Thread for basic questions

[testitemqlstudop]

Is there an actual rle of an UC building a spider with 35 gliders?

Read my post above; no - the slow-salvo construction and seed itself would already be way too challenging to construct, let alone clean the debris from the puffers.


Also, on the problem of aperiodic debris in the RCT puffers: The method for cleaning this debris up has to be encoded in the 35-glider recipe itself, making more aperiodic debris.

then your rct uc is bull*%#^
if it cant build anything

Reading this gives me a sudden urge to pick up the nearest heavy object and lunge it in your general direction.

SEE THE ****ING POST ABOVE LOL, dvgrn and calcyman both attempted to explain why the constructions would be too big. Long story short: It's a theoretical method, not truly meant to be used in practice.

EDIT: and it's not my RCT, go on lifewiki to search for attribution.

And then there's this.

So literally at the end of the RCT construction, the RCT will make 6 2-engine corderships just to clean up the BLSE?

And what about the mess made by switch engines colliding?

[calcyman]

So literally at the end of the RCT construction, the RCT will make 6 2-engine corderships just to clean up the BLSE?

Yes. (Although it doesn't have to be at the very end of the construction, provided you've already bootstrapped to the point that you no longer rely on the BLSE as your construction arm. A minimal-bounding-box RCT pattern would almost certainly use at least one -- and possibly multiple -- levels of bootstrapping, where it replaces the construction arm with a more efficient and complex alternative.)

And what about the mess made by switch engines colliding?

During the construction, the idea is to direct the construction arm to place lots of one-time eaters in front of all of the GPSEs, so that they're 'caught' before they would otherwise do any damage. One of those eaters produces a glider as a byproduct, and that glider heads towards a seed constellation designed to initiate the 'post-construction' tasks such as removing the periodic debris left by the GPSEs.

This, and more, is all explained in Dave's summary:

viewtopic.php?p=61663#p61663

[gameoflifemaniac]

Thanks, but I don't necessarily mean the phi-calculator-type calculators, but other too (the 8-bit computer or collatz generator or bounded unknown fate). I have a full collection of various computers and calculators and nothing new was emerging.

We don't actually have a "bounded unknown fate" pattern, do we? ... Oh, bounded population, right. I suppose we could build a fixed-bounding-box unknown fate pattern, just by making it big enough. Do an N-bit PRNG with a cycle bigger than we can simulate, let's say, and then test for k consecutive 1's for some value of k that we're not sure will ever show up, but it might. Not sure that's very interesting, really.

The next higher Mersenne prime calculator, period 2^86243-1, would be fun to have. That would be fairly easy to do with quadri-Snarks plus our standard adjustment toolkits. Would that count? People seem to have been unnecessarily scared of building it, but it's really very simple. Could even re-use the base gun and tricky adjustable reset mechanism from the 2^44477-1 oscillator, but of course we have much more compact alternatives these days.

So what else might we want to calculate? We already went over a lot of the optimization details a couple years ago, in the discussion of fine structure constant calculator.

Do you have a handy list of everything in your current collection? Maybe that would help remind people of any gaps. Have you included Dean Hickerson's various mathematical constructions from his Web pages, mostly the "Unusual growth rates" ones?

Yes, I literally included EVERY interesting pattern I could find in this forum and saved it in Golly. Too big to attach all of them.
Look, viewtopic.php?f=2&t=2031&start=825 is the kind of CGOL technology that is interesting to me.
Btw, is it possible to make a 0E0P metacell out of 0E0P metacells?
And it would be great if Calcyman would recreate/rebuild the long lost unbounded binary counter and pseudo-ruler generator from very large awesome patterns.

[dvgrn]

So literally at the end of the RCT construction, the RCT will make 6 2-engine corderships just to clean up the BLSE?

This, and more, is all explained in Dave's summary...

Re-reading that summary, I see there's technically one detail missing, and it's the hardest part of the cleanup problem. Before the six-Cordership fleet is built, and after the two gliders are sent ahead to stop the BLSE without letting any gliders escape, we'll probably also have to trigger a much larger seed, for a salvo that interacts with the terminal BLSE debris -- either to build clean one-time eaters for the six Corderships, or at least to provide something for them to crash into that doesn't allow any Corderships or gliders to escape.

As with the GPSEs, a second "meteor shower" can be arranged to follow along later and clean up any random junk left over at the BLSE crash site. The summary for GPSE cleanup implied that those cleanup Cordership fleets would be specially designed to crash into the junk at the beginning of the debris chains and stop themselves without letting any gliders out.

If that turns out not to be possible, then some gliders might have to be sent ahead to build clean one-time eaters for those Cordership fleets, just like for the BLSE case. Luckily that's a safe backup plan: there's a little extra debris sticking out to the side from the far ends of each of the periodic debris chains, that a glider salvo can get hold of to construct anything that might be wanted out there.

[dvgrn]

Do you have a handy list of everything in your current collection? Maybe that would help remind people of any gaps. Have you included Dean Hickerson's various mathematical constructions from his Web pages, mostly the "Unusual growth rates" ones?

Yes, I literally included EVERY interesting pattern I could find in this forum and saved it in Golly. Too big to attach all of them.

I wasn't looking for an attachment, just a list of the pattern filenames. Without that, it's hard to think of what might be missing. You could also try ZIPping up all the files in groups and sending them in emails to me at b3s23life (at) gmail.com. For whatever reason, moderators are allowed to attach somewhat bigger files to forum posts.

Btw, is it possible to make a 0E0P metacell out of 0E0P metacells?

Sure, that should be fairly straightforward, with a file size about twice as big as a single 0E0P; calcyman explains how to do it here.

[Gustone]

It's a theoretical method, not truly meant to be used in practice

then why invent it?

[Moosey]

It's a theoretical method, not truly meant to be used in practice

then why invent it?

I dunno, why make the 0E0P metacell?
It’s a proof of something (0E0P: all slopes are possible, Smoses, etc. RCT: all synthesizeable things can be made in 35G)

[Gustone]

It's a theoretical method, not truly meant to be used in practice

then why invent it?

I dunno, why make the 0E0P metacell?
It’s a proof of something (0E0P: all slopes are possible, Smoses, etc. RCT: all synthesizeable things can be made in 35G)

but test said it cant be used ...

[Moosey]

but test said it cant be used ...

The average RCT synth would be a few gliders plus one or multiple ridiculously distant glider(s); it could be used for a 35G of anything but it wouldn’t be used for anything in practice— it would be extremely slow and boring.
It looks something like some variation on this:

Code: Select all

#C Imagine you zoomed out a lot.
x = 91, y = 63, rule = B/S012345678
54b3o$55b2o$54bobo$53bo$36bo15bo$16b3obobob3ob2o2b3obob3o10bo$17bo2bob
obo3bobobo5bo11bo$17bo2b3ob3ob2o2b3o3b3o8bo$17bo2bobobo3bobobo7bo7bo$
17bo2bobob3obobob3o3b3o6bo$46bo$45bo$17b3o3b4o17bo$17bobo3bo19bo$17b3o
3bob2o15bo$17bobo3bo2bo14bo$17bobo3b4o13bo$39bo$38bo2$17b2o2b3ob3obo3b
o2bobo4b2o2b3ob3obo3bo3bobo3b2o2b3ob3obo3bo2bobo$17bobobo3bobobo3bo2bo
bo4bobobo3bobobo3bo3bobo3bobobo3bobobo3bo2bobo$17b2o2b3ob3obo3bo3bo5b
2o2b3ob3obo3bo4bo4b2o2b3ob3obo3bo3bo$17bobobo3bobobo3bo3bo5bobobo3bobo
bo3bo4bo4bobobo3bobobo3bo3bo$17bobob3obobob3ob3obo2bo2bobob3obobob3ob
3o2bobo2bobob3obobob3ob3obo$40bo25bo$17b3ob3ob2o4b3obo2bo$17bo3bobobob
o4bo2b2obo$17b3ob3ob2o5bo2bob2o$17bo3bobobobo4bo2bo2bo$17bo3bobobobo3b
3obo2bo2$17b3obobob3ob3o$18bo2bobo2bo2bo$18bo2b3o2bo2b3o$18bo2bobo2bo
4bo$18bo2bobob3ob3o2$17b2o2b3ob2o2b3ob3ob3ob3ob3obo2bo$17bobo2bo2bobob
o3bo4bo3bo2bobob2obo$17bobo2bo2b2o2b3obo4bo3bo2bobobob2o$17bobo2bo2bob
obo3bo4bo3bo2bobobo2bo$17b2o2b3obobob3ob3o2bo2b3ob3obo2bo10$b3o6bo6b3o
bobob3o5b3ob3obobob3ob2o2b3o$o3bo4b2o7bo2bobobo7bobo2bo2bobobo3bobobo$
o3bo3b7o3bo2b3ob3o5bobo2bo2b3ob3ob2o2b3o$o3bo4b2o7bo2bobobo7bobo2bo2bo
bobo3bobo3bo$b3o6bo7bo2bobob3o5b3o2bo2bobob3obobob3o2$18b3ob2o2b3o7bob
ob3ob2o2b3o$18bobobobobo9bobobo3bobobo$18b3ob2o2b3o7b3ob3ob2o2b3o$18bo
bobobobo9bobobo3bobobo$18bobobobob3o7bobob3obobob3o!

It totally works, but it’s not terribly useful otherwise.



So, think of it this way.
If you zoomed into a random 1000*1000 area in an RCT synthesis, the chances that you’ll see a glider are incredibly low.

@dvgrn or calcyman or somebody:
Is there a small bounding-box 35G RCT synth of, say, a block, if we don’t worry about:
Removing the excess junk
Anything else, save that the UCC must construct the block; it cannot be part of the junk.


Just a very simple proof-of-concept. Something that fits in lifeviewer (or, at least, is a reasonable size).

[dvgrn]

but test said it cant be used ...

The average RCT synth would be a few gliders plus one or multiple ridiculously distant glider(s); it could be used for a 35G of anything but it wouldn’t be used for anything in practice...

Might as well get the technicalities right: it's definitely several ridiculously distant gliders, namely the ones building the Sakapuffer. I think there are any number of possible starting locations for the glider that's bouncing back and forth between the two locations, basically producing a binary representation of the location of the Sakapuffer.

The GPSEs move at the same speed as the Sakapuffer and have to produce gliders to interact with every glider coming in from the Sakapuffer, so they'll have to start from equally far away, in various different directions. So the gliders constructing the GPSEs will also be ridiculously distant. The only gliders that could start near the eventual construction site would be the ones that build the BLSE elbow-block source (unless there turns out to be a way to use only 33 gliders, and skip the BLSE entirely).

Theory Vs. Practice
The issue that's showing up here is a very old problem, a deep division between mathematician-type people and engineer-type people. Engineers want to see real things actually working:

Here's a specific arrangement of Life cells, and when I run this specific search program on it I see that it's going through all the possible predecessors and none of them work, so it's a Garden of Eden -- beautiful!

Mathematicians are just as happy, or maybe happier, with non-constructive existence proofs:

A Garden of Eden must exist in an 1162907980-by-1162907980 square, so let's just make a big square that's 1162907980 * (2 ^ 676177484973840200) on a side. That pattern has to be a Garden of Eden, and we don't have to care which 1162907980-by-1162907980 squares are actually GoEs, or if there are GoEs smaller than that size -- beautiful!

Early Universality Proofs Were Like That
This is pretty much what Conway and Gosper did in their original 1970s-era proofs of the existence of universal constructors in Life. They never had any particular interest in actually building specific examples of self-replicating B3/S23 patterns, since they would have been far too big and complex to ever run through a full replication cycle. Those proofs were non-constructive existence proofs, but that was perfectly fine as far as they were concerned.

Then various unreasonable engineer-type people came along later and figured out how to build specific examples of self-constructing patterns. The engineers were much happier after that, but mathematicians like Conway were just puzzled: "yeah, we knew that was possible forty years ago -- why are you wasting time on this trivial stuff?"

RCT Recipes Are Actually Within Reach
The RCT mechanism is in a somewhat similar state at the moment, and a lot of people are reasonably contented to leave it like that.

However, probably if someone wanted to spend a few years on the problem, it would be possible to construct all the specific mechanisms needed to create an RCT recipe for a pulsar or loafer or spider or whatever.

