching and self-destruct stages, though. A regular LifeHistory pattern wouldn't be much good, since construction would put blue smears all over the place.

Here's a start: an early-ish circuit diagram from the design stages of the 0E0P -- calcyman sent it to me a while back.
routing109.mc
Routing diagram for 0E0P metacell (not current)
(607.72 KiB) Downloaded 321 times
All I can confirm so far is that N is identical to this blueprint. So someone could go ahead and start figuring out and labeling those glider inputs and outputs.

However, S is substantially different -- at least, a lot of the pieces are in different places. Apparently some adjustments had to be made.

I'll volunteer to try to produce a clean LifeHistory circuit diagram for the S corner, and label what I can figure out, like the self-destructing multi-semi-Snark timing gun. A lot of the structure will turn out to be the self-destruct circuits, which maybe we should leave in green and color everything else white or yellow in LifeHistory. It should be fairly easy to find the self-destruct circuitry -- basically it's everything that disappears if you send a glider in on the correct path.

If you send a glider on one of the blue lanes and it hits a block and makes a pi explosion, I believe that's one of the construction-arm lanes that the single-channel recipe will travel on, to build one of the four children. It appears that there's one of those blocks in each corner, N, S, E, and W. I'm not clear yet on exactly how the arm is extended with long-distance Cordership recipes and Snarkmakers, to reach the same starting point for every child (so that they all end up getting built in the same orientation.)

Maybe some other people can contribute an analysis of the other labeled points that I haven't mentioned yet. And/or possibly calcyman can be convinced to help us out on the hard parts --!

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Re: 0E0P constructions

Post by Hunting » March 2nd, 2019, 1:47 am

dvgrn wrote: Also the B1c/S replicator keeps returning to a four-cell population, which is slightly annoying if you want your replicator to, you know, take over the universe. It still counts as a replicator by most people's definitions, but it's a lousy model of a replicator -- we wouldn't want to send a real-life von Neumann machine version of it into space to turn the Moon's surface into solar panels. Macbi's version isn't all _that_ much better -- the old machines stop working too soon -- but at least the population keeps growing nicely.
Well, I thought only sawtooths count as replicators.
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Re: 0E0P constructions

Post by dvgrn » March 2nd, 2019, 6:54 am

Hunting wrote:Well, I thought only sawtooths count as replicators.
It's more like, only superlinear-growth things count as replicators. XOR-type replicators are definitely quadratic growth, except with severe population-crash problems every now and then, so they are generally considered to be "real" replicators.

However, the population crashes aren't actually a good thing, so a replicator such as a cell in B12345678/S12345678 certainly counts, too -- quadratic growth and no population crashes, all good.

The type of copy-making where there's some kind of general consensus that it doesn't count as a replicator, is if the growth rate is only linear -- even if the number of copies is strictly increasing over time.

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Re: 0E0P constructions

Post by Macbi » March 2nd, 2019, 7:08 am

dvgrn wrote:The type of copy-making where there's some kind of general consensus that it doesn't count as a replicator, is if the growth rate is only linear -- even if the number of copies is strictly increasing over time.
I think you mean to say that it's not a quadratic replicator. Replicators can still be linear, for example the everyone calls the pattern in HighLife a replicator and that's a linear XOR style replicator.

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Re: 0E0P constructions

Post by 77topaz » March 2nd, 2019, 7:10 am

dvgrn wrote:It's more like, only superlinear-growth things count as replicators. XOR-type replicators are definitely quadratic growth, except with severe population-crash problems every now and then, so they are generally considered to be "real" replicators.

However, the population crashes aren't actually a good thing, so a replicator such as a cell in B12345678/S12345678 certainly counts, too -- quadratic growth and no population crashes, all good.

The type of copy-making where there's some kind of general consensus that it doesn't count as a replicator, is if the growth rate is only linear -- even if the number of copies is strictly increasing over time.
But aren't there also valid linear replicators - HighLife's one being an example? Most of the natural patterns generally considered as replicators, be it linear or quadratic, tend to show XOR behaviour. Then again, that doesn't need to be the case either, as there exist replicators obeying other Wolfram rules as well, such as this one which is probably closest to the "non-crashing" behaviour you're talking about:

Code: Select all

x = 1, y = 1, rule = B1c2c4c/S
o!
EDIT: As a side note, that rule can show another, distinct non-XOR replicator behaviour on the agar created by the first replicator:

Code: Select all

x = 39, y = 39, rule = B1c2c4c/S
obobobobobobobobobobobobobobobobobobobo2$obobobobobobobobobobobobobobo
bobobobobo2$obobobobobobobobobobobobobobobobobobobo2$obobobobobobobobo
bobobobobobobobobobobo2$obobobobobobobobobobobobobobobobobobobo2$obobo
bobobobobobobobobobobobobobobobobo2$obobobobobobobobobobobobobobobobob
obobo2$obobobobobobobobobobobobobobobobobobobo2$obobobobobobobobobobob
obobobobobobobobo2$obobobobobobobobobobobobobobobobobobobo$19bo$obobob
obobobobobobobobobobobobobobobobo2$obobobobobobobobobobobobobobobobobo
bobo2$obobobobobobobobobobobobobobobobobobobo2$obobobobobobobobobobobo
bobobobobobobobo2$obobobobobobobobobobobobobobobobobobobo2$obobobobobo
bobobobobobobobobobobobobobo2$obobobobobobobobobobobobobobobobobobobo
2$obobobobobobobobobobobobobobobobobobobo2$obobobobobobobobobobobobobo
bobobobobobo2$obobobobobobobobobobobobobobobobobobobo!

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Re: 0E0P constructions

Post by calcyman » March 2nd, 2019, 9:44 am

dvgrn wrote:Here's a start: an early-ish circuit diagram from the design stages of the 0E0P -- calcyman sent it to me a while back.
routing109.mc
All I can confirm so far is that N is identical to this blueprint. So someone could go ahead and start figuring out and labeling those glider inputs and outputs.

However, S is substantially different -- at least, a lot of the pieces are in different places. Apparently some adjustments had to be made.
There's also the caveat that there's no individual timestep where all of the circuitry is simultaneously present.
I'm not clear yet on exactly how the arm is extended with long-distance Cordership recipes and Snarkmakers, to reach the same starting point for every child (so that they all end up getting built in the same orientation.)
It doesn't: the metacell is deliberately structured in terms of a symmetrical 'shell' (invariant under 90-degree rotations) containing an asymmetric 'kernel'. The parent metacell constructs the daughter's shell in the usual way, and then pumps a glider stream into the shell which constructs the kernel internally in the correct orientation. This channel is kept open for the tape to reenter a second time, copying it into the tape of the daughter cell and initiating the clock in the correct phase.
It may be a bit worse than that. I haven't tried to track exactly how incoming gliders from neighbors (encoding the state in unary) interact with the glider stream that encodes the rule.
To make things even more confusing, this part is present in the blueprint routing109.mc, but is absent from the phase complete_default.mc -- it's already been 'used up' and decided that the metacell will be in state 7. Here's the south corner, with the init eater removed, and a glider activating this part in isolation:

Code: Select all

x = 2830, y = 3052, rule = LifeHistory
1233.A$1232.A.A$1232.2A122$1178.A$1177.A.A$1177.2A10$1258.2A$1258.2A
5$1262.2A$1262.2A6$1247.A$1246.A.A$1247.2A18$1229.2A$1229.A.A$1230.A
18$1204.2A$1204.2A2$1196.A$1196.3A$1199.A$1198.2A6.2A$1205.A.A$1206.A
$1251.2A$1251.2A$1193.2A$1193.2A6.2A$1201.2A54.2A$1257.2A$1210.2A$
1190.A19.2A$1189.A.A$1189.A.A3.2A193.2A$1190.A3.A.A193.2A$1194.A$
1193.2A3$1374.2A$1218.2A154.2A19.2A$1187.2A29.2A175.2A$1187.2A38.2A$
1226.A2.A$1227.2A2$1224.A8.2A$1224.3A6.2A$1227.A$1226.2A13.2A$1176.2A
63.A$1176.2A61.A.A$1239.2A2$1167.2A63.2A$1167.A.A62.2A$1161.2A5.A$
1161.2A81.2A$1238.A5.2A$1173.2A62.A.A$1173.2A63.2A2$1166.2A$1165.A.A
61.2A$1165.A63.2A$1164.2A13.2A$1179.A$1172.2A6.3A$1172.2A8.A2$1178.2A
$1177.A2.A36.2A$1132.2A44.2A36.A2.A60.2A$1132.2A53.2A28.2A61.2A$1187.
2A$1141.A$1139.3A$1138.A$1130.2A6.2A118.2A24.2A63.2A$1130.A.A125.2A
24.2A42.2A19.2A$1131.A196.2A139.A$1267.A200.A.A$1062.A202.3A201.2A$
1061.A.A79.2A119.A$1062.2A71.2A6.2A111.2A6.2A56.A$1135.2A119.A.A62.A.
A20.2A$1257.A64.2A20.2A$1126.2A$1126.2A19.A$1146.A.A120.2A$1141.2A3.A
.A112.2A6.2A$1015.2A124.A.A3.A113.2A196.2A$1014.A2.A106.A18.A315.2A$
1014.A.A106.A.A17.2A107.2A$1015.A107.A.A126.2A19.A$1124.A147.A.A$
1267.2A3.A.A$1267.A.A3.A$1001.A147.2A99.A18.A$1000.A.A146.2A98.A.A17.
2A$1000.A2.A245.A.A$1001.2A247.A$1014.2A$1015.A$1015.A.A257.2A$1016.
2A34.A222.2A$1037.2A12.A.A$1037.2A5.2A5.A.A280.2A129.2A$1044.2A6.A
281.2A129.2A$1255.2A$1255.2A69.A$1013.2A27.2A282.3A$1013.2A27.2A285.A
128.2A$1048.2A278.2A6.2A120.2A$1048.2A8.A276.A.A$1007.2A47.3A190.2A
85.A$1007.2A46.A193.A$948.2A26.A34.2A42.2A190.A.A3.A$948.2A25.A.A33.
2A234.2A3.A.A68.2A$976.2A274.A.A68.2A6.2A$1232.2A19.A77.2A$1062.2A
168.2A$952.2A52.2A53.A2.A275.2A$952.2A52.2A54.A.A176.2A77.A19.2A$970.
2A91.A177.2A6.2A68.A.A$970.2A277.2A68.A.A3.2A$1147.2A171.A3.A.A$1147.
2A28.2A145.A$1138.2A36.A2.A57.A85.2A$1021.2A5.2A107.A2.A36.2A57.A.A$
1021.2A4.A2.A107.2A96.2A6.2A$1028.2A214.A$1132.2A8.A102.3A$1132.2A6.
3A104.A69.2A30.2A$1139.A177.2A30.2A$1060.2A62.2A13.2A97.2A118.2A$
1060.2A63.A63.2A47.2A117.A2.A$1053.2A70.A.A61.2A167.2A$1053.2A56.A14.
2A$1110.A.A242.A8.2A$976.2A85.2A45.2A21.2A63.2A155.3A6.2A$976.2A85.A.
A67.2A62.A.A158.A$1048.2A14.A133.A5.2A151.2A13.2A$1048.2A71.2A81.2A
166.A$1052.2A67.2A5.A241.A.A$969.2A81.2A73.A.A62.2A176.2A$969.2A40.2A
114.2A63.2A$1011.2A350.2A$1017.2A27.2A151.2A162.2A$1017.2A27.2A88.2A
61.A.A$1136.2A63.A173.2A$1186.2A13.2A166.A5.2A$1015.2A170.A180.A.A42.
2A$958.2A42.2A11.2A5.2A160.3A6.2A174.2A41.A.A$958.2A41.A.A18.2A160.A
8.2A211.2A4.A$1002.A401.A2.A2.2A.4A$1187.2A171.2A42.2A.A.A.A.A2.A$
1186.A2.A170.2A45.A.A.A.A$962.2A82.2A99.2A38.2A218.A.A.2A$962.2A82.A.
A98.2A29.2A55.2A171.A$1048.A129.2A55.2A$1048.2A160.2A209.2A$1210.2A
32.A74.A92.2A7.A$1242.3A73.A.A91.2A5.A.A$1153.2A86.A76.A.A29.2A67.2A$
1154.A78.2A6.2A76.A30.2A$979.2A169.A3.A.A76.A.A$979.2A168.A.A3.2A49.
2A26.A$1149.A.A54.2A$1150.A19.2A$974.2A194.2A74.2A96.2A$974.2A262.2A
6.2A96.A64.2A$964.2A195.2A75.2A102.A.A3.A61.A$964.2A187.2A6.2A179.2A
3.A.A57.3A$1153.2A74.2A116.A.A57.A$1229.2A19.A76.2A19.A$955.2A292.A.A
75.2A$955.A.A208.A77.2A3.A.A$949.2A5.A106.2A100.A.A76.A.A3.A85.2A$
949.2A112.A.A92.2A6.2A78.A89.2A6.2A$1064.A94.A86.2A96.2A$1156.3A$959.
2A195.A$959.2A371.A$954.2A208.2A165.A.A$953.A.A208.2A54.2A30.2A77.2A
6.2A$953.A266.2A30.2A85.A$952.2A13.2A242.2A127.3A$967.A242.A2.A128.A$
960.2A6.3A240.2A$960.2A8.A362.2A24.2A$1205.2A8.A117.2A24.2A$966.2A
237.2A6.3A$965.A2.A243.A$966.2A229.2A13.2A$975.2A221.A$975.2A221.A.A
154.2A10.A$1199.2A154.2A9.A.A$1366.2A$1206.2A$1206.2A2$1194.2A$1194.
2A5.A$1200.A.A$1200.2A251.A$1452.A.A$1452.2A$1209.2A$1209.2A297.A$
1022.2A483.A.A$1022.2A328.A155.2A$1351.A.A$1351.2A$1251.A$1250.A.A$
1016.2A201.2A29.A.A$1016.A202.2A30.A$1014.A.A3.A$1014.2A3.A.A$1019.A.
A$999.2A19.A$999.2A224.2A216.A$1226.A215.A.A$1222.A3.A.A214.2A$1016.
2A203.A.A3.2A$1009.2A5.2A203.A.A$1009.2A211.A19.2A187.A$1242.2A186.A.
A$1004.A292.2A131.2A$1003.A.A227.2A62.A.A$1003.2A6.2A212.2A6.2A63.A$
1011.A213.2A$1012.3A$1014.A$1238.A$1005.2A230.A.A$1005.2A223.2A6.2A$
1231.A$1228.3A$1228.A2$1236.2A$1236.2A14$1396.2A$1396.2A8$1334.A$
1334.3A$1337.A$1336.A.A$46.A1289.A.A$45.A.A1289.A$45.2A$1390.2A$1390.
2A$1324.2A$1181.A141.A2.A25.2A$1180.A.A134.2A5.A.A25.2A$1181.2A133.A
2.A5.A71.2A$1316.A.A78.2A$1317.A$1332.2A$1331.A.A$1331.A$1325.A4.2A7.
2A$1324.A.A12.2A$1304.2A17.A2.A$1303.A2.A17.2A21.2A.A$1303.A.A41.2A.
3A$1304.A48.A$1347.2A.3A$1348.A.A$52.2A20.2A1089.A182.A.A$52.2A20.A.A
1087.A.A182.A$75.A1089.2A$1350.A$1348.3A$1320.2A25.A$68.2A1249.A2.A
24.2A$47.2A19.2A1250.2A17.2A$47.2A1290.2A$1291.A$1290.A.A$1290.2A$
1309.A$1307.3A16.A$1281.2A23.A17.3A$1282.A23.2A15.A31.A$1149.A132.A.A
38.2A28.3A$1148.A.A132.2A2.2A63.A$1149.2A136.2A63.2A$1278.A415.A$
1278.3A411.3A$1281.A409.A$1280.2A34.2A373.2A$1316.2A2$1355.2A$1355.A.
A$1357.A$1277.2A78.2A$1277.2A40.2A$.A1297.2A10.2A7.A$A.A1296.A.A9.2A
4.3A25.2A3.2A$.2A1130.A167.A15.A27.2A3.2A16.2A22.A31.A$1132.A.A166.2A
65.2A20.3A14.2A13.3A$1133.2A154.2A98.A17.2A12.A$1289.A92.A6.2A10.2A
