Factorio (R3,C2,S2,B3,N+)

[Haycat2009]

The diagonal speed limit is c/2d.

Proof: A zigzagging c spaceship flipping and turning 90 degrees without stopping would be c/2d. However, I think that we can only get arbitrarily close to that, as everything I know pauses for a while while turning.

[Disaster16439]

5F p2:

Code: Select all

x = 22, y = 20, rule = R3,C2,S2,B3,N+
10bo3$10bo$10bo$10bo$16b3o2bo3$o2b3o2$12b3o2bo3$7bo$7bo$7bo3$7bo!

EDIT:
An attempt of salvo construction:

Code: Select all

x = 172, y = 20, rule = R3,C2,S2,B3,N+
51bo2b3o$33bo2b3o3$43bo2b3o$13bo2b3o6bo2b3o56bo2b3o4$bo2b3o$66bo2b3o43b
o2b3o2$o89bo2b3o5bo2b3o63b2o$171bo$170bo$bo2b3o106bo2b3o11bo2b3o$152b
o2b3o3$140bo2b3o!

The thing is, if we don't have a source of factorials, then this will be useless. So, the main goal is probably a factorio gun. The thing is, we don't have oscillators with complex enough sparks to make a factorio. This is why I don't think Factorio is a promising rule.
My 145th post!
145=5x29

[Haycat2009]

5F p2:

Code: Select all

x = 22, y = 20, rule = R3,C2,S2,B3,N+
10bo3$10bo$10bo$10bo$16b3o2bo3$o2b3o2$12b3o2bo3$7bo$7bo$7bo3$7bo!

EDIT:
An attempt of salvo construction:

Code: Select all

x = 172, y = 20, rule = R3,C2,S2,B3,N+
51bo2b3o$33bo2b3o3$43bo2b3o$13bo2b3o6bo2b3o56bo2b3o4$bo2b3o$66bo2b3o43b
o2b3o2$o89bo2b3o5bo2b3o63b2o$171bo$170bo$bo2b3o106bo2b3o11bo2b3o$152b
o2b3o3$140bo2b3o!

The thing is, if we don't have a source of factorials, then this will be useless. So, the main goal is probably a factorio gun. The thing is, we don't have oscillators with complex enough sparks to make a factorio. This is why I don't think Factorio is a promising rule.
My 145th post!
145=5x29

The issue is not sparks (We have very sparkly oscillators), the issue is how to create one.

[Disaster16439]

5F p2:

Code: Select all

x = 22, y = 20, rule = R3,C2,S2,B3,N+
10bo3$10bo$10bo$10bo$16b3o2bo3$o2b3o2$12b3o2bo3$7bo$7bo$7bo3$7bo!

EDIT:
An attempt of salvo construction:

Code: Select all

x = 172, y = 20, rule = R3,C2,S2,B3,N+
51bo2b3o$33bo2b3o3$43bo2b3o$13bo2b3o6bo2b3o56bo2b3o4$bo2b3o$66bo2b3o43b
o2b3o2$o89bo2b3o5bo2b3o63b2o$171bo$170bo$bo2b3o106bo2b3o11bo2b3o$152b
o2b3o3$140bo2b3o!

The thing is, if we don't have a source of factorials, then this will be useless. So, the main goal is probably a factorio gun. The thing is, we don't have oscillators with complex enough sparks to make a factorio. This is why I don't think Factorio is a promising rule.
My 145th post!
145=5x29

The issue is not sparks (We have very sparkly oscillators), the issue is how to create one.

No, the issue is that the sparks are not complex enough to make a factorio. Compare making a gun with multiple 3 block twin bee shuttles to making a gun out of Merzenich's p31s. I think the only way to do this is 1.make some ugly hack of Raucci's osc search program and JLS/WLS, 2.MORE APGSEARCHING!

So what combination of sparks makes a factorialship?

The thing is, we don't know! Even if we did find a combination of complex sparks that creates a factorio, the chance of an oscillator that produces that spark is low. So I think the best way is to keep searching until we find a suitable oscillator, and then run hacked gencols on it. Another major problem is that if a pattern has a gutter, then that gutter will stay. And so any D2_+1(the symmetry of the factorio) collision of 2 oscillators will never produce a factorio on the axis of symmetry(a factorio does not have a gutter). The factorio is rare. Maybe if we collided 2 sparks D2_x, then we could make a gun for the c/3d tooo!

[Haycat2009]

The thing is, if we don't have a source of factorials, then this will be useless. So, the main goal is probably a factorio gun. The thing is, we don't have oscillators with complex enough sparks to make a factorio. This is why I don't think Factorio is a promising rule.
My 145th post!
145=5x29

The issue is not sparks (We have very sparkly oscillators), the issue is how to create one.