And then if someone wrote a very customized RCT simulator program, and fed in a description of the locations of the 35 gliders, it would be possible to watch the whole construction process run to completion. The simulator would have to take a lot of special-purpose shortcuts -- e.g., just store start and end locations for debris chains, and don't bother tracking the position of each piece of junk; just fast-forward umpteen bajillion ticks and say "okay, that chain is all cleaned up".

Maybe that seems like cheating, but it's not really so different from what HashLife does today. We can prove that HashLife works, and we could also prove that our custom simulator doesn't take any illegal shortcuts.

[gameoflifemaniac]

Is it possible to recreate/rebuild the long lost unbounded binary counter and pseudo-ruler generator from "very large awesome patterns"?

[Moosey]

Is there an online snapshot of the post described here? http://www.conwaylife.com/wiki/IceNine
Also, is it possible that there’s a p(n*127) (n-ish)*(n-ish) 0e0P metacell?
On a related note, would we know by now if there was a spaceship composed solely of pis and rs?

[GUYTU6J]

Is there an online snapshot of the post described here? IceNine

Here

[toroidalet]

On a related note, would we know by now if there was a spaceship composed solely of pis and rs?

There is: use gliders from rs (or interactions of them and pis) to synthesise a universal constructor which reads a memory tape of ash from pis (or interactions again) and encode a seed that produces the whole thing again at an offset (using something fancy like firing-squad synchronization metacells that trigger 1g seeds for pis and rs to synchronise all the pis and rs).



Is there a p4 sparker that can be used to extract a glider from a Herschel conduit in the correct phase but doesn't do anything if the Herschel arrives in any of the other 3 phases mod 4?

[dvgrn]

Yes, I literally included EVERY interesting pattern I could find in this forum and saved it in Golly. Too big to attach all of them.

I wasn't looking for an attachment, just a list of the pattern filenames. Without that, it's hard to think of what might be missing. You could also try ZIPping up all the files in groups and sending them in emails to me at b3s23life (at) gmail.com. For whatever reason, moderators are allowed to attach somewhat bigger files to forum posts.

In the post quoted above I also mentioned the next higher Mersenne-prime oscillator, 2^86243-1, as a possible target. I didn't know that somebody had already posted one of those... in a comment on the Catagolue "pentadecathlon" page.

Why in Conway's name would someone hide the current record-breaking prime oscillator there? Anyway, here's the full pattern -- only 30K in macrocell format:

Code: Select all

[M2] (golly 3.2)
#R B3/S23
#C Pattern type: Oscillator
#C Oscillator type: Large prime oscillator
#C Number of cells: 3,020,026
#C Bounding Box: 8,875x4,005
#C Period: 2^86243-1
#C Mod: 2^86243-1
#C Heat: Unknown
#C Volatility: Unknown
#C Strict volatility: Unknown
#C Discovered by: Anonymous
#C Year of discovery: 2018
#C Rules:
#C Outer-totalistic rules: Unknown, probably B3/S23 only
#C Important rules: Conway Life
#C Number of rules: Probably 1
$$......**$......*$$....****$....*$.......*$
4 0 0 0 1
.......*$$..**$..*..*.*$....**.*$
4 0 3 0 0
5 0 2 0 4
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4 11 12 0 13
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4 0 15 16 17
5 10 2 14 18
6 0 0 5 19
7 0 0 0 20
6 0 0 19 19
7 0 0 22 22
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*..****$**.*$.*.*.**$.*.*.**$**.*$...*$...*.*$....**$
4 0 24 0 25
5 0 0 0 26
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4 0 28 0 0
5 0 29 0 0
6 0 27 0 30
$$$$$.......*$.......*$.....*.*$
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4 0 32 33 34
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4 36 0 37 0
5 0 0 35 38
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4 0 40 41 42
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4 44 45 46 47
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4 0 49 50 0
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4 52 0 53 0
5 43 48 51 54
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4 56 57 58 0
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4 64 65 0 66
5 59 63 0 67
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4 69 0 70 71
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4 73 74 75 45
5 72 63 76 67
6 39 55 68 77
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4 0 0 0 79
5 0 0 0 80
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4 0 82 0 83
5 0 84 0 0
6 0 81 0 85
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4 0 0 0 87
4 0 0 16 0
5 0 0 88 89
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4 0 91 0 92
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4 0 94 95 96
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4 98 99 100 101
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4 103 104 105 106
5 93 97 102 107
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4 0 120 121 122
5 113 116 119 123
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4 130 0 131 132
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6 90 108 124 134
7 31 78 86 135
6 55 55 77 77
6 108 108 134 134
7 137 137 138 138
8 21 23 136 139
9 0 0 0 140
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4 0 148 0 58
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5 258 262 0 265
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4 8 9 11 12
4 263 264 0 15
5 269 262 270 271
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6 266 272 275 280
4 0 25 0 28
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4 50 0 69 0
4 53 0 0 60
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4 0 66 0 0
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4 0 66 0 94
4 0 92 98 99
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......*$...***$...*$$$......**$......*$
4 0 1098 0 1194
$$$**$.*$*$
4 0 0 1196 0
5 0 1193 1195 1197
6 1190 1198 0 0
4 12 0 0 0
5 1200 0 0 0
6 1201 0 0 0
$$.......*$.......*$.....**$.....*$......*$.....**$
$$*.*$.**$...**..*$...*...*$....*$...**..*$
4 0 0 1203 1204
$$.**.*$.*.**$*$$*$*$
$$...**.*$...*.**$.......*$.......*$$.......*$
4 0 0 1206 1207
5 0 0 1205 1208
6 0 0 0 1209
$$...**$...**$*$...**$*..*.*.*$*....*.*$
$$**..**.*$**..*.**$$**$.*$
4 0 0 1211 1212
$$$$**$*$.*$**$
4 0 0 1214 0
5 0 0 1213 1215
6 0 0 1216 0
7 1199 1202 1210 1217
$$$.....**$.....**$$$...**$
4 0 0 0 1219
$......**$.......*$.......*$$....**$....**$
4 0 1221 0 0
$$$.*$**$
...**$
$$$$$.**$.**$
4 1223 1224 0 1225
5 0 1220 1222 1226
6 0 0 0 1227
$..**$..**$
4 0 0 1229 0
5 0 1230 0 0
6 0 1231 0 0
7 0 1228 0 1232
8 1169 1187 1218 1233
9 913 925 1065 1234
$.......*$$.....***$.....*$
4 0 0 0 1236
......**$......**$$$$.......*$
4 0 1192 178 1238
$$$$.**$.**$
**$**$$$$$.**$..*$
4 0 1240 1241 0
5 1237 1239 0 1242
*$.*$.*$.**$
$$$$*$.*$*$.***$
4 1244 0 1245 0
4 1130 0 0 0
$$...**$...**$
4 0 0 1248 0
5 1246 0 1247 1249
4 0 1192 0 0
**...**$....*.*$....*$...**$..*$..***$.....*$....**$
$$.....**$.....**$
4 1252 0 1253 0
$$$$$.....**$......*$.....*$
4 0 0 0 1255
$$$$$..**$.*.*$.*$
4 0 0 1257 0
5 1251 1254 1256 1258
$$$$$......**$......*$.......*$
$$..**$..**$
4 0 1260 0 1261
.*$
4 60 0 1263 0
$$$$$$..**$..*$
...***$.....*$
4 1265 0 1266 0
5 1262 1264 1267 0
6 1243 1250 1259 1268
$$$$$......*$.....*.*$......*$
.....***$$...*****$..*....*$.*..*$.*.**$.*.....*$.*....*$
.**..*$......**$
4 1270 1271 0 1272
**$$$$$$$*$
4 1274 214 118 219
$$$.....**$.....**$
$$$$$$......**$.....*.*$
4 0 1276 0 1277
5 1273 1275 1278 1251
$...**$.*..*$.**$......**$......*$....*.*$...*.*$
4 0 0 1280 0
*...*$*$
4 1282 0 0 0
.*$*.*$..*$**$
4 948 1284 0 0
5 1281 0 1283 1285
.....*$....**$
4 0 1287 0 1192
$$$$$$.**...**$..*...**$
$$$$$$.*$.***$
**$......**$.......*$.......*$
....*$.***$.*$.*$*$
4 1289 1290 1291 1292
5 1288 1293 0 0
4 0 87 0 1082
5 0 1295 0 0
6 1279 1286 1294 1296
7 0 1269 0 1297
4 0 0 0 1229
4 720 0 0 145
4 0 0 1011 0
5 1299 0 1300 1301
$$$.**$.**$$$*$
....*.*$......*$......**$
4 1303 1304 118 0
5 1305 0 0 0
6 1302 0 1306 0
7 0 0 1307 0
4 0 0 1098 1253
5 0 0 0 1309
$$....**$...*.*$...*$..**$
4 0 1311 1051 1074
$$$..**$..**$$$...**$
4 0 0 1313 0
4 0 1118 0 0
5 0 1312 1314 1315
6 0 0 1310 1316
7 0 0 0 1317
8 1298 1308 0 1318
$$$$$$...**.**$...*.**$
$$$$$$$...**.**$
4 0 1320 0 1321
...*.**$.**$.*$..*$.**$.*$..*$.**$
...**.**$...*.**$
4 0 1323 0 1324
5 0 1322 0 1325
.......*$.......*$.....**$.....*$......*$.....**$.*.....*$**.....*$
*.*$.**$...**..*$...*...*$....*$...**..*$*.*$.**$
..**$..*$...*$..**$..*$...*$..**$.*$
4 1327 1328 1329 0
.**.*$.*.**$*....**$.....*$*.....*$*....**$.**.*$.*.**$
...**.*$...*.**$.**$.*$..*$.**$...**.*$...*.**$
4 1331 1332 0 0
.*$**$
4 125 0 1334 0
5 1330 1333 1335 0
6 1326 1336 0 0
....**.*$**..*.**$.*$*$**$.*$*...**.*$**..*.**$
4 153 1338 0 0
$$**$*$.*$**$
$$$$$$.....**$.....*.*$
$$$$$$**.*$*.**$
4 1340 0 1341 1342
5 1339 1343 0 0
*$**$.*$*$**$.*$*$**$
4 698 0 1345 0
.*$*$**$.*$*$**$.*$*$
4 1347 0 125 0
5 1346 0 1348 0
6 1344 1349 0 0
7 1337 1350 0 0
4 0 0 0 981
5 0 0 0 1352
6 0 0 0 1353
4 1106 0 0 250
4 60 0 12 0
4 1119 0 0 0
$$$$**$*$.***$...*$
4 0 955 0 1358
5 1355 1356 1357 1359
$$$$$$......*$......**$
4 0 1361 1113 0
$$$$$$$*.....**$
.*...*$**...**$
4 1363 166 1364 1112
4 178 0 1051 1178
$.**$.**$
......**$......*$
4 0 0 1367 1368
5 1362 1365 1366 1369
6 0 0 1360 1370
4 0 914 0 0
....*$..*.*$..**$$$.......*$.......*$
4 96 145 0 1373
5 0 0 1372 1374
5 0 0 1054 0
$$$$$....**$....*$..*.*$
.*.*$..*$
$$$$$$.**$.**$
4 1377 0 1378 1379
$*$*$**$
4 0 1098 1381 34
$$.....**$.....*$......**$$...**$...*.*$
$$.......*$...**..*$*.*.*$*.*$.**$
.....*$.....**$
4 1383 1384 1385 0
5 1380 0 1382 1386
$$$.....**$.....*$...*.*$...**$
4 0 1388 0 0
$$$$......**$......*$$.......*$
$$$$$....**$....**$
4 0 1390 0 1391
4 45 0 0 0
.....*$.....*.*$..**.*.*$..*.**.*$.......*$.......*$
....**$*..*..*$....*.*$.....*$.**$..*$*....*$.*****$
4 157 0 1394 1395
5 1389 1392 1393 1396
6 1375 1376 1387 1397
7 0 1354 1371 1398
..**$.......*$.....***$....*$....**$
4 214 0 1400 0
5 0 0 0 1401
6 0 0 1402 0
$$$$..**$..**$
$$$$$$......**$.....*$
4 0 1404 1405 16
$$$$$$**$**$
4 0 1407 0 954
......*$.......*$
4 1409 118 0 0
5 1406 1408 1410 0
$.*$.***$....*$...*.*$....*$*$*$
4 1412 0 1079 0
$$$$.....*$....*.*$....*.*$...**.**$
4 0 0 0 1414
$$**$**$
4 0 0 0 1416
$...**.**$...**.*$$$$...**$...*.*$
4 0 1418 920 1385
5 1413 1415 1417 1419
.*$*$
4 1421 0 0 0
5 89 0 1422 0
6 1411 0 1420 1423
7 1403 0 1424 0
8 1351 0 1399 1425
4 1099 954 0 0
5 0 1427 0 0
...*$....***$......*$
4 1429 0 0 0
$$$.....**$.....*$**....**$*.*$..*$
4 0 1431 0 219
5 1430 1432 0 0
6 1428 1433 0 0
7 0 1434 0 0
8 0 1435 0 0
4 218 0 0 0
5 1437 0 0 0
6 1438 0 0 0
$...*$..*.*$...*$
4 0 1440 0 0
5 0 1441 0 0
6 0 1442 0 0
7 1439 1443 0 0
8 1444 0 0 0
9 1319 1426 1436 1445
10 670 1235 0 1446
$$$$..*.**$..**.*$$*****$
*....*$...*..*$...**.*$*.....*$.*....*$..*..**$**$
**$.*$*$**$
4 1448 0 1449 1450
5 1451 0 0 0
..**$..*$...***$.....*$
4 1453 0 0 0
5 1454 0 0 0
6 1452 0 1455 0
7 0 0 1456 0
8 0 0 1457 0
....*.*$....*.*$..***.**$.*$..***.**$....*.**$
$$......*$....***$...*$...**$
4 715 0 1459 1460
$$$$......*$......**$
4 0 1462 0 87
$$**$*$*$
4 1464 0 16 0
5 1461 0 1463 1465
6 0 0 0 1466
....**$...*..*$...*.*$....*$
4 1468 0 0 0
$$$$$.......*$.......*$......**$
$$.....**$.*...**$*.*$.*$
...**$.*..*$.**$
4 1470 1471 0 1472
$$*$***$...*$..**$
4 0 0 0 1474
5 1469 1473 0 1475
$$$..**$..**$
$$......**$.....*$.....*.*$......*$
4 0 1082 1477 1478
$$$*..**$....*..*$....*.*$.**.*..*$.*..*$
4 118 0 1480 36
......*$......**$$....****$....*$..*.*..*$..**...*$
4 0 1482 0 0
...*$***$$*$*$$*$
4 1484 0 0 0
5 1479 1481 1483 1485
$$$....*$....***$.......*$......**$
4 0 0 0 1487
..**$..**$
4 0 0 1489 0
.**$.**$
4 0 0 0 1491
5 1488 1490 1492 0
*$*$$$**$*$.***$...*$
4 0 0 1192 1494
.**$.*$.*....*$*...***$...*$...**$
$$$$$$...**$...**$
4 965 1496 1497 33
5 1495 0 1498 0
6 1476 1486 1493 1499
7 1467 0 1500 0
8 0 0 1501 0
9 1458 0 1502 0
$$$..*$..***$.....*$....*.*$.....*$
4 0 1504 0 1045
...**$....*$....*.*$.....**$$$$.....**$
....*.*$....*$...**$
4 0 1506 0 1507
5 0 1505 0 1508
......**$.....*$.....**$
4 0 0 0 1510
4 16 0 118 0
$$$$$$......**$......**$
4 0 1513 0 1013
5 1511 1512 1514 0
4 0 1046 0 0
$$$$$$$....*$
....***$.......*$......**$
4 0 1517 0 1518
5 0 1516 0 1519
......**$......**$
4 218 1082 1521 0
$$$$$...**$...*$.*.*$
4 1334 0 1523 0
4 583 0 0 0
5 1522 1524 0 1525
6 1509 1515 1520 1526
$$$*$$***$..*$
4 0 1031 1051 1528
5 0 1529 0 0
4 0 930 0 1039
..**$..*$*.*$**$$.....*$...***$..*$
4 0 0 0 1532
**$**$
4 1534 0 0 0
4 0 219 0 0
5 1531 1533 1535 1536
4 0 0 0 965
$$......**$......*$....*.*$**..**$**$
$$*$*....**$.....**$
4 1539 0 1540 0
4 1048 0 0 0
5 1538 1541 0 1542
6 1530 1537 0 1543
7 1527 0 1544 0
8 1545 0 0 0
9 1546 0 0 0
10 1503 0 1547 0
11 910 0 1447 1548
12 660 888 672 1549
13 600 645 673 1550
14 595 1551 0 0
$$$$......**$.....*.*$.....*$....**$
4 0 0 0 1553
$.......*$......*$......**$
.*$**$$$$$......**$.......*$
.......*$*....***$*...*$....****$.......*$....***$...*$....****$
4 1555 1556 955 1557
5 0 0 1554 1558
.**$..*$**$$$$$*$
4 0 0 1560 0
5 0 0 1561 0
5 1172 0 0 0
6 1559 1562 252 1563
7 0 1564 0 0
8 0 1565 0 0
9 0 1566 0 0
10 0 0 1567 0
11 0 0 1568 0
12 1569 0 0 0
13 0 0 1570 0
14 1571 0 0 0
15 1552 1572 0 0
16 0 0 0 1573