11.A6.2A$1290.3A76.2A10.A.A16.A2.A9.A.A$1292.A76.2A11.A17.A.A11.A$
1300.A11.A88.A$1299.A.A9.A.A$1300.2A8.A2.A80.2A7.2A21.2A$1311.2A73.2A
6.2A6.A2.A12.2A6.2A$11.A1358.2A14.2A15.A.A12.2A$10.A.A1357.A.A31.A$
11.2A1358.A5.2A30.2A$1377.2A30.2A2$1392.2A5.2A23.2A$1117.A274.A.A4.A.
A22.A.A$1116.A.A275.A5.A25.A$1117.2A275.2A30.2A6$1418.2A$1418.A.A73.A
$1419.A73.A.A$1493.2A2$1543.2A$1378.2A30.2A131.2A$1378.A31.A$1101.A
274.A.A29.A.A$1100.A.A273.2A30.2A$1101.2A$1361.2A30.2A132.2A$1361.2A
30.2A22.2A108.2A19.2A$1417.2A129.2A$1370.2A30.2A$1370.2A6.2A22.2A6.2A
28.A$1378.2A30.2A29.2A$1440.2A2$1366.A31.A$1365.A.A29.A.A$1366.A6.2A
23.A6.2A$126.2A1245.A31.A$126.2A19.2A1225.3A29.3A$147.2A936.A290.A31.
A$1084.A.A336.2A138.A$1085.2A336.2A41.A94.3A$1464.3A93.A68.2A47.A$
154.A1308.A96.2A67.A.A45.A.A$131.2A20.A.A1307.2A165.A47.2A$131.2A20.
2A1275.2A$76.A1353.2A$74.3A1394.2A$73.A1398.A$73.2A1155.2A240.A.2A$
1229.A.A232.2A4.3A2.A40.2A$1230.A233.2A3.A3.2A41.2A$1469.4A$1455.2A
15.A$1454.A.A12.3A$1069.A384.A13.A$63.2A1003.A.A382.2A14.5A$62.A.A5.
2A997.2A402.A$62.A7.2A1399.A$61.2A1408.2A2$75.A1348.2A$71.2A.A.A1347.
2A$70.A.A.A.A$67.A2.A.A.A.A.2A$67.4A.2A2.A2.A94.A$71.A4.2A95.A.A1346.
2A$69.A.A101.2A1347.2A$69.2A2$1344.2A$1345.A169.2A$1345.A.A167.2A$
1346.2A6$1563.2A$1563.A.A$1564.A3$1304.2A$1304.2A2$180.2A20.2A$180.2A
20.A.A1094.2A$203.A1095.2A127.2D$99.2A382.2A944.D$99.A.A381.2A941.3D$
100.A1325.D$196.2A$175.2A19.2A$175.2A3$491.2A$491.2A4$1513.2A$1411.A
101.2A$1410.A.A$499.2A910.2A$499.2A$1520.2A$1363.2A155.2A$1342.2A19.
2A$1342.2A3$507.2A$507.2A502.2A$1011.A.A344.2A406.A$129.A882.A345.2A
38.A366.A.A$128.A.A1266.A.A365.2A$129.2A1267.2A3$515.2A480.2A$515.2A
480.2A$1514.2A$1514.2A3$1001.2A$139.A861.2A471.2A$138.A.A382.2A949.A.
A43.2A$139.2A382.2A950.A43.A.A$1520.A3$1498.2A$1497.A.A$1498.A$531.2A
$531.2A2$1130.2A65.A$1131.A64.A.A$1128.3A65.2A$1128.A2$539.2A1202.A$
539.2A1201.A.A$1743.2A12$1426.2A$1426.A.A$1427.A32.A$1340.2A117.A.A$
1105.A234.2A118.2A$254.2A848.A.A$254.2A19.2A290.2A536.2A205.A$275.2A
290.A.A741.A.A$568.A743.2A5.2A7.2A$1319.2A8.A$1329.A.A$282.A1047.2A$
259.2A20.A.A$259.2A20.2A$204.A$202.3A$201.A$201.2A$1742.A$1470.2A269.
A.A$1270.A199.2A269.2A$1270.3A$583.2A688.A$583.A.A686.2A$191.2A391.A
881.2A$190.A.A5.2A1266.2A$190.A7.2A$189.2A2$203.A1280.2A$199.2A.A.A
1279.2A$198.A.A.A.A$195.A2.A.A.A.A.2A$195.4A.2A2.A2.A1271.2A238.2A$
199.A4.2A1273.2A238.A.A$197.A.A1520.A$197.2A2$599.2A$599.A.A$600.A2$
1069.2A152.2A$1070.A151.A.A$1067.3A153.A$1067.A648.2A$1716.2A2$1522.
2A184.A$1521.A.A184.3A$1522.A188.A$1710.2A6.2A$1717.A.A$1051.2A665.A
163.2A$615.2A434.2A829.2A$615.A.A$616.A1088.2A55.2A$1056.2A247.2A398.
2A6.2A47.2A$227.2A827.2A247.2A309.A96.2A$227.A.A1311.A73.A.A248.2A
807.A$228.A1311.A.A73.2A104.2A142.2A19.2A785.A.A$1541.2A159.A19.2A
163.2A786.2A$1701.A.A62.2A$1701.A.A3.2A48.A8.2A$1702.A3.A.A47.A.A$
1706.A50.2A$1705.2A3$1729.2A$1729.2A$1460.2A190.2A45.2A37.2A$1460.2A
190.A46.2A36.A2.A$1650.A.A85.2A$509.2A30.2A30.2A462.2A611.2A$509.2A
30.2A30.2A463.A696.A8.2A$1035.3A697.3A6.2A$1035.A420.2A280.A$1456.2A
232.2A45.2A13.2A$1690.2A60.A$484.2A39.2A30.2A30.2A1159.A.A$483.A.A18.
2A19.2A9.2A19.2A9.2A19.2A1159.2A$484.A19.2A30.2A30.2A1111.2A$1681.A.A
59.2A$1675.2A5.A60.2A$1019.2A654.2A$1019.2A734.2A$1687.2A60.A5.2A20.
2A$1687.2A59.A.A27.A$606.2A416.2A608.A114.2A27.A.A$606.2A416.2A607.A.
A44.2A97.2A$520.2A30.2A1080.2A43.A.A$520.2A30.2A926.A198.A60.2A$1479.
A.A196.2A13.2A45.2A$1479.2A212.A$491.2A32.2A30.2A31.2A1094.2A6.3A36.
2A$491.A.A31.2A30.2A31.2A19.2A1073.2A8.A35.A2.A$492.A118.2A1120.2A$
1692.2A$1624.A66.A2.A$1623.A.A66.2A$1624.2A75.2A89.A$1565.2A134.2A88.
A.A$1247.2A315.A.A224.2A$1247.2A240.2A74.A$1488.A.A$1005.2A482.A$
1006.A245.2A642.A$1003.3A246.2A641.A.A$1003.A610.A280.2A$1613.A.A$
1614.2A186.A$1801.A.A$1801.2A2$1364.2A$1364.2A19.2A$987.2A396.2A$987.
2A$1604.A$910.2A691.A.A$910.2A80.2A610.2A206.A$992.2A375.2A440.A.A$
1369.2A440.2A2$906.2A$906.2A3$1594.A$1593.A.A$1594.2A226.A$1821.A.A$
1821.2A2$853.A$852.A.A561.A$853.2A560.A.A$973.2A440.2A$974.A609.A$
971.3A609.A.A$971.A612.2A246.A941.A$1831.A.A939.A.A$1678.2A151.2A941.
2A$1678.2A2$707.2A1046.2A$543.2A162.A.A499.2A544.2A$542.A.A163.A500.
2A1557.2A$543.A1030.A1193.2A$1573.A.A$1574.2A2$1668.2A$1668.2A2$1765.
2A$1765.2A4$1852.A$690.2A31.2A822.2A302.A.A$690.2A31.A.A820.A.A109.2A
191.2A$724.A461.2A359.A110.2A1114.2A$1186.2A1586.2A$1775.2A$814.2A20.
2A937.2A$813.A.A20.2A105.2A246.2A$814.A128.A.A245.2A1574.2A$944.A
1822.2A$1862.A$1861.A.A$820.2A826.2A211.2A$820.2A19.2A805.2A$841.2A$
1785.2A$1785.2A$696.2A41.2A842.2A$696.2A41.A.A435.2A404.2A$740.A436.
2A$1575.A$1575.3A$689.2A887.A59.2A$689.2A886.2A6.2A51.2A$1584.A.A$
1585.A209.2A$898.A896.2A$897.A.A$897.2A673.2A$1572.2A6.2A$1580.2A2$
1589.2A37.2A$675.2A13.2A63.2A812.A19.2A37.2A1115.2A$675.2A13.2A63.A.A
810.A.A1174.A$756.A397.2A412.A.A3.2A1171.A$1154.2A413.A3.A.A1151.2A
14.5A$1573.A155.2A18.A978.A13.A$679.2A891.2A19.A135.2A17.A.A977.A.A
12.3A$679.2A360.2A116.2A431.A.A108.2A43.2A979.2A15.A$1041.A.A115.2A