No, the issue is that the sparks are not complex enough to make a factorio. Compare making a gun with multiple 3 block twin bee shuttles to making a gun out of Merzenich's p31s.

So what combination of sparks makes a factorialship?

[confocaloid]

Agree, more apgsearching (across all 16 symmetries) could yield an unexpected sparky oscillator that would lead to a gun.
"Hacked gencols" would be another possibility if it exists (does it?) I used modified gencols to find a p98 glider reflector in B357/S238; the p98 oscillators there are not very sparky, but happened to be sparky enough to control passing reactions. Maybe a similar approach would work for this rule as well.

[...]
No, the issue is that the sparks are not complex enough to make a factorio. Compare making a gun with multiple 3 block twin bee shuttles to making a gun out of Merzenich's p31s. I think the only way to do this is 1.make some ugly hack of Raucci's osc search program and JLS/WLS, 2.MORE APGSEARCHING!
[...]
Even if we did find a combination of complex sparks that creates a factorio, the chance of an oscillator that produces that spark is low. So I think the best way is to keep searching until we find a suitable oscillator, and then run hacked gencols on it. [...]

[Haycat2009]

Agree, more apgsearching (across all 16 symmetries) could yield an unexpected sparky oscillator that would lead to a gun.
"Hacked gencols" would be another possibility if it exists (does it?) I used modified gencols to find a p98 glider reflector in B357/S238; the p98 oscillators there are not very sparky, but happened to be sparky enough to control passing reactions. Maybe a similar approach would work for this rule as well.

[...]
No, the issue is that the sparks are not complex enough to make a factorio. Compare making a gun with multiple 3 block twin bee shuttles to making a gun out of Merzenich's p31s. I think the only way to do this is 1.make some ugly hack of Raucci's osc search program and JLS/WLS, 2.MORE APGSEARCHING!
[...]
Even if we did find a combination of complex sparks that creates a factorio, the chance of an oscillator that produces that spark is low. So I think the best way is to keep searching until we find a suitable oscillator, and then run hacked gencols on it. [...]

Nice, but what is gencols?

[confocaloid]

Nice, but what is gencols?

Search is your friend search.php?keywords=gencols gencols

[AlephAlpha]

My factoriosrc is still in development. Currently it is still slow and lacks many features, but at least it shows that rlifesrc's algorithm does work for Factorio.

There isn't a web version yet. In fact, making a GUI is much more complicated than writing the core algorithm. I think I cannot finish it in this year.

Here are some spaceships I've found:

c/2o:

Code: Select all

x = 13, y = 5, rule = R3,C2,S2,B3,N+
.....o.......$
..o..o.o.....$
.ooo...o.o.oo$
..o..o.o.....$
.....o.......!

Code: Select all

x = 24, y = 10, rule = R3,C2,S2,B3,N+
....o.......o.o..o......$
.ooo....oo.......o.o..oo$
..o..o....o..o..........$
..o...o.o...o.o.........$
.........o...o..........$
.........o...o..........$
..o...o.o...o.o.........$
..o..o....o..o..........$
.ooo....oo.......o.o..oo$
....o.......o.o..o......!

Code: Select all

x = 11, y = 14, rule = R3,C2,S2,B3,N+
.......oo.o$
...........$
oo.o..o..o.$
.......o...$
...........$
...oo......$
...........$
...........$
...oo......$
...........$
.......o...$
oo.o..o..o.$
...........$
.......oo.o!

c/3o:

Code: Select all

x = 44, y = 9, rule = R3,C2,S2,B3,N+
..............o.o...............o.........oo$
...........o.o.......ooo.o..o..........o...o$
.ooo......o.ooo............o.....oo.oooo....$
......o.........o..........oo..o.o.oo..o....$
...............................o......o..o..$
......o.........o..........oo..o.o.oo..o....$
.ooo......o.ooo............o.....oo.oooo....$
...........o.o.......ooo.o..o..........o...o$
..............o.o...............o.........oo!

Code: Select all

x = 28, y = 11, rule = R3,C2,S2,B3,N+
........................oo.o$
...............o.o..........$
............o.o.......ooo...$
..ooo......o.ooo...........o$
.......o.........o..........$
............................$
.......o.........o..........$
..ooo......o.ooo...........o$
............o.o.......ooo...$
...............o.o..........$
........................oo.o!