I did confirm that this pattern is in fact a period 2^86,243-1 oscillator: 43114 quadri-Snarks, two CP semi-Snarks, and two CC semi-Snarks attached to a base gun with period 8192 = 2^13. 43113*2+4+13 = 86243, and it can be easily seen that the reset mechanism is adjusted to subtract one tick.

Again, this pattern is only 30K, so clearly we're not being nearly ambitious enough. Anyone want to build an oscillator for the largest Mersenne prime currently known,

2^82,589,933-1 ?

[gameoflifemaniac]

Also, I don't think Golly would handle an oscillator with the largest known prime period.
Is it possible to recreate/rebuild the long lost unbounded binary counter and pseudo-ruler generator from Calcyman's "very large awesome patterns" thread?

[dvgrn]

Also, I don't think Golly would handle an oscillator with the largest known prime period.

I don't think Golly will have any more trouble than it has with period 2^86,243-1, really. Sure, you won't be able to run it through a full cycle, but you'll be able to see all the circuitry working and do some simple math to confirm the period.

Is it possible to recreate/rebuild the long lost unbounded binary counter and pseudo-ruler generator from Calcyman's "very large awesome patterns" thread?

The O(log(t)) binary counter doesn't seem terribly interesting compared to O(sqrt(log(t))), but it would be very easy to re-create with today's technology. It would end up much more compact than whatever calcyman came up with way back in 2010, pre-Snark and pre-syringe. Start a thread for the project and make a credible attempt to do some of the wiring for it, and I'm fairly sure someone would come along to help complete the pattern.

The pseudo-ruler generator is a bit trickier. If I'm reading the linked message above correctly, it might have been a first use of calcyman's diagonal block-matrix printer (later used in the phi and pi calculators). I guess maybe similar N-state computer wiring could have been attached to it, but with a simpler program / fewer states than the 177-line or 188-line code for the phi and pi calculators.

Not sure what happened when the pseudo-ruler sequence got up into two-digit numbers (if I even have the right sequence -- A087230?) Did the printer print spaces between successive terms in the sequence? Or was it some other sequence that never gets to two digits?

It would be neat to reverse-engineer the N-state computer part of the phi calculator, and get to where we could compile similar code to do other calculations. Could replace the old Silver reflectors with something more modern -- Scorbie Splitters, maybe.

EDIT: Just tried writing a script to pack enough quadri-Snarks into a square, to get to the largest known Mersenne prime. The unit of repetition turned out to be something like 60x32, so I made it 64x32 to reduce the size of the macrocell file.

Boy, did it ever keep the size down! I accidentally calculated the number of multipliers as if they were semi-Snarks instead of quadri-Snarks, so ended up was twice as many quadri-Snarks as the highest Mersenne prime needs -- and the macrocell file is still less than 5K, even though the pattern is 200K cells on a side and the RLE would be humongous:

Code: Select all

[M2] (golly 3.2)
#R B3/S23
$$$$$$$....*..*$
4 0 0 0 1
$$$$$$$*$
4 0 0 3 0
5 0 0 2 4
6 0 0 0 5
6 0 0 5 5
7 0 0 6 7
7 0 0 7 7
8 0 0 8 9
8 0 0 9 9
9 0 0 10 11
9 0 0 11 11
10 0 0 12 13
10 0 0 13 13
11 0 0 14 15
11 0 0 15 15
12 0 0 16 17
12 0 0 17 17
13 0 0 18 19
13 0 0 19 19
14 0 0 20 21
14 0 0 21 21
15 0 0 22 23
15 0 0 23 23
16 0 0 24 25
16 0 0 25 25
17 0 0 26 27
6 0 0 5 0
7 0 0 29 0
8 0 0 30 0
9 0 0 31 0
10 0 0 32 0
11 0 0 33 0
12 0 0 17 34
13 0 0 19 35
14 0 0 36 0
15 0 0 37 0
16 0 0 38 0
17 0 0 27 39
18 0 0 28 40
$$$$$....**$....*$......*$
....****$$..******$.*$.**..**$.....**$
..*****$..*$.....***$.....*$$**$*..*.**$..**.**$
$$*$*....**$.....**$
4 42 43 44 45
.*$.*$*.**$*.*..*$*...**$**$
4 47 0 0 0
$$...*$.***$*$**$
$$$$$$$...**..*$
4 49 0 0 50
$$$$**$*$.***$...*$
$$..**.**$*..*.**$**$$.....*$.....***$
$$$$$.....**$*....**$*$
4 52 0 53 54
5 46 48 51 55
$$$$....**$.....*$...*$...**$
4 0 0 57 0
$$$$$$.......*$.......*$
$$$$$$*$..*$
4 0 0 59 60
.**...*$*..****$**.*$.*.*.**$.*.*.**$**.*$...*$...*.*$
$$$....**$....**$
....**$$$$......*$......**$
$...**$...*$**.*...*$.*.**..*$.*$.*.....*$.**$
4 62 63 64 65
.....*.*$.....**$
.**$*$*$***$...*$..**$
$$$*$*$$*$*$
$$$$$.....**$.....**$
4 67 68 69 70
5 58 61 66 71
$$$......*$......**$
..*.****$..*$**.*****$.*.*$...*.**$..**.**$
$$$.....**$.....**$
4 73 74 0 75
..*$..******$**...*$..*$.**$$$...*..*$
$*$*$$.....**$.**..**$.*$..******$
...*****$$...****$...*..*$$$.....**$.....**$
**$.*..****$....*..*$$$..**$*..*$**$
4 77 78 79 80
$$$$..**$...*$***$*$
$$.....**$.....**$$$...*..*$...****$
$$**$*..*$..**$$$....*..*$
4 0 82 83 84
$$*$***$...*$..**$
4 0 86 3 70
5 76 81 85 87
6 0 56 72 88
$$$......*$**....**$*...**$*.*..*$*.**$
.*$.*$*$
4 90 74 91 75
5 92 81 85 87
6 56 56 93 93
......*$......**$
4 0 95 0 0
$$$$$......**$......*$
$$$$..**.**$...*.**$.*.*$**.*****$
..*$..*.****$...**..*$
4 97 98 0 99
5 96 100 0 0
$...*****$...*..*$$$.**$..*$**...*$
.*..****$**$..******$.*$.**..**$.....**$$*$
..******$..*$.....***$.....*$$**$*..*.**$..**.**$
*$$*$*....**$.....**$
4 102 103 104 105
.*$.*$*.**$*.*..*$*...**$**....**$......*$
4 107 98 0 99
5 106 108 51 55
6 101 109 72 88
6 109 109 93 93
7 89 94 110 111
7 94 94 111 111
7 110 111 110 111
7 111 111 111 111
8 112 113 114 115
8 113 113 115 115
8 114 115 114 115
8 115 115 115 115
9 116 117 118 119
9 117 117 119 119
9 118 119 118 119
9 119 119 119 119
10 120 121 122 123
10 121 121 123 123
10 122 123 122 123
10 123 123 123 123
11 124 125 126 127
11 125 125 127 127
11 126 127 126 127
11 127 127 127 127
12 128 129 130 131
12 129 129 131 131
12 130 131 130 131
12 131 131 131 131
13 132 133 134 135
13 133 133 135 135
13 134 135 134 135
13 135 135 135 135
14 136 137 138 139
14 137 137 139 139
14 138 139 138 139
14 139 139 139 139
15 140 141 142 143
15 141 141 143 143
15 142 143 142 143
15 143 143 143 143
16 144 145 146 147
16 145 145 147 147
16 146 147 146 147
16 147 147 147 147
17 148 149 150 151
$$$$$$...**$.*..*$
4 0 0 153 0
$$$$......**$......*$$.......*$
$$$$$$*$*$
4 0 0 155 156
.**.*.*$...*.**$...*$.***$*$**$
$$$......**$......**$
$.......*$$...**$...**..*$$...**$...*$
4 158 159 0 160
.....*$.....***$$.....**$.....**$$$......*$
.**$*..*$*.**$*.*$*.*$*.**$*$*$
......**$*$*$*.**$*.*..*$..*.**$..*$.**$
4 162 163 164 0
5 154 157 161 165
4 0 86 3 0
5 92 81 85 167
$$$$**$*...**$*.*..*$*.**$
.....*$....**$
4 169 170 91 0
5 171 0 0 0
6 56 166 168 172
5 106 48 51 55
6 174 166 168 172
7 173 0 175 0
7 175 0 175 0
8 176 0 177 0
8 177 0 177 0
9 178 0 179 0
9 179 0 179 0
10 180 0 181 0
10 181 0 181 0
11 182 0 183 0
11 183 0 183 0
12 129 184 131 185
12 131 185 131 185
13 133 186 135 187
13 135 187 135 187
14 188 0 189 0
14 189 0 189 0
15 190 0 191 0
15 191 0 191 0
16 192 0 193 0
16 193 0 193 0
17 149 194 151 195
4 49 0 0 0
5 106 108 197 55
.....*.*$.....**$**$*.*$*$
4 199 68 69 0
5 58 61 66 200
..*$..*****$......*$....*$....**$
$$$$.....**$.**..**$.*$..******$
$....****$....*..*$
4 202 203 0 204
5 0 205 0 0
6 101 198 201 206
4 169 0 91 0
5 208 205 0 0
6 198 198 209 209
5 96 0 0 0
6 211 0 0 0
7 207 210 212 0
7 210 210 0 0
8 114 115 213 214
8 115 115 214 214
9 215 216 0 0
9 216 216 0 0
10 122 123 217 218
10 123 123 218 218
11 126 127 219 220
11 127 127 220 220
12 130 131 221 222
12 131 131 222 222
13 223 224 0 0
13 224 224 0 0
14 138 139 225 226
14 139 139 226 226
15 227 228 0 0
15 228 228 0 0
16 229 230 0 0
16 230 230 0 0
17 150 151 231 232
5 106 48 197 55
6 234 166 209 172
7 235 0 0 0
8 177 0 236 0
9 237 0 0 0
10 181 0 238 0
11 183 0 239 0
12 131 185 222 240
13 224 241 0 0
14 189 0 242 0
15 243 0 0 0
16 244 0 0 0
17 151 195 232 245
18 152 196 233 246
19 0 41 0 247