431.A.A107.A2.A1037.4A$1042.A550.A109.A.A1032.2A3.A3.2A79.A$1618.2A
84.A1033.2A4.3A2.A77.A.A$1566.2A50.2A1126.A.2A77.2A$1566.2A1178.A$
1815.2A928.2A$1718.A96.2A$1563.2A152.A.A7.2A150.2A$878.A683.A2.A150.A
2.A7.2A150.2A856.2A$696.2A179.A.A683.2A152.2A1018.A$696.2A179.2A266.
2A410.2A145.2A165.A866.3A$1145.2A410.2A145.A166.3A866.A$1702.A.A169.A
$1667.A34.2A169.2A6.2A$689.2A857.2A116.A.A12.2A197.A.A$689.2A857.A.A
115.A.A5.2A5.2A142.2A54.A$1542.2A5.A117.A6.2A149.2A$1542.2A191.2A$
1735.2A131.2A$1554.2A120.2A27.2A161.2A6.2A$1554.2A120.2A27.2A169.2A$
1670.2A$1547.2A112.A8.2A213.2A$744.A801.A.A112.3A47.2A152.A19.2A$743.
A.A800.A117.A46.2A151.A.A$675.2A13.2A52.2A799.2A13.2A101.2A42.2A34.A
120.A.A3.2A$675.2A13.2A868.A146.2A33.A.A120.A3.A.A$1122.2A429.2A6.3A
178.2A125.A$1122.2A429.2A8.A304.2A$1656.2A$679.2A802.2A74.2A94.A2.A
53.2A$679.2A446.2A353.A.A73.A2.A36.2A55.A.A54.2A178.2A$1127.2A354.A
75.2A37.2A56.A91.2A142.2A$1568.2A178.2A112.2A37.2A$1568.2A292.2A36.A
2.A$1901.2A2$1592.2A96.2A5.2A199.A8.2A$1592.A96.A2.A4.2A199.3A6.2A$
1590.A.A3.A28.2A63.2A209.A$1473.2A115.2A3.A.A27.2A273.2A13.2A$696.2A
774.A.A120.A.A317.A$696.2A775.A40.A60.2A19.A316.A.A$763.2A748.A.A59.
2A81.2A253.2A$742.2A19.2A748.2A143.2A1117.2A$742.2A787.A52.2A79.2A
239.2A869.A.A$689.2A839.A.A51.2A6.2A71.2A239.2A870.A$689.2A840.2A59.
2A$1655.2A85.2A174.2A$736.A898.2A17.A.A85.2A168.A5.2A$735.A.A20.2A
703.2A56.2A57.A54.2A18.A14.2A239.A.A$736.2A20.2A702.A.A56.2A56.A.A88.
2A240.2A$814.A648.A115.2A6.2A77.2A$814.3A770.A78.2A81.2A$817.A770.3A
116.2A40.2A152.2A$816.2A772.A116.2A194.2A$1525.2A145.2A27.2A$1525.2A
54.2A89.2A27.2A$675.A905.2A$674.A.A24.2A942.2A$675.2A23.A.A750.2A190.
2A56.2A$701.A750.A.A241.2A5.2A11.2A42.2A132.2A$826.2A625.A242.2A18.A.
A41.2A132.2A$819.2A5.A.A359.2A527.A$819.2A7.A359.A679.A$828.2A356.A.A
364.A313.A.A$690.2A494.2A365.3A116.2A82.2A109.A.A$689.A.A123.A740.A
114.A.A82.2A110.A19.2A$690.A123.A.A.2A735.2A114.A216.A$814.A.A.A.A
834.2A13.2A214.A.A3.A$811.2A.A.A.A.A2.A619.2A210.2A229.2A3.A.A$811.A
2.A2.2A.4A618.A.A446.A.A$813.2A4.A623.A427.2A19.A79.2A$819.A.A1049.2A
99.A.A$820.2A917.2A89.2A141.A$1739.2A89.2A48.2A$1880.2A6.2A$1888.2A$
1744.2A$1744.2A$1433.2A319.2A120.A$1432.A.A319.2A119.A.A$1433.A441.2A
6.2A97.2A$1572.2A309.A98.A.A$1571.A.A189.2A55.2A62.3A96.A$1369.A202.A
189.A.A55.2A64.A$1367.3A393.A5.2A$1366.A402.2A106.2A$1356.2A8.2A509.
2A$1357.A317.2A$1325.2A11.A18.A.A63.2A250.2A82.2A$847.2A476.2A10.A.A
18.2A62.A.A334.2A$847.2A488.A.A32.2A49.A340.2A226.2A18.2A$1336.2A.3A
2.2A26.2A208.2A180.A.A138.A86.A.A17.2A$1342.A2.A39.A195.A.A182.A43.2A
92.A.A86.A$842.2A492.2A.3A3.A.A35.3A196.A168.2A13.2A42.2A92.2A$790.2A
50.2A492.2A.A6.2A34.A369.A$789.A.A580.2A8.2A365.3A6.2A$790.A581.2A
375.A8.2A$1685.2A225.2A$1685.2A65.2A158.2A$1751.A2.A$1752.2A248.2A$
1333.2A13.2A242.2A149.2A148.A12.2A94.A.A$1333.2A13.2A241.A.A149.2A55.
2A89.3A12.2A95.A$773.2A543.2A64.A3.2A202.A207.2A88.A$774.A453.2A87.A
2.A62.A.A2.2A500.2A$771.3A454.2A19.2A65.A.2A63.A.A$771.A477.2A65.A67.
A$1315.2A378.2A$1330.2A363.2A$1330.A$1331.3A678.2A$1233.2A98.A268.2A
408.A.A$1233.2A366.A.A186.2A221.A$1344.A257.A187.2A87.2A$1134.2A207.A
.A533.A.A$1133.A.A202.A4.A.A8.2A524.A$1134.A202.A.A4.A10.A340.2A$
1337.A2.A14.A.A338.2A$1338.2A16.2A2$2022.2A$1343.A26.2A650.A.A$1342.A
.A25.A.A329.2A76.2A241.A$1342.2A28.A330.A76.2A87.2A$1363.2A7.2A325.A
3.A.A163.A.A$1363.2A333.A.A3.2A164.A$1698.A.A632.A$1699.A19.2A611.A.A
$1719.2A612.2A$1338.A$1337.A.A33.2A657.2A$1337.2A33.A2.A246.2A78.2A
328.A.A$1353.2A18.2A246.A.A78.2A5.2A59.2A261.A$1354.A267.A86.2A59.2A
87.2A$1354.A.A502.A.A$1355.2A358.A144.A$1714.A.A$1349.2A356.2A6.2A$
1348.A.A357.A$934.A414.A24.A330.3A$933.A.A436.3A330.A$933.2A436.A260.
2A$1371.2A258.A.A79.2A$1346.A285.A80.2A134.2A$1009.2A334.A.A501.A.A$
1009.2A334.A.A244.2A256.A$1102.2A242.A245.A.A$1101.A.A489.A$1102.A$
1347.2A$1003.2A342.A.A402.2A$1003.2A343.A293.2A108.A.A$1641.A.A109.A$
1358.2A282.A196.2A$813.2A543.2A479.A.A$813.A.A766.2A256.A$814.A182.2A
376.2A205.A.A$997.2A358.2A16.A.A205.A$1358.A18.A$1355.3A19.2A$1355.A$
1366.2A$1367.A$1364.3A462.2A$1212.A151.A464.A.A$1211.A.A358.2A256.A$
1212.2A222.2A134.A.A154.2A$764.2A670.A.A134.A155.2A$764.2A219.2A450.A
$985.2A2$769.2A$769.2A962.2A$1733.2A84.2A$855.2A122.2A838.A.A$854.A.A
122.2A581.2A256.A$855.A706.A.A109.2A$1329.2A232.A110.A.A512.A191.2A$
1070.2A236.2A19.2A344.A512.A.A190.2A7.2A$1069.A.A236.2A879.2A199.A$
1070.A1317.A.A$2388.2A6.A$2394.3A$1453.2A938.A$1324.2A127.A.A727.2A
208.2A$969.2A353.2A128.A97.2A629.2A$969.A.A580.A.A129.2A$970.A582.A
130.A.A705.2A$1685.A706.2A$2375.2A$962.A1411.A.A22.2A$961.A.A1410.A
24.A.A$948.2A12.2A1409.2A25.A$948.2A2$1228.A313.2A$1226.3A313.A.A$
1225.A317.A$1225.2A$2371.A7.2A$2189.2A179.A.A7.A$2189.2A179.2A5.3A$
2377.A$2414.2A$2413.A2.A$1215.2A315.2A648.2A230.A.A$1214.A.A5.2A308.A
.A169.2A476.2A211.2A18.A$1214.A7.2A309.A170.A.A688.A.A$942.2A269.2A
490.A691.A$942.2A1453.2A$1038.2A187.A1142.A$1037.A.A183.2A.A.A1140.A.
A7.2A$1038.A183.A.A.A.A1140.A2.A6.2A$949.2A268.A2.A.A.A.A.2A1138.2A$
949.2A268.4A.2A2.A2.A$1223.A4.2A$1221.A.A490.2A671.2A34.2A$1221.2A