Code: Select all

x = 48, y = 12, rule = R3,C2,S2,B3,N+
..o..o..........................................$
....o.......o...o.ooo....o.....o.o.o............$
...oo..oo.o....o...o..o.o....oo.......o..oo...o.$
.o.o....o.....o.....o.o........o.o.o.........o.o$
.....o..o.....o.........o......o.o.o.......o....$
........o....oo.......o.................oooo....$
........o....oo.......o.................oooo....$
.....o..o.....o.........o......o.o.o.......o....$
.o.o....o.....o.....o.o........o.o.o.........o.o$
...oo..oo.o....o...o..o.o....oo.......o..oo...o.$
....o.......o...o.ooo....o.....o.o.o............$
..o..o..........................................!

2c/3o:

Code: Select all

x = 100, y = 17, rule = R3,C2,S2,B3,N+
....oo...ooo......................o....o....oo..o...o...o...........................................$
......oo...o..o...ooo.ooo...........................................................................$
....oooo..o...o......oo........o...ooo....oo..ooo.oo..o...ooo......ooo.o.o.o....o.o...o..oo........o$
........o.o...o....o.oo.......o.....o.................o.......oo......o.o.....o.........o....o..ooo.$
..............oo......oo...o...........o.o.................o......o.o...o..o......oo.........o......$
..ooo...oo....o.o..oo.......ooo.....o......o...o..o..o.o...................o.......o..o..o..o...o...$
.............o.......o.o......o...oo..........oo......o..o......ooo......o..o.....o.o.o.............$
........................ooo.o...o.o..o...........o.......o....oo...o..........o..o..........o.......$
.........................oo..o.oo......................o.........o............o...oo................$
........................ooo.o...o.o..o...........o.......o....oo...o..........o..o..........o.......$
.............o.......o.o......o...oo..........oo......o..o......ooo......o..o.....o.o.o.............$
..ooo...oo....o.o..oo.......ooo.....o......o...o..o..o.o...................o.......o..o..o..o...o...$
..............oo......oo...o...........o.o.................o......o.o...o..o......oo.........o......$
........o.o...o....o.oo.......o.....o.................o.......oo......o.o.....o.........o....o..ooo.$
....oooo..o...o......oo........o...ooo....oo..ooo.oo..o...ooo......ooo.o.o.o....o.o...o..oo........o$
......oo...o..o...ooo.ooo...........................................................................$
....oo...ooo......................o....o....oo..o...o...o...........................................!

Code: Select all

x = 100, y = 18, rule = R3,C2,S2,B3,N+
....oo...o.oo.o..o.o..............................ooo.o..................................oo..o.oo...$
......oo..oo......o........o.....................o.....o......o.........ooo.........................$
....ooo.......o...o........oo..........o.oo....o....o.o.......oo......o..o....o...oo....o..o...o..o.$
........o.o..o...oo.....ooo.o.o........oo..o...........o.oo...o...oo........................o.o.o...$
.................o....oo.o..o.......oo.o.......oo....o.........o..........oooo...o..................$
..ooo..oo....o.o......oo.....o.......o...........o...o.o..o...oo..oo.o.o......................oo....$
.................o.o.......o......o...oo...oo.oooo...o..........................oo...o..........o...$
........o.o..o...o..o..o...o.....o..oo..o.o..o...oo....o.oo........................o................$
..........o..o.o.o...oo....o..o.oo..o.......o...oo...o.........o....................................$
..........o..o.o.o...oo....o..o.oo..o.......o...oo...o.........o....................................$
........o.o..o...o..o..o...o.....o..oo..o.o..o...oo....o.oo........................o................$
.................o.o.......o......o...oo...oo.oooo...o..........................oo...o..........o...$
..ooo..oo....o.o......oo.....o.......o...........o...o.o..o...oo..oo.o.o......................oo....$
.................o....oo.o..o.......oo.o.......oo....o.........o..........oooo...o..................$
........o.o..o...oo.....ooo.o.o........oo..o...........o.oo...o...oo........................o.o.o...$
....ooo.......o...o........oo..........o.oo....o....o.o.......oo......o..o....o...oo....o..o...o..o.$
......oo..oo......o........o.....................o.....o......o.........ooo.........................$
....oo...o.oo.o..o.o..............................ooo.o..................................oo..o.oo...!

c/3d:

Code: Select all

x = 7, y = 7, rule = R3,C2,S2,B3,N+
.......$
....o..$
......o$
....oo.$
.o.o.oo$
...oo..$
..o.o..!

[HerscheltheHerschel]

Does anyone have a rule file? I want to play with this in Golly.
Also, is it possible to make a rule with the same rules as Factorio but with the neighborhood below?

Code: Select all

bobobo$o2bo2bo$3bo$3ob3o$3bo$o2bo2bo$bobobo!

Also, where is the self-coded search program?

[confocaloid]

A zigzagging c spaceship flipping and turning 90 degrees without stopping would be c/2d. However, I think that we can only get arbitrarily close to that, as everything I know pauses for a while while turning.