I'll rework the script a bit and then post it along with a new candidate record-biggest-prime oscillator.

[gameoflifemaniac]

Also, I don't think Golly would handle an oscillator with the largest known prime period.

I don't think Golly will have any more trouble than it has with period 2^86,243-1, really. Sure, you won't be able to run it through a full cycle, but you'll be able to see all the circuitry working and do some simple math to confirm the period.

Is it possible to recreate/rebuild the long lost unbounded binary counter and pseudo-ruler generator from Calcyman's "very large awesome patterns" thread?

stuff

Actually, I made an unbounded binary counter a year ago.

Code: Select all

x = 1300, y = 317, rule = B3/S23
1283bo$1177b2o102bo3bo$1175bo4bo105bo$1181bo99bo4bo8b3o$1175bo5bo14b4o
24b2o56b5o7b5o$1115bo60b6o13bo3bo21b3ob2o67b3ob2o$1009b2o102bo3bo81bo
21b5o71b2o$760bo246bo4bo105bo76bo2bo23b3o$654b2o102bo3bo250bo99bo4bo8b
3o165bo$652bo4bo105bo243bo5bo14b4o24b2o13bo42b5o7b5o166bo$658bo99bo4bo
8b3o233b6o13bo3bo21b3ob2o12bo54b3ob2o135bo3bob2o18bo4bo$652bo5bo14b4o
24b2o56b5o7b5o255bo21b5o71b2o136bob3obob2obo3bo3bo3bo3bo3bo$653b6o13bo
3bo21b3ob2o67b3ob2o250bo2bo23b3o14bob3o143bobo53bo2bo3bo3bo3bo4b4o$
676bo21b5o71b2o293b2o2b3o51bo91b2o46bob3obob2obo3bo3bo3bo$672bo2bo23b
3o367b2o4b2o19bo28bo3bo89b2o46bo3bob2o$713b2o57bo297bo3b2o15b3obobo32b
o$710b2ob2o26bo28bo3bo316b3obob4o3bo3bo3bo3bo3bo3bo5bo161b4o$712b2obob
2o18b3o2bob2o29bo324bo3bo3bo3bo3bo3bo3b7o27b4o129b6o$714b2ob2o18b3ob2o
b2o3bo3bo3bo3bo3bo3bo5bo315b3obob4o3bo3bo3bo3bo3bo36b6o53b6o69b4ob2o$
746bo2bo3bo3bo3bo3bo3b7o294bo3b2o15b3obobo59b4ob2o51bo5bo73b2o$714b2ob
2o18b3ob2ob2o3bo3bo3bo3bo3bo303b2o4b2o19bo64b2o58bo60b5o$712b2obob2o
18b3o2bob2o323b2o2b3o48b4o87bo4bo60bo4bo$710b2ob2o26bo329bob3o47b6o88b
2o67bo$713b2o54b4o275b6o69b4ob2o78b2o71bo3bo$768b6o273bo5bo17bo55b2o
77bo4bo71bo$693b6o69b4ob2o278bo17bo42b5o93bo$692bo5bo73b2o273bo4bo60bo
4bo87bo5bo$698bo60b5o285b2o67bo88b6o$692bo4bo60bo4bo276b2o71bo3bo$694b
2o67bo274bo4bo71bo$685b2o71bo3bo281bo126b3o$683bo4bo71bo277bo5bo125b5o
$689bo349b6o125b3ob2o$683bo5bo483b2o$684b6o468b6o$1157bo5bo$1163bo$
947b5o205bo4bo$841b6o13bo2bo23b3o56bo4bo207b2o$840bo5bo17bo21b5o60bo
10b2o$846bo13bo3bo21b3ob2o54bo3bo8b3ob2o$840bo4bo15b4o24b2o57bo10b5o$
842b2o116b3o2$728bo3bo33b5o166bo$587b5o68b6o13bo2bo23b3o18bobobobo31bo
4bo165bobo2bob2o14b5o$481b6o13bo2bo23b3o56bo4bo67bo5bo17bo21b5o60bo10b
2o155b4obob2obo3bo3bo6bo$480bo5bo17bo21b5o60bo10b2o61bo13bo3bo21b3ob2o
17b2ob2o32bo3bo8b3ob2o161bo2bo3bo3bo6bo248b3o$486bo13bo3bo21b3ob2o54bo
3bo8b3ob2o54bo4bo15b4o24b2o7b3o47bo10b5o155b4obob2obo3bo3bo5bo143b4o
42bo58b5o$480bo4bo15b4o24b2o57bo10b5o57b2o53bo6b2o3b2ob2o3b2o41b3o85b
3o66bobo2bob2o15bo144b6o39bo3bo56b3ob2o$482b2o116b3o120b2o11b3o127b2ob
2o66bo167b4ob2o15b2o26bo58b2o8b5o$723b2obo2bobo2bob4o2b2o122b2o14b2o
225b2o14b2ob2o20bo4bo67bo4bo$584bo130bob4o3bo11bo2bo4b2o32b5o85b3o9bo
4bo74b2o18bo144b4o22b5o72bo$498b3o79b3o2bob2o10b5o112bo2b2o4b3o5b3o6bo
b2o3bo3bo3bo3bo3bo3bo3bo3bo4bo85bo2bo14bo61bo7b4ob2o18b2o143b2o95bo3bo
$497bo3bo78b3ob2ob2o3bo3bo6bo142bo2bo3bo3bo3bo3bo3bo3bo3bo4bo85bo3bo7b
o5bo59bo3bo5b6o18b2o86bo156bo$496bo5bo86bo2bo3bo6bo112bo2b2o4b3o5b3o6b
ob2o3bo3bo3bo3bo3bo3bo3bo4bo2bo86bo3bo8b6o64bo5b4o106bo136bo3bo15b3o$
496bo5bo77b3ob2ob2o3bo3bo5bo20bo91bob4o3bo11bo2bo4b2o123b2obo73bo4bo
115b3o57b2o74bobobobobo12b4o$496bo5bo77b3o2bob2o11bo23b2o97b2obo2bobo
2bob4o2b2o203b5o251bobo3b4o11b2ob2o$497bo3bo82bo38b2o76b2o20b2o11b3o
387bo2bo83bob3ob3o4b2o$498b3o21b2o175bo4bo11bo6b2o3b2ob2o3b2o41b2o345b
3o74bobo3b4o$520bo4bo74b2o103bo11b3o47bo7b4ob2o90b6o325bobobobobo$502b
2o22bo61bo7b4ob2o96bo5bo22b2ob2o32bo3bo5b6o90bo5bo326bo3bo$502b2o16bo
5bo59bo3bo5b6o98b6o64bo5b4o97bo$521b6o64bo5b4o126bobobobo31bo4bo100bo
4bo344b6o$586bo4bo136bo3bo33b5o102b2o255b2o17b2o69bo5bo$587b5o538b2o
13b4ob2o74bo$1145b6o63b2o4bo4bo$691b6o449b4o61b3ob2o5b2o$512b6o172bo5b
o514b5o$511bo5bo178bo515b3o$517bo172bo4bo441b4o$511bo4bo175b2o442b6o$
513b2o621b4ob2o$1140b2o5$1130b3o$1128b3ob3o28b5o$1102b4o21b2obobob2o
26bo4bo$640bobo458b6o20bo2bobo2bo31bo5b4o$64bo119bo119bo119bo119bo96b
2o21bo119bo119bo119bo76b4ob2o21b2ob2o28bo3bo5b6o$62b3o117b3o117b3o117b
3o117b3o96bo20b3o117b3o117b3o117b3o80b2o22b2ob2o30bo7b4ob2o$61bo119bo
119bo119bo119bo119bo119bo119bo119bo98bo5b2o7b2o5bo33b2o$54bo6b2o111bo
6b2o111bo6b2o111bo6b2o111bo6b2o118b2o118b2o118b2o118b2o96b6o2b2o5b2o2b
6o$53bobo117bobo117bobo117bobo117bobo582bo3b4ob2o5b2ob4o3bo$54bo119bo
119bo119bo119bo584b2o6bo2bobo2bo6b2o$1120b7ob2o3b2ob7o3bo3bo3bo3bo3bo
3bo3bo4bo2bo$59b2o118b2o118b2o118b2o118b2o118b2o118b2o365bo3bo3bo3bo3b
o3bo3bo3bo4bo$59b2o5b2o111b2o5b2o111b2o5b2o111b2o5b2o111b2o5b2o111b2o
5b2o111b2o5b2o118b2o118b2o92b7ob2o3b2ob7o3bo3bo3bo3bo3bo3bo3bo3bo4bo$
66b2o118b2o118b2o118b2o118b2o118b2o118b2o118b2o118b2o91b2o6bo2bobo2bo
6b2o31b5o$1118bo3b4ob2o5b2ob4o3bo$1119b6o2b2o5b2o2b6o$31b2o16b2o118b2o
118b2o118b2o709bo5b2o7b2o5bo33b3o$31b2o5b2o9b2o118b2o118b2o118b2o718b
2ob2o30bo10b5o$38b2o1089b2ob2o28bo3bo8b3ob2o$64b2o118b2o118b2o118b2o
118b2o94b2o22b2o118b2o118b2o221bo2bobo2bo31bo10b2o$64bobo117bobo117bob
o117bobo117bobo92bobo22bobo117bobo117bobo220b2obobob2o26bo4bo$7b2o8b2o
17b2o28bo119bo119bo119bo119bo94bo24bo119bo119bo221b3ob3o28b5o$7b2o9bo
17b2o28b2o118b2o118b2o118b2o118b2o118b2o118b2o118b2o222b3o$18bobo21b2o
$19b2o21b2o$b2o1141b2o$b2o1139bo4bo$5b2o1141bo$5b2o161b2o972bo5bo$168b
obo337b2o633b6o$169bo336bo4bo349b2o$512bo346bo4bo$2o504bo5bo352bo352b
5o$2o505b6o346bo5bo247bo103bo4bo$860b6o247b2o37b6o64bo5b4o$1112bobo36b
o5bo59bo3bo5b6o$582b5o570bo61bo7b4ob2o$35bo545bo4bo111b2o235b5o211bo4b
o74b2o$12bo21b2o480b6o64bo5b4o98b4ob2o233bo4bo170b2o41b2o$11bo24bo478b
o5bo59bo3bo5b6o97b6o169b6o64bo5b4o160b3o109bo$11b3o19b3o485bo61bo7b4ob
2o97b4o169bo5bo59bo3bo5b6o158b3obo103b3obobo$34bo477bo2bo4bo74b2o173b
3o101bo61bo7b4ob2o156b2o107b3obob4o4bo2bo$511b3o3b2o250b5o94bo4bo74b2o
275bo3bo4bo$510bo64bo128b4o28bo32b3ob2o5b2o88b2o236bo107b3obob4o3bo4bo
$7b2o501b2ob2o57bobobo18bo107b6o25b4o34b2o4bo4bo135bo189bobo104b3obobo
7b5o$8bo502bob2o53b5obob4o3bo3bo3bo5bo105b4ob2o24bo2bo46bo89b2o42bobo
2bob2o182b3o109bo$5b3o504bo66bo3bo3bo3bo6bo108b2o25bo43bo5bo88bo2bo43b
4obob2obo3bo3bo3bo4bo2bo$5bo41b2o519b5obob4o3bo3bo3bo6bo117bo20bo41b6o
89b2o51bo2bo3bo3bo3bo3bo4bo161b2o116b3o$47b2o523bobobo17b5o118bo18bobo
134bobo44b4obob2obo3bo3bo3bo3bo4bo159bo4bo15b4o24b2o57bo10b5o$575bo
141bo18bo11bo169bobo2bob2o20b5o165bo13bo3bo21b3ob2o54bo3bo8b3ob2o$736b
3o8bobobo121b2o44bo191bo5bo17bo21b5o60bo10b2o$477b2o116b3o151b4o359b6o
13bo2bo23b3o56bo4bo$42b2o431bo4bo15b4o24b2o57bo10b5o154bob3ob3ob3ob3ob