491.A.A661.2A7.2A33.A2.A$1715.A663.A43.A.A$2379.A.A22.A19.A$2380.2A
21.A.A$1019.2A1382.A.A$1018.A.A1217.2A164.A$859.2A158.A492.A725.2A
154.2A20.A9.A$859.A.A649.A.A880.A.A18.A.A7.A.A$860.A651.2A882.A18.A2.
A5.A2.A$1724.2A670.2A18.2A7.2A$1317.A406.A.A$1316.A.A406.A$911.2A336.
2A66.2A$911.2A336.2A19.2A1146.A$1270.2A1146.3A$2421.A$1502.A917.2A$
1501.A.A931.2A$974.A302.A224.2A931.A$973.A.A278.2A20.A.A455.2A696.2A.
A$973.2A28.2A249.2A20.2A456.A.A694.A2.A$1002.A.A730.A508.2A186.2A$
1003.A1240.2A156.2A13.2A$2402.2A13.2A3$1492.A654.2A88.2A$1491.A.A653.
A89.2A$905.2A117.2A466.2A655.A228.2A$905.2A116.A.A160.2A941.2A14.5A
228.2A$1024.A161.2A942.A13.A259.2A6.A.2A$2130.A.A12.3A256.A.A3.3A.2A$
2131.2A15.A257.A2.A$912.2A1231.4A229.2A26.2A2.3A.2A$912.2A265.2A959.
2A3.A3.2A227.2A32.A.A$1179.2A959.2A4.3A2.A240.2A18.A.A10.2A$987.2A
493.A665.A.2A240.A.A18.A11.2A$986.A.A492.A.A664.A245.A$987.A494.2A
663.2A235.2A8.2A$1754.2A629.A$1754.A.A625.3A$1755.A383.2A241.A$2139.A
307.2A$2140.3A304.A.A$938.A1203.A210.2A93.A$937.A.A1413.A.A$938.2A
532.A881.A$1471.A.A$1472.2A2$1185.2A$1185.2A$971.2A$970.A.A1369.A$
971.A1369.A.A$2342.2A$1462.A$1461.A.A$1462.2A4$1211.2A$1211.2A$2232.A
$2231.A.A$1452.A779.2A$1442.2A7.A.A$1442.2A8.2A3$1433.2A$1013.2A30.2A
30.2A354.A.A746.2A$1013.2A30.2A30.2A348.2A5.A747.2A19.2A$1427.2A774.
2A117.2A$2321.A.A$2321.A$1155.2A280.2A781.2A98.2A$997.2A30.2A30.2A39.
2A51.2A48.2A230.2A781.2A$997.2A19.2A9.2A19.2A9.2A19.2A18.A.A100.2A
225.2A753.2A$1018.2A30.2A30.2A19.A327.A.A753.2A$1431.A$1159.2A269.2A
13.2A$1159.2A51.2A231.A$1212.2A224.2A6.3A$1438.2A8.A2$1444.2A$1443.A
2.A840.2A4.A$1034.2A30.2A376.2A841.2A3.A.A4.2A$1034.2A30.2A385.2A836.
A2.A4.2A$973.A479.2A837.2A$972.A.A1288.2A$972.2A55.2A30.2A32.2A1129.
2A34.A2.A$1029.2A30.2A31.A.A1129.2A34.A.A$1095.A1167.A26.A$2290.3A$
2293.A$999.2A1218.2A71.2A$998.A.A1218.2A86.2A89.A$999.A1307.A89.A.A$
2304.2A.A89.2A$2303.A2.A$2304.2A$2274.2A13.2A$2205.2A44.2A21.2A13.2A$
2205.2A44.2A5$972.2A1235.2A$971.A.A1235.2A73.A.2A$972.A1309.3A.2A19.
2A$2281.A24.A.A$2282.3A.2A19.A$2284.A.A$2257.2A8.2A.A13.A.A10.2A$
2258.A8.2A.3A12.A11.2A$2255.3A15.A$2255.A11.2A.3A$2268.A.A$2268.A.A$
2269.A2$1911.A$1910.A.A$956.2A953.2A$955.A.A$956.A3$1261.2A$1260.A.A$
1261.A$918.2A586.2A804.2A$918.2A585.A.A141.2A661.A.A$1506.A141.A.A
662.A$1649.A2$922.2A$922.2A1020.A$1943.A.A$940.2A1002.2A$939.A.A$940.
A575.2A$1515.A.A121.2A$1516.A121.A.A$1639.A298.2A$1938.2A7$1629.2A$
1628.A.A$1629.A6$1944.2A$1536.2A406.2A$1535.A.A81.2A$1536.A81.A.A$
1619.A$1937.2A$1937.2A4$1253.2A$1252.A.A291.2A$1253.A291.A.A61.2A$
1546.A61.A.A$1609.A$998.2A30.2A30.2A$998.2A30.2A30.2A2$1856.2A$1835.
2A19.2A$1835.2A$982.2A30.2A30.2A508.2A$982.2A19.2A9.2A19.2A9.2A19.2A
486.A.A41.2A$1003.2A30.2A30.2A487.A41.A.A$1599.A$1851.2A$1851.2A4$
1915.2A$1566.2A347.A$987.2A30.2A30.2A512.A.A21.2A326.A$987.2A30.2A30.
2A513.A21.A.A306.2A14.5A$1589.A308.A13.A$1898.A.A12.3A$982.2A30.2A30.
2A851.2A15.A$982.2A30.2A30.2A865.4A$1908.2A3.A3.2A79.A$1908.2A4.3A2.A
77.A.A$1501.A414.A.2A77.2A$1499.3A414.A$1498.A416.2A$1488.2A8.2A$
1489.A$1457.2A11.A18.A.A415.2A$1457.2A10.A.A18.2A415.A$1469.A.A32.2A
402.3A$1468.2A.3A2.2A26.2A404.A$1474.A2.A39.A$1468.2A.3A3.A.A35.3A$
1468.2A.A6.2A34.A71.2A$1504.2A8.2A69.A.A$1504.2A80.A5$1465.2A13.2A$
1465.2A13.2A$1450.2A64.A3.2A$1449.A2.A62.A.A2.2A$1448.A.2A63.A.A$
1448.A67.A$1447.2A$1462.2A$1462.A$1463.3A136.2A$1465.A135.A.A$1602.A$
1476.A$1475.A.A$1470.A4.A.A8.2A$1469.A.A4.A10.A$1469.A2.A14.A.A$1470.
2A16.2A2$1612.2A$1475.A26.2A107.A.A$1474.A.A25.A.A107.A$1474.2A28.A$
1431.A63.2A7.2A441.2A$1429.3A63.2A450.A.A$1428.A519.A$1428.2A2$1470.A
$1469.A.A33.2A115.2A$1469.2A33.A2.A113.A.A$1485.2A18.2A115.A$1486.A$
1418.2A66.A.A$1417.A.A5.2A60.2A$1417.A7.2A$1416.2A63.2A$1480.A.A$
1430.A50.A24.A$1426.2A.A.A72.3A125.2A$1425.A.A.A.A71.A127.A.A$1422.A
2.A.A.A.A.2A68.2A127.A$1422.4A.2A2.A2.A43.A$1426.A4.2A44.A.A$1424.A.A
50.A.A$1424.2A52.A3$1479.2A$1479.A.A160.2A$1480.A160.A.A$1642.A$1490.
2A$1490.2A2$1507.2A$1489.2A16.A.A$1490.A18.A$1487.3A19.2A$1487.A164.
2A$1498.2A151.A.A$1499.A152.A$1496.3A$1496.A2$1568.2A$1568.A.A$1569.A
2$1662.2A$1661.A.A$1662.A11$1585.2A$1585.A.A$1586.A8$1685.2A$1685.A$
1686.3A$1688.A6$1483.2A20.2A$1483.2A20.A.A$1506.A$1280.2A$1280.2A68.
2A$1349.A.A$1350.A148.2A$1478.2A19.2A$1478.2A6$1712.2A$1712.2A3$1706.
2A$1706.2A17$1313.2A$1313.2A4$1320.2A$1320.2A4$1641.2A$1640.A.A$1641.
A9$1314.2A$1314.2A12$1287.2A$1287.2A3$1412.2A$1412.A.A$1413.A6$1353.
2A$1353.2A256.A$1610.A.A$1611.2A$1293.2A$1293.2A4$1286.2A$1286.2A6$
1359.2A$1359.2A4$1352.2A$1352.2A30$1992.2A$1992.2A3$1314.2A671.2A$
1314.2A671.2A4$1318.2A$1318.2A21$1610.A$1608.3A$1607.A$1607.2A2$1361.
2A$1361.2A4$1597.2A$1596.A.A5.2A$1596.A7.2A$1595.2A2$1609.A$1605.2A.A
.A$1604.A.A.A.A$1601.A2.A.A.A.A.2A$1601.4A.2A2.A2.A$1605.A4.2A$1367.
2A234.A.A$1367.2A234.2A2$1727.2A$1727.2A$1360.2A$1360.2A2$1723.2A$
1723.2A6$1348.A$1347.A.A$1348.2A7$1364.2A$1363.A.A$1364.A17$1610.A$
1608.3A$1607.A$1607.2A7$1597.2A$1596.A.A5.2A$1596.A7.2A$1595.2A2$