3ob3o2b2o2b2o44b2o116b3o267b5o$42b2o437bo13bo3bo21b3ob2o54bo3bo8b3ob2o
149b4o27bob2ob2o41bo4bo15b4o24b2o57bo10b5o$46b2o427bo5bo17bo21b5o60bo
10b2o137b3o8bobobo29b5o48bo13bo3bo21b3ob2o54bo3bo8b3ob2o$46b2o428b6o
13bo2bo23b3o56bo4bo130bo18bo11bo33b3o43bo5bo17bo21b5o60bo10b2o$5b2o21b
2o552b5o130bo18bobo44bo45b6o13bo2bo23b3o56bo4bo$5b2o21bobo653b2o30bo
20bo43bo3bo149b5o$11b2o17bo9b2o641b4o22b5o20bo51bo$11b2o17b2o8b2o625b
2o14b2ob2o20bo4bo20bo2bo43bo4bo$663b4ob2o15b2o26bo20b4o34b2o8b5o$663b
6o39bo3bo23bo32b3ob2o$9b2o653b4o42bo58b5o$9b2o5b2o752b3o$16b2o33$650b
3o$544b4o42bo58b5o$543b6o39bo3bo23bo32b3ob2o$543b4ob2o15b2o26bo20b4o
34b2o8b5o$547b2o14b2ob2o20bo4bo20bo2bo43bo4bo$563b4o22b5o20bo51bo$564b
2o30bo20bo43bo3bo149b5o$462b5o130bo18bobo44bo45b6o13bo2bo23b3o56bo4bo$
356b6o13bo2bo23b3o56bo4bo130bo18bo11bo33b3o43bo5bo17bo21b5o60bo10b2o$
355bo5bo17bo21b5o60bo10b2o137b3o8bobobo29b5o48bo13bo3bo21b3ob2o54bo3bo
8b3ob2o$361bo13bo3bo21b3ob2o54bo3bo8b3ob2o149b4o27bob2ob2o41bo4bo15b4o
24b2o57bo10b5o$355bo4bo15b4o24b2o57bo10b5o154bob3ob3ob3ob3ob3ob3o2b2o
2b2o44b2o116b3o267b5o$357b2o116b3o151b4o359b6o13bo2bo23b3o56bo4bo$616b
3o8bobobo121b2o44bo191bo5bo17bo21b5o60bo10b2o$455bo141bo18bo11bo169bob
o2bob2o20b5o165bo13bo3bo21b3ob2o54bo3bo8b3ob2o$452bobobo17b5o118bo18bo
bo134bobo44b4obob2obo3bo3bo3bo3bo4bo159bo4bo15b4o24b2o57bo10b5o$448b5o
bob4o3bo3bo3bo6bo117bo20bo41b6o89b2o51bo2bo3bo3bo3bo3bo4bo161b2o116b3o
$392bo66bo3bo3bo3bo6bo108b2o25bo43bo5bo88bo2bo43b4obob2obo3bo3bo3bo4bo
2bo$391bob2o53b5obob4o3bo3bo3bo5bo105b4ob2o24bo2bo46bo89b2o42bobo2bob
2o182b3o109bo$390b2ob2o57bobobo18bo107b6o25b4o34b2o4bo4bo135bo189bobo
104b3obobo7b5o$390bo64bo128b4o28bo32b3ob2o5b2o88b2o236bo107b3obob4o3bo
4bo$391b3o3b2o250b5o94bo4bo74b2o275bo3bo4bo$392bo2bo4bo74b2o173b3o101b
o61bo7b4ob2o156b2o107b3obob4o4bo2bo$401bo61bo7b4ob2o97b4o169bo5bo59bo
3bo5b6o158b3obo103b3obobo$395bo5bo59bo3bo5b6o97b6o169b6o64bo5b4o160b3o
109bo$396b6o64bo5b4o98b4ob2o233bo4bo170b2o41b2o$461bo4bo111b2o235b5o
211bo4bo74b2o$462b5o570bo61bo7b4ob2o$992bobo36bo5bo59bo3bo5b6o$740b6o
247b2o37b6o64bo5b4o$387b6o346bo5bo247bo103bo4bo$386bo5bo352bo352b5o$
392bo346bo4bo$386bo4bo349b2o$388b2o633b6o$1022bo5bo$1028bo$1022bo4bo$
1024b2o3$186b2o118b2o118b2o118b2o118b2o118b2o222b3o$186bo119bo119bo94b
o24bo119bo119bo221b3ob3o28b5o$184bobo117bobo117bobo92bobo22bobo117bobo
117bobo220b2obobob2o26bo4bo$184b2o118b2o118b2o94b2o22b2o118b2o118b2o
221bo2bobo2bo31bo10b2o$1009b2ob2o28bo3bo8b3ob2o$169b2o118b2o718b2ob2o
30bo10b5o$169b2o118b2o709bo5b2o7b2o5bo33b3o$999b6o2b2o5b2o2b6o$998bo3b
4ob2o5b2ob4o3bo$186b2o118b2o118b2o118b2o118b2o118b2o118b2o91b2o6bo2bob
o2bo6b2o31b5o$179b2o5b2o111b2o5b2o111b2o5b2o111b2o5b2o111b2o5b2o118b2o
118b2o92b7ob2o3b2ob7o3bo3bo3bo3bo3bo3bo3bo3bo4bo$179b2o118b2o118b2o
118b2o118b2o365bo3bo3bo3bo3bo3bo3bo3bo4bo$1000b7ob2o3b2ob7o3bo3bo3bo3b
o3bo3bo3bo4bo2bo$174bo119bo119bo584b2o6bo2bobo2bo6b2o$173bobo117bobo
117bobo582bo3b4ob2o5b2ob4o3bo$174bo6b2o111bo6b2o111bo6b2o118b2o118b2o
118b2o118b2o96b6o2b2o5b2o2b6o$181bo119bo119bo119bo119bo119bo119bo98bo
5b2o7b2o5bo33b2o$182b3o117b3o117b3o96bo20b3o117b3o117b3o117b3o80b2o22b
2ob2o30bo7b4ob2o$184bo119bo119bo96b2o21bo119bo119bo119bo76b4ob2o21b2ob
2o28bo3bo5b6o$520bobo458b6o20bo2bobo2bo31bo5b4o$982b4o21b2obobob2o26bo
4bo$1008b3ob3o28b5o$1010b3o5$1020b2o$393b2o621b4ob2o$391bo4bo175b2o
442b6o$397bo172bo4bo441b4o$391bo5bo178bo515b3o$392b6o172bo5bo514b5o$
571b6o449b4o61b3ob2o5b2o$1025b6o63b2o4bo4bo$467b5o538b2o13b4ob2o74bo$
466bo4bo136bo3bo33b5o102b2o255b2o17b2o69bo5bo$401b6o64bo5b4o126bobobob
o31bo4bo100bo4bo344b6o$382b2o16bo5bo59bo3bo5b6o98b6o64bo5b4o97bo$382b
2o22bo61bo7b4ob2o96bo5bo22b2ob2o32bo3bo5b6o90bo5bo326bo3bo$400bo4bo74b
2o103bo11b3o47bo7b4ob2o90b6o325bobobobobo$378b3o21b2o175bo4bo11bo6b2o
3b2ob2o3b2o41b2o345b3o74bobo3b4o$377bo3bo82bo38b2o76b2o20b2o11b3o387bo
2bo83bob3ob3o4b2o$376bo5bo77b3o2bob2o11bo23b2o97b2obo2bobo2bob4o2b2o
203b5o251bobo3b4o11b2ob2o$376bo5bo77b3ob2ob2o3bo3bo5bo20bo91bob4o3bo
11bo2bo4b2o123b2obo73bo4bo115b3o57b2o74bobobobobo12b4o$376bo5bo86bo2bo
3bo6bo112bo2b2o4b3o5b3o6bob2o3bo3bo3bo3bo3bo3bo3bo4bo2bo86bo3bo8b6o64b
o5b4o106bo136bo3bo15b3o$377bo3bo78b3ob2ob2o3bo3bo6bo142bo2bo3bo3bo3bo
3bo3bo3bo3bo4bo85bo3bo7bo5bo59bo3bo5b6o18b2o86bo156bo$378b3o79b3o2bob
2o10b5o112bo2b2o4b3o5b3o6bob2o3bo3bo3bo3bo3bo3bo3bo3bo4bo85bo2bo14bo
61bo7b4ob2o18b2o143b2o95bo3bo$464bo130bob4o3bo11bo2bo4b2o32b5o85b3o9bo
4bo74b2o18bo144b4o22b5o72bo$603b2obo2bobo2bob4o2b2o122b2o14b2o225b2o
14b2ob2o20bo4bo67bo4bo$362b2o116b3o120b2o11b3o127b2ob2o66bo167b4ob2o
15b2o26bo58b2o8b5o$360bo4bo15b4o24b2o57bo10b5o57b2o53bo6b2o3b2ob2o3b2o
41b3o85b3o66bobo2bob2o15bo144b6o39bo3bo56b3ob2o$366bo13bo3bo21b3ob2o
54bo3bo8b3ob2o54bo4bo15b4o24b2o7b3o47bo10b5o155b4obob2obo3bo3bo5bo143b
4o42bo58b5o$360bo5bo17bo21b5o60bo10b2o61bo13bo3bo21b3ob2o17b2ob2o32bo
3bo8b3ob2o161bo2bo3bo3bo6bo248b3o$361b6o13bo2bo23b3o56bo4bo67bo5bo17bo
21b5o60bo10b2o155b4obob2obo3bo3bo6bo$467b5o68b6o13bo2bo23b3o18bobobobo
31bo4bo165bobo2bob2o14b5o$608bo3bo33b5o166bo2$722b2o116b3o$720bo4bo15b
4o24b2o57bo10b5o$726bo13bo3bo21b3ob2o54bo3bo8b3ob2o$720bo5bo17bo21b5o
60bo10b2o$721b6o13bo2bo23b3o56bo4bo207b2o$827b5o205bo4bo$1043bo$1037bo
5bo$564b6o468b6o$563bo5bo483b2o$569bo349b6o125b3ob2o$563bo4bo71bo277bo
5bo125b5o$565b2o71bo3bo281bo126b3o$574b2o67bo274bo4bo71bo$572bo4bo60bo
4bo276b2o71bo3bo$578bo60b5o285b2o67bo88b6o$572bo5bo73b2o273bo4bo60bo4b
o87bo5bo$573b6o69b4ob2o278bo17bo42b5o93bo$648b6o273bo5bo17bo55b2o77bo
4bo71bo$593b2o54b4o275b6o69b4ob2o78b2o71bo3bo$590b2ob2o26bo329bob3o47b
6o88b2o67bo$592b2obob2o18b3o2bob2o323b2o2b3o48b4o87bo4bo60bo4bo$594b2o
b2o18b3ob2ob2o3bo3bo3bo3bo3bo303b2o4b2o19bo64b2o58bo60b5o$626bo2bo3bo
3bo3bo3bo3b7o294bo3b2o15b3obobo59b4ob2o51bo5bo73b2o$594b2ob2o18b3ob2ob
2o3bo3bo3bo3bo3bo3bo5bo315b3obob4o3bo3bo3bo3bo3bo36b6o53b6o69b4ob2o$
592b2obob2o18b3o2bob2o29bo324bo3bo3bo3bo3bo3bo3b7o27b4o129b6o$590b2ob
2o26bo28bo3bo316b3obob4o3bo3bo3bo3bo3bo3bo5bo161b4o$593b2o57bo297bo3b
2o15b3obobo32bo$552bo2bo23b3o367b2o4b2o19bo28bo3bo89b2o46bo3bob2o$556b
o21b5o71b2o293b2o2b3o51bo91b2o46bob3obob2obo3bo3bo3bo$533b6o13bo3bo21b
3ob2o67b3ob2o250bo2bo23b3o14bob3o143bobo53bo2bo3bo3bo3bo4b4o$532bo5bo
14b4o24b2o56b5o7b5o255bo21b5o71b2o136bob3obob2obo3bo3bo3bo3bo3bo$538bo
99bo4bo8b3o233b6o13bo3bo21b3ob2o12bo54b3ob2o135bo3bob2o18bo4bo$532bo4b
o105bo243bo5bo14b4o24b2o13bo42b5o7b5o166bo$534b2o102bo3bo250bo99bo4bo
8b3o165bo$640bo246bo4bo105bo76bo2bo23b3o$889b2o102bo3bo81bo21b5o71b2o$
995bo60b6o13bo3bo21b3ob2o67b3ob2o$1055bo5bo14b4o24b2o56b5o7b5o$1061bo
99bo4bo8b3o$1055bo4bo105bo$1057b2o102bo3bo$1163bo!

It sucks because you can barely see the counting. But look at the bounding box! It's a modified version of a slow population growth pattern, but I don't remember what rate.

[dvgrn]

Actually, I made an unbounded binary counter a year ago...

Well... that's one way of doing linear binary counting, sure, but it's no good as a replacement for the pattern that calcyman described. Your pattern is a c/2 double rake for semi-Snarks, so the diameter grows linearly at half lightspeed, not O(log t).

A clean binary counter with O(log t) growth is a bit trickier. It might possibly be doable with a very clever repeated salvo of gliders or *WSSes crashing into something, along the lines of Jason Summers' O(log t) loggrow-diam pattern from jslife-oversize, but that would take a lot of new research. And without a lot of cleverness it would stop being a proper binary counter after a while, anyway: with a fixed input period, no matter how high, eventually the next salvo will start to do the next increment before the previous increment finishes.

I thought that that pattern was in Golly's collection, but it doesn't seem to be there. (EDIT: Oh, there it is -- "logarithmic-width.mc" in the HashLife folder. That's what I get for renaming things.) Here's a rebuild of loggrow-diam made by Gabriel Nivasch in 2006, as an experiment with HashLife-friendliness (though it didn't make much difference):

Code: Select all

#C loggrow-diam with p256 logic
x = 1325, y = 315, rule = B3/S23
855b2o$848b2o5b2o$848b2o$307b2o$300b2o5b2o751b2o$300b2o548b2o17b2o8b2o
172b2o5b2o$850b2o17bo9b2o172b2o$844b2o21bobo$302b2o17b2o8b2o511b2o21b
2o$302b2o17bo9b2o552b2o168b2o17b2o8b2o$296b2o21bobo496b2o65b2o168b2o
17bo9b2o$296b2o15bo5b2o423b2o72b2o5b2o50bo3b2o166b2o21bobo59b2o$312b2o
23b2o56b2o340b2o5b2o79b2o49b3ob3o166b2o21b2o60b2o5b2o$270b2o39bo2b2o
21b2o56b2o5b2o85b2o246b2o136bo3b2o209b2o49b2o$270b2o5b2o32b2o4bo15b2o
67b2o85b2o5b2o376b2o2b2o50b2o158b2o$277b2o36b3o15b2o161b2o209b2o85b2o
8b2o17b2o50b2o53b2o5b2o85b2o60b2o$316b2o389b2o5b2o23b2o17b2o8b2o24b2o
9bo17b2o51b2o8b2o49b2o85b2o5b2o33bo19b2o22b2o8b2o17b2o$371b2o8b2o17b2o
312b2o23b2o17bo9b2o35bobo21b2o13bo32b2o7b2o143b2o33b2o42b2o9bo17b2o$
246b2o8b2o17b2o94b2o9bo17b2o63b2o8b2o17b2o237b2o21bobo47b2o21b2o13b3o
32bo185bobo53bobo21b2o$246b2o9bo17b2o61b2o42bobo21b2o57b2o9bo17b2o237b
2o21b2o30b2o57bo30b2o26b2o8b2o17b2o185b2o21b2o$257bobo21b2o13bo41b2o
43b2o5bo15b2o68bobo21b2o181b2o8b2o17b2o60b2o12b2o56b2o58b2o9bo17b2o63b
2o8b2o17b2o60b2o11b2o$258b2o21b2o13b3o66b2o23b2o85b2o21b2o181b2o9bo17b
2o60b2o16b2o123bobo21b2o57b2o9bo17b2o18bo41b2o11b2o$240b2o57bo65b2o21b
2o2bo66b2o233bobo21b2o50b2o20b2o124b2o21b2o68bobo21b2o12b3o56b2o$240b
2o56b2o69b2o15bo4b2o66b2o234b2o21b2o50b2o108b2o18b2o110b2o21b2o15bo55b
2o$149b2o95bo3b2o117b2o15b3o74b2o212b2o201b2o18b2o92b2o55b2o$39b2o108b
2o5b2o88bo6bo132b2o75b2o212b2o225b2o16bo2bo68b2o$39b2o5b2o108b2o88bo7b
o426b2o104b2o115b2o13b2obo2b2o71b2o$46b2o198bo3bo3bo426b2o92b2o10b2o
41bo88b2obo4bo70b2o103b2o$252b3o109b2o367bo41b2o51b3o40bo7b2o38b2o182b
2o41bo$125b2o8b2o17b2o83b2o5b3o115b2o41bo50b2o273b3o91bo41b2o8bo41bo4b
2o216b3o$15b2o8b2o17b2o79b2o9bo17b2o83b2o41bo122b3o50b2o41bo234bo90b2o
41b2o8b3o16b2o20b2ob2o217bo$15b2o9bo17b2o90bobo21b2o85b2o31b3o48b2o71b
o84b2o8b3o174b2o57b2o60b3o39b2o41bo16b2o41bo50b2o148b2o$26bobo21b2o85b
2o21b2o85b2o30bo51bo72b2o82b2o8bo177b2o41bo77bo41b2o99b3o50b2o41bo47b
2o$27b3o20b2o67b2o126bo31b2o51b3o155bo7b2o217b3o77b3o139bo94b3o47bo$9b
2o18b3o87b2o170b2o41bo381bo222b2o85bo6bo51b3o$9b2o18b2o92b2o166b2o423b
2o80bo226b2o6b2o9b2o41bo$13b2o16bo91b2o120b2o551b3o43b2o179bobo16b2o2b
2o13bo2bo$13b2o230b2o252b2o299b3o41b2o209b2o5b2o3bo$499b2o293b2o4b2o
38b2o206bo3bo2b2o6bo3bo$296b2o447bo22b2o25bo44b2o211bo9bo3bo42b2o$118b
2o176b2o73b2o371b2o22bo23b3o86b2o150b3o13bo13bo2bo44bo$8b2o108b2o41bo
84b2o44b2o78bo92b2o277bobo22b3o20bo41b2o45b2o147bo4bo13b2o3bo9bo43b3o
21b2o$8b2o41bo107b3o85bo9bo34b2o18bo56b3o94bo30b2o229b2o32bo8bo62b2o
10b2o27b2o29b2o122bo5bo8b2o6bo54bo24b2o15b2o$49b3o106bo85b3o11bo51b2o
21b2o34bo41b2o50b3o32bo184b2o22bo20b2o31b3o82b2o27b2o30bo92b2o34bo8b2o
85bo17b2o$48bo81bobo25b2o84bo11b3o27b2o23b2o20b2o76b2o50bo32b2o7b2o
177bo22b2o51bo2b2o139b3o94bo28b2o54b2o$48b2o79bo4bo151b2o10b2o27b2o
166b2o8b2o174b3o22bobo51b3o141bo41b2o50b3o27bo3bo53b2o29bo$129bo4bo21b
o141b2o27b2o165b2o185bo8bo32b2o104b2o46b2o67b2o50bo29bob2o2bo5b2o9b2o
27b2o34b3o$129b2o362b2o2b2o190b3o31b2o8b2o94b2o39b2o5b2o149bo3bo7b2o9b
2o27b2o34bob2o25b2o$406b2o86bo3b2o188b2o2bo40b2o98b2o35b2o158bobo81bob
o2b3o23b2o$129b2o2b2o146b2o46b2o75b2o87b3ob3o188b3o36b2o102b2o195b3o
80bo4bo30b2o$129b2o2b2o146b2o39b2o5b2o79b2o84bo3b2o227b2o28bo3bo28b2o
147b2o139b2o30b2ob3o2bo26b2o$129b3obo151b2o35b2o67bo18b2o92b2o212b2o
40b2ob2o5b2o20b2o130bo16b2o92b2o38b2o5b2o24b2o4b2obob4o$125b2o3bo154b
2o82b2o21b2o110b2o212b2o32b2o3b2obo4bo4b2o26b2o27b2o96b2o18b2o88b2o38b
2o31b2o16b2o$15b2o109bo4bo112b2o123b2o20b2o70b2o257b2o11b2o15b2o4b2o3b
2o33b2o27b2o95b2o19b2o92b2o73b2o10b2o15b2o$16bo106b3o118b2o129b2o27b2o
57b2o224bo3bo28b2o11b2o26bo140b2o133b2o102b2o$13b3o107bo41b2o83b2o27b
2o94b2o27b2o63b2o27b2o181b2o5b2ob2o211b2o92b2o$13bo41b2o108b2o83b2o27b
2o188b2o27b2o181b2o4bo4bob2o3b2o95b2o112b2o27b2o57b2o294b2o6b2o$30b2ob
2o20b2o631b2o3b2o4b2o15b2o48b2o28b2o5b2o105b2o27b2o63b2o27b2o77b2o180b
o7bo$28b2o4bo338b2o314bo26b2o41b2o5b2o35b2o199b2o27b2o77b2o5b2o171bobo
5bobo$35b2o211b2o123b2o5b2o85b2o290b2o358b2o171b2o6b2o$28bo4bob2o123b
2o86b2o5b2o123b2o85b2o5b2o432b2o$29b2o2bob2o13b2o108b2o93b2o217b2o209b
2o221b2o5b2o85b2o$30bo2bo16b2o112b2o519b2o5b2o221b2o85b2o5b2o$54b2o
108b2o526b2o315b2o$54b2o67b2o$13b2o108b2o$13b2o114b2o27b2o1133b2o$19b
2o27b2o79b2o27b2o1133b2o$19b2o27b2o309b5o123b5o123b5o123b5o123b5o14b4o
105b5o14b4o105b5o14b4o$358bo4bo122bo4bo122bo4bo122bo4bo122bo4bo13bo3bo
104bo4bo13bo3bo9b2o93bo4bo13bo3bo9b2o$127b2o234bo127bo5b2o120bo5b2o
120bo5b2o120bo5b2o10bo109bo5b2o10bo8b4o97bo5b2o10bo8b4o22b2o$17b2o108b
2o5b2o222bo3bo123bo3bo5b4o114bo3bo5b4o114bo3bo5b4o114bo3bo5b4o5bo2bo
105bo3bo5b4o5bo2bo9b2ob2o6bo2bo81bo3bo5b4o5bo2bo9b2ob2o6bo2bo9b2ob2o$
17b2o5b2o108b2o224bo127bo7b2ob2o115bo7b2ob2o115bo7b2ob2o115bo7b2ob2o
115bo7b2ob2o19b2o11bo82bo7b2ob2o19b2o11bo8b4o$24b2o472b2o6bo119b2o126b
2o126b2o126b2o29bo3bo92b2o29bo3bo9b2o$507b2o533b4o124b4o$506b2o$760b4o
124b4o124b4o124b4o$79b2o126b2o126b2o126b2o126b2o31b5o90b2o31b5o2bo3bo
83b2o31b5o2bo3bo83b2o31b5o2bo3bo83b2o31b5o2bo3bo$78b4o124b4o124b4o124b
4o124b4o29bo4bo89b4o29bo4bo6bo82b4o29bo4bo6bo82b4o29bo4bo6bo82b4o29bo
4bo6bo$78b2ob2o123b2ob2o123b2ob2o123b2ob2o123b2ob2o33bo89b2ob2o33bo2bo
2bo83b2ob2o33bo2bo2bo83b2ob2o33bo2bo2bo83b2ob2o33bo2bo2bo$80b2o126b2o
126b2o126b2o126b2o29bo3bo92b2o29bo3bo92b2o29bo3bo92b2o29bo3bo92b2o29bo
3bo$219b2o126b2o126b2o126b2o20bo105b2o20bo105b2o20bo105b2o20bo105b2o
20bo$217b2ob2o123b2ob2o123b2ob2o34b2o87b2ob2o123b2ob2o123b2ob2o123b2ob
2o123b2ob2o$217b4o124b4o124b4o35bobo86b4o124b4o124b4o124b4o124b4o$218b
2o126b2o126b2o36bo8bo80b2o126b2o126b2o126b2o126b2o$520b2o$520bobo$625b
2o$16b2o420b2o61b3o114b2o5b2o293b2o87b2o$9b2o5b2o352b2o66b2o5b2o35b2o
19bo114b2o79b2o200b2o16bobo80b2o5b2o97b2o$9b2o352b2o5b2o15b2o56b2o28b
2o5b2o18bo189b2o5b2o97b2o94b2o5b2o18bo51b2o27b2o97b2o5b2o70b2o$363b2o
21bobo86b2o215b2o97b2o5b2o94b2o77b2o5b2o119b2o76bo2bo4b2o$129b2o107b2o
148bo231b2o17b2o8b2o140b2o164b2o21b2o200bo4b2o$11b2o27b2o80b2o5b2o100b
2o5b2o174b2o27b2o175b2o17bo9b2o306bobo44b2o27b2o144bo2bo$11b2o27b2o80b
2o107b2o132b2o27b2o18b2o10b2o15b2o32b2o27b2o106b2o21bobo54b2o9bo17b2o
171b2o27b2o30bo46b2o27b2o68b2o27b2o44b2ob2o$5b2o13b2o231b3o109b2o27b2o
30bobo20b2o26b2o27b2o106b2o21b2o55b2o11bo15b2o68b2o27b2o72b2o27b2o22b
2o27b2o18b2o103b2o27b2o22b2o16b4o9bo$5b2o12b2obo232bo103b2o65bo22b2o