1609.A274.2A$1605.2A.A.A273.2A$1604.A.A.A.A$1601.A2.A.A.A.A.2A$1601.
4A.2A2.A2.A$1605.A4.2A268.2A$1603.A.A274.2A$1603.2A9$1714.2A$1714.2A
5$1698.2A$1698.2A19.2A$1719.2A29.2A105.A$1637.2A111.2A104.A.A$1637.2A
19.2A197.2A$1658.2A2$1754.2A$1754.2A$1665.A$1642.2A20.A.A$1642.2A20.
2A3$1568.2A$1568.2A4$1561.2A$1561.2A3$1885.2A$1884.A.A$1742.2A141.A$
1741.A.A$1742.A8$1567.2A$1567.2A8$1474.2A$1474.2A4$1467.2A$1467.2A6$
1601.2A$1601.2A19.2A$1622.2A5$1606.2A$1606.2A$1473.2A$1473.2A7$1756.
2A$1756.2A2$1753.A$1752.A.A$1642.2A109.A.A$1641.A.A29.2A79.A$1642.A
30.2A3$1678.2A$1678.2A2$1507.2A$1507.2A19.2A$1528.2A5$1512.2A$1512.2A
7$1760.2A$1760.2A2$1757.A$1756.A.A$1757.A.A$1758.A8$1542.A$1541.A.A$
1542.2A2$1417.A$1416.A.A$1417.2A2$1718.A$1717.A.A$1716.A.A$1716.2A$
1462.A$1461.A.A231.2A$1461.2A232.A.A$1696.A.A$1697.A2$1716.A$1715.A.A
$1715.A.A$1716.A35.2A$1752.2A2$874.2A643.2A228.A$874.2A643.2A227.A.A$
1749.A.A$1750.A$869.2A$869.2A641.2A$1512.2A6$1735.2A$1734.A2.A$1602.
2A131.A2.A$1581.2A19.2A132.2A$1581.2A2$1731.2A$1731.2A2$1518.2A77.2A$
1518.2A77.2A15$1420.A$1419.A.A79.2A$1420.2A79.A.A45.2A$1502.A46.2A19.
2A$1570.2A5$917.2A635.2A$917.2A19.2A614.2A$794.2A142.2A$794.2A3$789.
2A$789.2A131.2A$922.2A8$805.2A$805.2A19.2A$826.2A5$810.2A$810.2A10$
1563.2A12.A$1563.2A3.A7.A.A$1567.A.A6.A.A$1567.A2.A6.A$1568.2A4$1544.
2A23.A$1544.2A23.3A$1572.A$1571.2A$1586.2A$1586.A$1583.2A.A$1524.A57.
A2.A$714.2A807.A.A57.2A$714.2A808.2A27.2A13.2A$1530.2A21.2A13.2A$
1530.2A$709.2A$709.2A4$1525.2A36.A.2A$1524.A2.A33.3A.2A$1525.2A33.A$
1561.3A.2A$1563.A.A$725.2A809.2A8.2A.A13.A.A10.2A$725.2A19.2A789.A8.
2A.3A12.A11.2A$746.2A786.3A15.A$1534.A11.2A.3A$1547.A.A$1547.A.A$
1548.A$730.2A$730.2A8$1685.A$1684.A.A$1684.2A4$1664.A$1663.A.A$1663.
2A18$657.2A$657.2A4$661.2A$661.2A33$1584.A$1583.A.A$1583.2A7$1542.A4.
2A$1535.2A4.A.A3.2A$1535.2A4.A2.A$1542.2A$1571.2A$1570.A2.A$1571.A.A$
1545.A26.A$1543.3A$1542.A$1542.2A$1527.2A$1528.A$1528.A.2A$1529.A2.A$
1530.2A$1545.2A13.2A$1545.2A13.2A21.2A$1583.2A6$1548.2A.A$1527.2A19.
2A.3A$1527.A.A24.A$1528.A19.2A.3A$1549.A.A$1537.2A10.A.A13.A.2A8.2A$
1537.2A11.A12.3A.2A8.A$1562.A15.3A$1563.3A.2A11.A$1565.A.A$1565.A.A$
1566.A12$1580.A$1579.A.A$1580.2A38$1623.A$1623.3A$1626.A$1625.2A3$
1617.2A$1617.A$1614.2A.A$1614.A2.3A4.2A$1615.2A3.A3.2A$1617.4A$1617.A
15.2A$1618.3A12.A.A$1621.A13.A$1616.5A14.2A$1616.A$1618.A$1617.2A88$
1912.2A$1912.2A24$1402.2A$1401.A.A$1402.A37$1442.2A$1442.2A4$1449.2A$
1436.2A11.2A$1435.A.A$1436.A13$1443.2A$1443.2A5$1449.2A$1448.A.A466.
2A$1449.A467.2A3$1912.2A$1912.2A23$1964.2A$1964.2A5$1948.2A$1948.2A
19.2A$1969.2A29$1747.A$1747.3A$1750.A$1749.2A6$2060.A$1759.2A298.A.A$
1752.2A5.A.A297.2A$1752.2A7.A$1761.2A2$1748.A$1747.A.A.2A$1747.A.A.A.
A$1744.2A.A.A.A.A2.A$1744.A2.A2.2A.4A319.2A$1746.2A4.A323.A.A$1752.A.
A322.A$1753.2A22$2051.2A$2030.2A19.2A$2030.2A5$2046.2A$2046.2A7$1604.
2A$1604.2A5$1588.2A$1588.2A19.2A$1609.2A30$1499.2A$1498.A.A$1497.A.A$
1498.A2$1974.2A$1974.2A6$1558.2A$1537.2A19.2A$1537.2A5$1553.2A$1553.
2A5$1517.2A$1517.2A19.2A$1538.2A4$1747.A$1522.2A223.3A$1522.2A226.A$
1749.2A7$1759.2A$1752.2A5.A.A$1752.2A7.A$1761.2A2$1748.A$1747.A.A.2A$
1747.A.A.A.A$1744.2A.A.A.A.A2.A$1744.A2.A2.2A.4A$1746.2A4.A$1752.A.A$
1753.2A18$1719.2A$1698.2A19.2A$1698.2A2$1903.2A$1902.A.A$1692.A209.A$
1691.A.A20.2A185.2A$1692.2A20.2A2$1795.2A$1795.A.A$1796.A10$1591.A$
1590.A.A$1591.A.A$1592.2A3$1590.2A$1589.A.A$1590.A29$1267.A$1265.3A
485.2A$1264.A487.A.A$1264.2A487.A16$1237.2A$1237.2A6$1233.2A$1233.2A
2$1747.A$1747.3A$1750.A$1749.2A7$1759.2A$1752.2A5.A.A$1752.2A7.A$
1761.2A2$1748.A$1667.2A78.A.A.2A$1666.A.A78.A.A.A.A$1667.A76.2A.A.A.A
.A2.A$1744.A2.A2.2A.4A$1746.2A4.A$1752.A.A$1753.2A18$1719.2A$1698.2A
19.2A$1698.2A4$1692.A$1691.A.A20.2A$1692.2A20.2A2$1795.2A$1795.A.A$
1796.A48$1753.2A$1752.A.A$1753.A10$1403.2A$1403.2A3$1408.2A$1408.2A8$
1696.A$1695.A.A$1695.2A$1747.A$1747.3A$1750.A$1749.2A7$1673.A85.2A$
1672.A.A77.2A5.A.A$1673.2A77.2A7.A$1761.2A2$1748.A$1747.A.A.2A$1747.A
.A.A.A$1744.2A.A.A.A.A2.A$1744.A2.A2.2A.4A$1746.2A4.A$1752.A.A$1753.
2A18$1719.2A$1698.2A19.2A$1698.2A4$1692.A$1691.A.A20.2A$1692.2A20.2A
2$1795.2A$1795.A.A$1796.A$1417.2A$1417.A.A$1418.A32$1837.A$1836.A.A$
1837.2A11$1753.2A$1752.A.A$1753.A17$1798.2A20.2A$1797.A.A20.2A$1798.A
4$1696.A107.2A$1695.A.A106.2A19.2A$1695.2A128.2A$1747.A$1747.3A$1750.
A$1749.2A7$1673.A85.2A$1672.A.A77.2A5.A.A120.A$1673.2A77.2A7.A119.A.A
$1761.2A118.2A2$1748.A$1747.A.A.2A$1747.A.A.A.A$1744.2A.A.A.A.A2.A$
1744.A2.A2.2A.4A$1746.2A4.A$1752.A.A$1753.2A11$1862.A$1861.A.A$1861.
2A5$1719.2A$1698.2A19.2A$1698.2A4$1692.A$1691.A.A20.2A$1692.2A20.2A2$
1795.2A$1795.A.A$1796.A48$1753.2A$1752.A.A$1753.A17$1696.2A$1675.2A
19.2A$1675.2A4$1669.A$1668.A.A20.2A$1669.2A20.2A$1747.A$1747.3A$1750.
A$1749.2A7$1759.2A$1752.2A5.A.A$1752.2A7.A$1761.2A2$1748.A$1747.A.A.
2A$1747.A.A.A.A$1744.2A.A.A.A.A2.A$1744.A2.A2.2A.4A$1746.2A4.A$1752.A
.A$1753.2A22$1723.2A$1722.A.A$1723.A!
If we run this to its completion, you can see that an eater and a block have been removed in relatively short succession:

Code: Select all

x = 370, y = 274, rule = LifeHistory
29.4B$30.4B$31.4B$32.4B$33.4B$34.4B$35.4B$36.4B$37.4B$38.4B$39.4B$40.
4B$41.4B$42.4B$43.4B$44.4B$45.4B$46.4B$47.4B$48.4B$49.4B$50.4B$51.4B$
52.4B$53.4B$54.4B$55.4B$56.4B$57.4B$58.4B$B58.4B$2B58.4B$3B58.4B$4B
58.4B$.4B58.4B$2.4B58.4B$3.4B58.4B$4.4B58.4B$5.4B58.4B$6.4B58.4B$7.4B
58.4B$8.4B58.4B$9.4B58.4B$10.4B58.4B$11.4B58.4B$12.4B58.4B175.A$13.4B
58.4B173.A.A$14.4B58.4B173.2A$15.4B58.4B$16.4B58.4B$17.4B58.4B$18.4B
58.4B$19.4B58.4B$20.4B58.4B$21.4B58.4B$22.4B58.4B$23.4B58.4B$24.4B58.
4B$25.4B58.4B$26.4B58.4B$27.4B58.4B$28.4B58.4B$29.4B58.4B$30.4B58.4B$
31.4B58.4B$32.4B58.4B$33.4B58.4B$34.4B58.4B$35.4B58.4B$36.4B58.4B$37.
4B58.4B$38.4B58.4B$39.4B58.4B$40.4B58.4B$41.4B58.4B$42.4B58.4B$43.4B
58.4B$44.4B58.4B$45.4B58.4B$46.4B58.4B$47.4B58.4B$48.4B58.4B$49.4B58.
4B$50.4B58.4B$51.4B58.4B$52.4B58.4B$53.4B58.4B$54.4B58.4B$55.4B58.4B$
56.4B58.4B$57.4B58.4B$58.4B58.4B$59.4B58.4B$60.4B58.4B$61.4B58.4B$62.
4B58.4B$63.4B42.A15.4B172.2A$64.4B40.A.A15.4B171.2A7.2A$65.4B40.2A16.
4B179.A$66.4B58.4B176.A.A$67.4B58.4B175.2A6.A$68.4B58.4B180.3A$69.4B
58.4B178.A$70.4B29.2A27.4B177.2A$71.4B28.2A28.4B$72.4B58.4B$73.4B58.
4B173.2A$74.4B58.4B172.2A$75.4B58.4B154.2A$76.4B58.4B152.A.A22.2A$77.
4B58.4B151.A24.A.A$78.4B58.4B149.2A25.A$79.4B58.4B$80.4B58.4B$81.4B
58.4B$82.4B58.4B$83.4B58.4B$84.4B58.4B$85.4B58.4B140.A7.2A$86.4B19.2A
37.4B138.A.A7.A$87.4B18.2A38.4B137.2A5.3A$88.4B58.4B143.A$89.4B58.4B
179.2A$90.4B58.4B177.A2.A$91.4B7.2A49.4B177.A.A$92.4B6.2A50.4B157.2A
18.A$93.4B58.4B156.A.A$94.4B58.4B157.A$95.4B58.4B156.2A$96.4B58.4B
128.A$97.4B58.4B126.A.A7.2A$98.4B58.4B125.A2.A6.2A$99.4B58.4B125.2A$
100.4B58.4B$101.4B58.4B$102.4B58.4B139.2A34.2A$103.4B58.4B129.2A7.2A
33.A2.A$104.4B58.4B129.A43.A.A$105.4B58.4B128.A.A22.A19.A$106.4B58.4B
128.2A21.A.A$107.4B58.4B150.A.A$108.4B46.2A10.4B150.A$109.4B45.2A11.
4B139.2A20.A9.A$110.4B58.4B138.A.A18.A.A7.A.A$111.4B58.4B139.A18.A2.A
5.A2.A$112.4B58.4B138.2A18.2A7.2A$113.4B58.4B$114.4B58.4B$115.4B58.4B
$116.4B58.4B156.A$117.4B58.4B155.3A$118.4B58.4B157.A$119.4B58.4B155.
2A$120.4B58.4B169.2A$121.4B58.4B168.A$122.4B58.4B164.2A.A$123.4B58.4B
162.A2.A$124.4B36.2A20.4B162.2A$125.4B35.2A21.4B131.2A13.2A$126.4B58.
4B130.2A13.2A$127.4B58.4B$128.4B58.4B$67.2A60.4B24.2A32.4B$67.A62.4B
23.2A33.4B$69.A61.4B58.4B101.2A$49.2A14.5A62.4B58.4B100.2A$50.A13.A
68.4B58.4B125.2A6.A.2A$50.A.A12.3A66.4B58.4B124.A.A3.3A.2A$51.2A15.A
66.4B58.4B125.A2.A$65.4A67.4B58.4B96.2A26.2A2.3A.2A$60.2A3.A3.2A66.4B
58.4B95.2A32.A.A$60.2A4.3A2.A66.4B58.4B108.2A18.A.A10.2A$68.A.2A67.4B
58.4B107.A.A18.A11.2A$68.A71.4B58.4B108.A$67.2A72.4B58.4B97.2A8.2A$
142.4B58.4B97.A$143.4B58.4B93.3A$59.2A83.4B58.4B92.A$59.A85.4B58.4B
156.2A$60.3A83.4B58.4B155.A.A$62.A84.4B58.4B60.2A93.A$148.4B58.4B59.A
.A$149.4B58.4B59.A$150.4B58.4B$151.4B58.4B$152.4B58.4B$153.4B58.4B$
154.4B58.4B$155.4B58.4B$156.4B58.4B40.A$157.4B58.4B38.A.A$158.4B58.4B
38.2A$159.4B58.4B$160.4B58.4B$161.4B58.4B$162.4B58.4B$163.4B58.4B$
164.4B58.4B$165.4B58.4B$166.4B58.4B$152.A14.4B58.4B$151.A.A14.4B58.4B
$152.2A15.4B58.4B$170.4B58.4B$171.4B58.4B$172.4B58.4B$173.4B58.4B$
174.4B58.4B$102.2A71.4B58.5B$102.2A19.2A51.4B58.4B$123.2A52.4B58.5B$
178.4B59.3B$179.4B57.4B$140.2A38.4B56.3B$140.2A39.4B$107.2A73.4B$107.
2A74.4B$184.4B$185.4B$186.4B$187.4B$188.4B$189.4B$190.4B$191.4B12.2A
4.A$192.4B11.2A3.A.A4.2A$193.4B14.A2.A4.2A$194.4B14.2A$183.2A10.4B$
146.2A34.A2.A10.4B$146.2A34.A.A12.4B$183.A14.4B8.A$199.4B7.3A$200.4B
9.A$139.2A60.4B7.2A$139.2A61.4B21.2A89.A$203.4B20.A89.A.A$204.4B16.2A
.A89.2A$205.4B14.A2.A$206.3B15.2A$194.2A12.3B$125.2A44.2A21.2A12.3B$
125.2A44.2A5$129.2A$129.2A73.A.2A$202.3A.2A19.2A$201.A24.A.A$202.3A.
2A19.A$204.A.A$177.2A8.2A.A13.A.A10.2A$178.A8.2A.3A12.A11.2A$175.3A
15.A$175.A11.2A.3A$188.A.A$188.A.A$189.A12$232.2A$232.A.A$233.A!
The removal of the eater 'opens' a stream from the tape, and the removal of the block 'closes' it by causing the syringe's eater2 to absorb the remainder of the tape. This is sufficient to extract about 1000 generations from the tape, which pulls out the unary encoding of the new state. (The part of the tape that's extracted is determined by the inputs from the neighbours.)
What do you do with ill crystallographers? Take them to the mono-clinic!