20b2o182b2o31b2o16b2o85b2o27b2o66b2o57b2o27b2o18b2o97b2o57b2o15bo11b2o
b2o$18bobob2o22b2o76b2o27b2o78b2o19bo7b2o95b2o47b2o61b2o182b2o31b2o8bo
88b2o101b2o92b2o53b2o56b2o74bo11b2ob5o$17b2obo2bo22b2o76b2o27b2o78b2o
27b2o136b2o6b2o102b2o131b2o3bo45b2o3b3o25b2o56b2o142b2o51b2o48bo4b2o
97b2o34b4o6bo2bo2b3o$18b2o22b2o74b2o107b2o171b2o10b2o98b2o129bo6bo45bo
4bo27b2o97b2o101b2o10b2o88b3o102b2o10b2o33b2o$19b4o3bo15b2o74b2o107b2o
167b2o14b2o94b2o132bo7bo45bo2bo2b2o21b2o101b2o97b2o14b2o80b2o5b3obo97b
2o14b2o$27bo131b2o107b2o126b2o110b2o132bo3bo3bo46bo27b2o97b2o101b2o18b
2o74b2o2bo106b2o18b2o26b2o$25b3o55b2o74b2o107b2o372b3o53bo125b2o121b2o
74bo2b3o125b2o25bo2bo$83b2o5b2o63b2o38b2o67b2o382b3o5b2o365bo4bo155bo$
47b2o41b2o63b2o38b2o5b2o60b2o141b2o205bo41b2o54bo311b5o5b3o3b2o141b3o$
5bo41b2o153b2o197b2o4b2o41bo62b2o99b3o31b2o60bobo17b2o69b3o128b2o64bo
27b2o4b5o3b2o97b2o43b2o$5b3o351bo41b2o45b3o20bo41b2o102bo30b2o38bo22b
2o17b2o71bo25b2o59bo41b2o8b2o54b3o31b2ob2o60bo41b2o8b2o30b2o$8bo50b2o
27b2o269b3o85bo23b3o142b2o31bo38b3o96bo14bo26b2o59b3o49b2o41bo15bo32bo
62b3o49b2o29bo2bo8bo$7b2o50b2o27b2o70b2o9b2o27b2o67b2o91bo84b2o25bo
216bo95b3o103bo89b3o14b2o98bo89b3o$94b2o22bo41b2o9b2o27b2o25bo41b2o90b
2o110b2o215b2o98bo101b2o88bo116b2o83b2o3bo$94b2o22b3o85b2o19b3o420b2o
137b2o191b2o120bobo56bo18bo2bo3b2o$53b2o66bo84b2o22bo419b2o382b2o68bo
2bo55bobo16b3o$53b2o65b2o4bobo36b2o62b2o803b2o68bo2bo21bo33b2o$57b2o
69bo36b2o937bo3bo18bobo$57b2o65bobo42b2o617b2o315bobo20b2o$124bo44b2o
617b2o316bo$40b2o81bobo288b2o65b2o156bo393b2o$40bo82b2o269b2o19bo65bob
o22b2o130bo84b2o175b3o22b2o106bo98b2o$41b3o8b2o68bo271bo17b3o66bo17b3o
4bo102b2o27b3o82bo65bo32b2o76bo24bo23b2o83b3o95bo23b2o$2o41bo8b2o41bo
27b2o39b2o205b3o21b3o14bo41b2o43bo2bo4b3o99b2o113b3o61b3o31bo78bo16b3o
5b3o21bo42b2o26bo14bo96b3o21bo$2o91b3o28bo28b2o9b2o27b3o11bo54b2o90b2o
15bo25bo56b2o10b2o30bo3bo6bo173b2o41bo60b3obo31b3o59b2o30bo2bo7bo18b3o
43b2o26bobo68b2o41bo18b3o$92bo60bo39bo11b3o54bo91b2o16bo93b2o31bo2b2o
179b2o97b2o2b2o37bo59b2o30bo3bo25bo22b3o16b2o30b2o69b2o60bo41b2o$92b2o
60b3o37bo9bo58b3o235bo167b2obo109b2o3bo6b2o3bo116b2obobo50bo16b2o205b
2o$87bo25b2o41bo47b2o16b2o17b2o22bo121b3o41b3o65b2o113b2o53bob2o121b3o
bob2o114b2ob2o50bo$5b2o57bo21b2o25b2o107b2o17bobo142bo2bo38bo4bo15b2o
47b3o113b2o178b3o4bo115b3o78b2o$5b2o56bo24bo152bo117b2o28bo37b2o3bo16b
2o20b2o25b3o109b2o50b2o24b2o107bo3bo88b2o106b2o97b2o$b2o60b3o19b3o271b
2o24bo4bo35b2o25b2o16b2o137b2o50b2o24b2o100b2o6b3o89b2o63b3o26b2o8b2o
101b2o92b2o$b2o83bo118b2o48bo99b2o27bo4bo2bo34bo2bo22b2o12b2o159b2o21b
2o31b2o103bobo6bo87b2o66bo2bo2bo23b2o8b2o97b2o96b2o$19b2o21b2o74b2o85b
2o20b2o27bo98b2o26bo4bobobo19b2o14b2o5b2o30b2o27bo5b2o123bobo21b2o31b
2o97b2o4b2o95b2o27b2o4bo32bo4bo28b2o22b2o21b2o56b2o100b2o$18bobo21b2o
74b2o107b2o21b2o2bo2bo115b2o8b4obob2o4b2o14b2o21bobo47b2o8bo6bobo3b2o
106b2o9bo17b2o55b2o21b2o56b2o4bo114b2o9b2o4b2o4b2o25bobo2bobo26b2o21bo
bo21b2o74b2o21b2o59b2o$7b2o9bo17b2o21b2o53b2o107b2o27bo4bo114bobo3b2o
4b2o3bo6b2o20b2o17bo9b2o35bobo3b2o2b3o6b3o2b2o106b2o8b2o17b2o54bobo21b
2o74b2o21b2o77bobo3b2o3bob2o3b3o3b2o18b2o6b2o3b2o8b2o28b2o9bo17b2o79bo
bo21b2o18b2o21b2o$7b2o8b2o17b2o22bo53b2o55b2o31bo18b2o25b3o3b2o103b2o
9bo5b2o38b2o17b2o8b2o24b2o9bo5b2o3b2o193b2o9bo17b2o79bobo21b2o66b2o9bo
5b2o4b3o4bo24b2o16b2o3bobo27b2o8b2o17b2o68b2o9bo17b2o24b2o21bobo$57b3o
72b2o21b2o15bo30b2o36b2o12bo8b2o95b2o8b2o100b2o8b2o11b3o153bo22bo14b2o
8b2o17b2o68b2o9bo17b2o72b2o8b2o11b3o3bo31b2o10b2o5bo9b2o115b2o8b2o17b
2o30b2o17bo9b2o$57bo41b2o30bobo21b2o12b3o31b2o35bobo3b2o16b2o231bo149b
2o3b3o18b3o113b2o8b2o17b2o133b2o17b2o8b2o176b2o17b2o8b2o$38b2o59b2o19b
2o9bo17b2o18bo41b2o16b2o9bo5bo11b2o156b2o222b2o5b2o6bo16bo358b2o$31b2o
5b2o80b2o8b2o17b2o52b3o5b2o16b2o8b2o7bo9b2o132b2o22b2o5b2o79b2o134b2o
12b2o16b2o47b2o200b2o99b2o5b2o97b2o$31b2o164b3o185b2o5b2o29b2o72b2o5b
2o208b2o5b2o97b2o94b2o5b2o26b2o71b2o97b2o5b2o26b2o$197bo3bo3bo179b2o
110b2o215b2o97b2o5b2o94b2o33b2o5b2o163b2o33b2o5b2o$94b2o55b2o44bo7bo
54b2o551b2o143b2o205b2o$94b2o48b2o5b2o45bo6bo47b2o5b2o$98b2o44b2o54b2o
3bo47b2o$98b2o110b2o1019b2o$57b2o21b2o128b2o1012b2o5b2o$57b2o21bobo86b
2o21b2o421bo20bo587b2o$63b2o17bo9b2o75b2o21bobo418b3o20b3o29b2o$63b2o
17b2o8b2o81b2o17bo9b2o406bo6bo19bo26bo4bo$175b2o17b2o8b2o370b2o34b2o4b
obo17b2o586b2o17b2o8b2o$576bobo39bobo45bo5bo553b2o17bo9b2o$61b2o513bo
8bo10bo20b2ob3o44b2o551b2o21bobo$61b2o5b2o103b2o409b2o10b3o24bo596b2o
21b2o$68b2o103b2o5b2o402bobo12bo17b2ob3o6bo631b2o$180b2o416b2o17b2obo
6b3o40bo3b2o585b2o$626bo31bobo9bo4bo581b2o$626b2o25b3o7b2o6bo585b2o$
601b2o50bo2b2o4bobo6bo2bo$600bo2bo49b2ob4o7b2o$601b2o52b3o8bob2o36b2o$
666b2ob2o35b2o5b2o547b2o$666b2ob3ob2o38b2o505bo41b2o$673b2o545b3o$
1223bo$682b2o27b2o509b2o$638b2o27b2o13b2o27b2o$613b2o23b2o11b2o14b2o
48b2o507b3o$614bo36bo65b2o508b2o$611b3o38b3o21b2o547bobo$611bo42bo21b
2o20b2o525bo$680b2o15b2o524b2o$680b2o17bo524bobo27bobo$1225b2o28b2o$
1255bo$637b2o$594b2o41bo37b2o538b2o$593bobo42b3o34b2o41bo465b2o29b2o$
593bo46bo75b3o466b2o$592b2o121bo458b2o8bo$715b2o458b2o$1174bo45b2o$
1220b2o$1216b2o$1216b2o$629b2o603b2o21b2o33b2o$629bo2bo3b2o518bo76bobo
21b2o2b2o22b2o5b2o$636b2o518b3o63b2o9bo17b2o9bo22b2o$625bo56b2o475bo
62b2o8b2o17b2o9bob2o$623bo7b2o3bo46bo474b2o99b2obo2bo$605b2o22b2o4b2o
43b3o577bobo24b2o17b2o8b2o$605b2o15bo11b3o43bo41b2o459b2o68b2o5bobo2bo
21b2o17bo9b2o$622bo3bo6b2o5b2o80b2o459bo62b2o5b2o2b2obo5bo14b2o21bobo$
626bo6bob2o3b2o55b2o2b2o478bobo62b2o10bob2o3bo2bo12b2o21b2o$599b2o22bo
bo8b3o59b3o2b2o478b2o75bo6bo56b2o$599b2o96b2o2b3o473bo79b2o6bo3bo52b2o
$603b2o26b2o65bo2b2o14b2o457bobo83b2obo3bo48b2o$603b2o26bo85b2o457bobo
82bobobo52b2o$632bo88b2o454bo84b2obo2bo$721b2o541bobo$630bo49b2o21b2o
557b2o2b2o$598b2o33bo46b2o21bobo555bo4b2o55b2o$598b2o30bo2bo7bo44b2o
17bo9b2o543bobobo2bo55b2o$632b3o4b3o44b2o17b2o8b2o543bobo3bo$632b3o3bo
574b2o46bo2b2o$612bo18bo2bo3b2o566b2o5b2o47b2ob2o$611bo19bobo50b2o480b
2o38b2o57bo$611b3o17b3o50b2o5b2o474bo18b2o74b4ob2o40b3o$691b2o474bobo
16bobo72bo24b3o19bo3bo$1126b2o40b2o18bo19b2o17b2o8b2o22b2ob2o20bo26bo$
1119b2o5b2o60b2o18b2o17bo9b2o23bobo22bo$1119b2o81b2o21bobo34bobo43b2o
3bo$1181b2obo17b2o21b2o36bo46b3o$605b2o574b2ob3o56b2o71b2o$606bo514b2o
27b2o35bo55b2o71bo$603b3o515b2o10b2o15b2o29b2ob3o52b2o76b3o$603bo41b2o
468b2o5b2o9b2o47bobo54b2o35b2o41bo$645b2o468b2o6b2o3b2o52bobo91b2o$
1122bobo2bobo26b2o25bo$1121b2o3b2o28b2o$1122bo2b2o25b2o90b2o$640b2o
481b3o26b2o25b2o21bo41b2o35b2o$640b2o482bo54bobo20b3o76b2o$644b2o535bo
23bo71b2o$644b2o535b2o21b2o71b2o$603b2o21b2o510bobo16b2o136b2o21b2o$
603b2o21bobo486bo23b2o16b2o135bobo21b2o$609b2o17bo9b2o475b3o21bo143b2o
9bo17b2o$609b2o17b2o8b2o478bo164b2o8b2o17b2o$1117b2o2$607b2o579b2o22b
2o100b2o$607b2o5b2o544b2o26bo23bobo22b2o68b2o5b2o$614b2o543bobo7b2o15b
obo23bo17b3o4bo69b2o$1159bo9b2o15b2o42bo2bo4b3o$1158b2o37b2o30bo3bo6bo
$1197b2o31bo2b2o$1150b2o80bo$1150bo79b2o$1151b3o75b3o$1110b2o41bo48b2o
25b3o$1110b2o90b2o$1198b2o$1198b2o27bo5b2o$1226bo6bobo3b2o$1115b2o61bo
42b2o2b3o6b3o2b2o$1115b2o51b2o7b3o24b2o15b2o3b2o$1111b2o54bobo6bo22b2o
3b2o21b3o$1111b2o54bo9b2o20bo28bo$1129b2o21b2o12b2o9bo19bobo$1128bobo
21b2o43b2o36b2o$1117b2o9bo17b2o80b2o5b2o$1117b2o8b2o17b2o80b2o3$1148b
2o$1141b2o5b2o$1141b2o63b2o$1206b2o4$1169b2o$1169b2o$1175b2o32b2o$
1175b2o33bo$1209bo$1197b2o10b2o$1173b2o22bobo$1173b2o5b2o17bo$1159b2o
19b2o17b2o$1159b2o5b2o$1166b2o3$1135b2o8b2o17b2o$1135b2o9bo17b2o$1146b
obo21b2o$1147b2o21b2o$1129b2o$1129b2o$1133b2o$1133b2o4$1128b2o$1128b2o
3$1167bo$1138b3o26b2o$1138bo27bobo$1138b3o2$1139bo$1139b3o$1141b3o$
1135b2o4b2o$1136bo$1133b3o$1133bo41b2o$1175b2o4$1170b2o$1170b2o$1174b
2o$1174b2o$1133b2o21b2o$1133b2o21bobo$1139b2o17bo9b2o$1139b2o17b2o8b2o
3$1137b2o$1137b2o5b2o$1144b2o!

The easy way to do a true binary counter would be to use a diagonal static tape with 1 = (some still life), 0 = empty space, with a resettable elbow running alongside. Arrange it so that when a TEST signal is sent, 0's change to 1's and send back a RESET signal, moving the elbow back to the first bit on the tape. 1's change to 0's and send back a CARRY signal that moves the elbow to the next position on the tape, and then a TEST signal is sent again.

[Moosey]

Based on a pattern by scorbie:

Maybe... It can be run with Bellman to make a pretty small sgr or a G2H converter?

Code: Select all

x = 13, y = 16, rule = B3/S23
o$3o$3bo4bobo$2b2o5b2o$9bo3$7b2o$7b2o2b2o$11b2o3$4b2o$5bo$2b3o$2bo!

Could this be used to make a small G reflector?
This is almost that but it fails to restore a block.

Code: Select all

x = 22, y = 16, rule = B3/S23
o$3o$3bo4bobo$2b2o5b2o9b2o$9bo10bo$18bobo$18b2o$7b2o$7b2o2b2o$11b2o2b
2o$15b2o2$4b2o$5bo$2b3o$2bo!

Really all we need is a small block factory:

Code: Select all

x = 21, y = 31, rule = LifeHistory
A$3A$3.A4.A.A$2.2A5.2A$9.A3$7.2A$7.2A2.2E$11.2E3$4.2A$5.A$2.3A$2.A12$
20.C$11.2D5.3C$11.2D5.C.C$18.C!

[dvgrn]

Based on a pattern by scorbie:

Maybe... It can be run with Bellman to make a pretty small sgr or a G2H converter?

Code: Select all

x = 13, y = 16, rule = B3/S23
o$3o$3bo4bobo$2b2o5b2o$9bo3$7b2o$7b2o2b2o$11b2o3$4b2o$5bo$2b3o$2bo!

Could this be used to make a small G reflector?

Something similar has been investigated, but I'm not sure if Bellman was ever tried on it. Guam was able to extract a B-heptomino or Herschel, but it went in the opposite direction relative to the initial collision (and needed another glider to do the cleanup):

Code: Select all

x = 109, y = 47, rule = LifeHistory
7.3D5.D2.4D2.5D.4D35.3D5.D2.D3.D.5D2.3D2.5D3.D$6.D3.D3.2D2.D3.D.D5.D
3.D33.D3.D3.2D2.2D2.D.D5.D3.D3.D4.2D$6.D6.D.D2.D3.D.D5.D3.D33.D6.D.D
2.D.D.D.D9.D3.D5.D$6.D2.2D.D2.D2.4D3.3D2.4D34.D2.2D.D2.D2.D2.2D.3D6.D
4.D5.D$6.D3.D.5D.D3.D5.D.D2.D34.D3.D.5D.D3.D.D7.D5.D5.D$6.D3.D4.D2.D
3.D.D3.D.D3.D33.D3.D4.D2.D3.D.D6.D6.D5.D$7.3D5.D2.4D3.3D2.D3.D34.3D5.
D2.D3.D.5D.5D3.D4.3D5$2.A$.2BA$.3AB$.5B$7B$8B61.2B$.8B59.4B$2.8B59.4B
$3.8B26.B32.4B$4.8B24.2B33.4B$5.8B22.3B34.4B$6.8B20.4B35.4B24.4B$7.8B
18.4B37.4B22.4B$8.8B16.4B39.4B20.4B$9.8B7.2A5.4B41.4B3.A7.2A5.4B$10.
8B5.B2AB3.4B43.4B.2BA5.B2AB3.4B$11.8B4.3B3.4B45.4B3AB4.3B3.4B$12.8B4.
B2.5B47.8B4.B2.5B$13.3BA4B.9B49.8B.9B$14.3BA12B.3B47.16B.3B$15.3A16B
48.19B$16.21B3.B42.21B3.B$10.B3.B.22B.B2A36.2A4.21B.B2A$8.32B2A37.A5.
3BA18B2A$7.D31B.B38.A.AB2.4BA16B.B$6.2D21B2A7B42.2AB.3B3A6B2A7B$5.2D
11B2D9B2A4B.B45.14B2A4B.B$6.D10B2C14B49.2B2A14B$7.D10BC2B2A7B3.A50.2A
2B2A7B3.A$11.3B2.5B2A5B5.3A49.3B2A5B5.3A$9.3B3.13B8.A50.8B8.A$9.2A5.
4B.5B9.2A51.5B9.2A$10.A4.2B4.2B2AB62.2B2AB$7.3A4.2BAB5.2A65.2A$7.A7.A
.A$16.A!

It's interesting that the B-heptomino output in Scorbie's pattern restores one of the blocks... but it appears that I said the same thing the last time this pattern was posted. Looks like Scorbie tried to find a completion, but I'm not sure if he used any search tools besides Bellman. CatForce or ptbsearch might also produce results, though it's probably a long shot either way.

It's worth throwing everything we have at it, though, since if it could be made to work -- even as a 90-degree reflector, let alone a G-to-H -- it would be a color-changing Snark, possibly even small and fast enough to win MikeP's prize.

[Moosey]

No to mention how close it is to spartan— I’m rather surprised I didn’t find an eater placement restoring the other block.

My goal was to find a 90 degree reflector since it only requires a reasonable-looking block factory.

[gameoflifemaniac]

Where can I find the script for making 0E0P metacell patterns?

[Gustone]

Where can I find the script for making 0E0P metacell patterns?

in golly/scripts/python/metafier

[Moosey]

Where can I find the script for making 0E0P metacell patterns?

in golly/scripts/python/metafier

That doesn’t do 0E0Ps, as far as I know.