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dvgrn
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Re: 0E0P constructions

Post by dvgrn » March 2nd, 2019, 10:09 am

calcyman wrote:There's also the caveat that there's no individual timestep where all of the circuitry is simultaneously present.
That's okay, it's still worth labeling a new LifeHistory routing blueprint to show all the circuitry, and the tracks where all signals go through the entire cycle. Or maybe a custom rule would be better, with enough states to allow each set of one-time circuits that get used up at a particular stage to be a different color... and maybe something subtle to show glider direction that doesn't prevent the pattern from being run, unlike this sample:

Code: Select all

x = 14, y = 16, rule = LifeHistory
12.B$11.FB$10.BF2B$9.FB2F$8.BF2B$7.FB2F$6.BF2B$5.FB2F$4.BF2B$3.FB2F$
2.BF2B$.FB2F$AF2B$AFA$2A!
#C [[ VIEWONLY THUMBNAIL THUMBSIZE 3 ]]
calcyman wrote:The removal of the eater 'opens' a stream from the tape, and the removal of the block 'closes' it by causing the syringe's eater2 to absorb the remainder of the tape. This is sufficient to extract about 1000 generations from the tape, which pulls out the unary encoding of the new state. (The part of the tape that's extracted is determined by the inputs from the neighbours.)
Aha, that makes more sense. Thanks for the pointers. Did I guess more or less right about the likely minimum-population time, then? (as late as possible in the cycle before the first construction arm starts to extend)

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calcyman
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Re: 0E0P constructions

Post by calcyman » March 2nd, 2019, 10:40 am

dvgrn wrote:Aha, that makes more sense. Thanks for the pointers. Did I guess more or less right about the likely minimum-population time, then? (as late as possible in the cycle before the first construction arm starts to extend)
Yes, and it looks like it will be during the first billion generations after the phase of complete_default.mc (which is the phase of the output of isotropic_metafier.py). Rather than being the first time the 'construction arm starts to extend', it will be as late as possible before the front of the construction recipe enters the glider splitter. So it's after this eater2 is deleted, and before the first glider subsequently enters this circuitry:

Code: Select all

x = 321, y = 293, rule = LifeHistory
204.A$203.A.A$204.2A49$60.A191.2A$59.A.A190.2A7.2A$60.2A199.A$259.A.A
$259.2A6.A$265.3A$264.A$54.2A208.2A$54.2A2$263.2A$263.2A$246.2A$245.A
.A22.2A$245.A24.A.A$244.2A25.A7$242.A7.2A$60.2A179.A.A7.A$60.2A179.2A
5.3A$248.A$285.2A$284.A2.A$53.2A230.A.A$53.2A211.2A18.A$266.A.A$268.A
$268.2A$241.A$240.A.A7.2A$240.A2.A6.2A$241.2A3$258.2A34.2A$249.2A7.2A
33.A2.A$250.A43.A.A$250.A.A22.A19.A$251.2A21.A.A$274.A.A$109.2A164.A$
109.2A154.2A20.A9.A$265.A.A18.A.A7.A.A$267.A18.A2.A5.A2.A$267.2A18.2A
7.2A4$289.A$289.3A$292.A$291.2A$306.2A$306.A$303.2A.A$302.A2.A$115.2A
186.2A$115.2A156.2A13.2A$273.2A13.2A3$18.2A88.2A$18.A89.2A$20.A228.2A
$2A14.5A228.2A$.A13.A259.2A6.A.2A$.A.A12.3A256.A.A3.3A.2A$2.2A15.A
257.A2.A$16.4A229.2A26.2A2.3A.2A$11.2A3.A3.2A227.2A32.A.A$11.2A4.3A2.
A240.2A18.A.A10.2A$19.A.2A240.A.A18.A11.2A$19.A245.A$18.2A235.2A8.2A$
256.A$253.3A$10.2A241.A$10.A307.2A$11.3A304.A.A$13.A305.A20$103.A$
102.A.A$103.2A6$53.2A$53.2A19.2A$74.2A3$91.2A$91.2A$58.2A$58.2A8$158.
2A4.A$158.2A3.A.A4.2A$162.A2.A4.2A$163.2A$134.2A$97.2A34.A2.A$97.2A
34.A.A$134.A26.A$161.3A$164.A$90.2A71.2A$90.2A86.2A$178.A$175.2A.A$
174.A2.A$175.2A$145.2A$76.2A44.2A21.2A$76.2A44.2A5$80.2A$80.2A73.4B$
153.3B.3B18.2A$152.8B17.A.A$151.9B18.A$152.7B$128.2A8.2A.A13.3B10.2A$
129.A8.2A.3A12.4B8.2A$126.3A15.A11.5B$126.A11.2A.3A13.5B$139.A.A17.4B
$139.A.A18.4B$140.A20.4B$162.4B$163.4B$164.4B$165.4B$166.4B$167.4B$
168.4B$169.4B$170.4B$171.4B8.3B$172.4B6.4B$173.4B5.5B$174.4B3.6B$175.
4B.7B$176.10B$177.9B$177.9B$176.10B$175.4B.6B$174.4B3.4B$173.4B$172.
4B$171.4B$170.4B$169.4B$168.4B$167.4B$166.4B$165.4B$164.4B$163.4B$
162.4B$161.4B$160.4B$159.4B$158.4B$157.4B$156.4B$155.4B$154.4B$153.4B
$152.4B$151.4B$150.4B$149.4B$148.4B$147.4B$146.4B$145.4B$144.4B$143.
4B$142.4B$141.4B$140.4B$139.4B$138.4B$137.4B$136.4B$135.4B$134.4B$
133.4B$132.4B$131.4B$130.4B$129.4B$128.4B$127.4B$126.4B$125.4B$124.4B
$123.4B$122.4B$121.4B$120.4B$119.4B$118.4B$117.4B$116.4B!
I'm not exactly sure why there's any interest in finding the minimum-population phase, though. A more worthwhile effort would be to implement some parallelised (multi-CPU? Or CUDA, maybe?) implementation of streamlife, so it only takes hours rather than days to run these patterns.
What do you do with ill crystallographers? Take them to the mono-clinic!

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dvgrn
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Re: 0E0P constructions

Post by dvgrn » March 2nd, 2019, 1:44 pm

calcyman wrote:I'm not exactly sure why there's any interest in finding the minimum-population phase, though. A more worthwhile effort would be to implement some parallelised (multi-CPU? Or CUDA, maybe?) implementation of streamlife, so it only takes hours rather than days to run these patterns.
Whenever I think about it, I have the same question for most of the statistics in LifeWiki infoboxes, actually. Heat, volatility, strict volatility -- why are these even a thing, and what for example do the oscillators with strict volatility 0.79 have to do with each other, really?

But I try not to think about it. As long as there's a "Number of cells" line in the infobox, somebody is going to want to know what the number is.

Maybe it won't matter so much once somebody builds a more Golly-friendly CGoL replicator, SMOS and RRO -- they're certainly possible with much lower population.

-- Meant to ask: do you still happen to have the once-per-hour saved snapshots of your one-metatick run for a single cell, especially near the billion ticks that you mentioned? I suppose the whole collection might be useful for generating a routing blueprint.

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