I'm not convinced by this.
(1) A diagonal spaceship does not have to zigzag by "flipping and turning 90 degrees". There may be a faster spaceship that goes diagonally without zigzagging.
(2) One needs to prove (or disprove) that the speed limit for spaceships is 1 cell/generation. A fuse can burn faster:

Code: Select all

x = 388, y = 100, rule = R3,C0,S2,B3,N+
381b3o2bo3$2o$2o$5b2o$5b2o$10b2o$10b2o$15b2o$15b2o368b2o$20b2o363b2o$
20b2o358b2o5bo$25b2o353b2o$25b2o348b2o$30b2o343b2o$30b2o338b2o$35b2o
333b2o$35b2o328b2o$40b2o323b2o$40b2o318b2o$45b2o313b2o$45b2o308b2o$50b
2o303b2o$50b2o298b2o$55b2o293b2o$55b2o288b2o$60b2o283b2o$60b2o278b2o$
65b2o273b2o$65b2o268b2o$70b2o263b2o$70b2o258b2o$75b2o253b2o$75b2o248b
2o$80b2o243b2o$80b2o238b2o$85b2o233b2o$85b2o228b2o$90b2o223b2o$90b2o
218b2o$95b2o213b2o$95b2o208b2o$100b2o203b2o$100b2o198b2o$105b2o193b2o$
105b2o188b2o$110b2o183b2o$110b2o178b2o$115b2o173b2o$115b2o168b2o$120b
2o163b2o$120b2o158b2o$125b2o153b2o$125b2o148b2o$130b2o143b2o$130b2o
138b2o$135b2o133b2o$135b2o128b2o$140b2o123b2o$140b2o118b2o$145b2o113b
2o$145b2o108b2o$150b2o103b2o$150b2o98b2o$155b2o93b2o$155b2o88b2o$160b
2o83b2o$160b2o78b2o$240b2o$235b2o$235b2o$230b2o$230b2o$225b2o$225b2o$
220b2o$220b2o$215b2o$215b2o$210b2o$210b2o$205b2o$205b2o$200b2o$200b2o$
195b2o$195b2o$190b2o$190b2o$185b2o$165b2o18b2o$165b2o13b2o$180b2o$175b
2o$175b2o$170b2o$170b2o$165b2o$165b2o!

Does anyone have a rule file? I want to play with this in Golly.

For Golly, the rulestring "R3,C0,S2,B3,N+" should work, without a rule file. A rule file for apgsearch was posted in viewtopic.php?p=168690#p168690

Also, where is the self-coded search program?

In the first post of the thread. Generally, it is a good idea to read through the thread before posting.

[Haycat2009]

(2) One needs to prove (or disprove) that the speed limit for spaceships is 1 cell/generation. A fuse can burn faster:

H. H. P. M. P. Cole already proved this. While it is pretty obvious that a fuse can burn at 3c, max spaceship speed is c. Also, do you have to doubt everything I do? It feels like harassment.

[confocaloid]

H. H. P. M. P. Cole already proved this.

Where I can read this? You did not link to the place where that was proven.

do you have to doubt everything

When you write "proof", you need to give a convincing proof. If it is not convincing, or if there are gaps, or errors, then there's no proof.

The diagonal speed limit is c/2d.

Proof: [...]

[Haycat2009]

H. H. P. M. P. Cole already proved this.

Where I can read this? You did not link to the place where that was proven.

Edit: p2 photon:

Code: Select all

x = 4, y = 8, rule = R3,C0,S2,B3,N+
2bo$2bo$obo$3bo$bo$o2$3bo!

I feel it shouldn't be called a photon because the rule is range-3. Photons in this case should be reserved for spaceships with a simplified speed of 3c/1o (which do not exist in Factorio).

Instead, since c is the terminal velocity for orthogonal spaceships, I would just call this a plain old 2c/2o spaceship.

EDIT: Updated pattern collection. The smallest periods undiscovered are 7, 10, 11, c/2o, and c/2d:

Code: Select all

# Factorio pattern collection 1.1
# Rule by H. H. P. M. P. Cole
# With contributions by H. H. P. M. P. Cole, FWKnightship, and May13
# p1, p2, p3, p4, p5, p6, p8, p9, p12, c/1o, 2c/2o
x = 396, y = 354, rule = R3,C2,S2,B3,N+
191bo12bo12bo10bo$191bo12bo12bo10bo$171bo19bo12bo12bo10bo15bobobo$171b
o$65bo11bo8bo15bo7bo9bo8bo41b2o14bo12bo12bo10bo23bo$65bo11bo8bo15bo7b
o9bo8bo57bo3bo8bo3bo8bo3bo6bo3bo$41bobobo19bo11bo8bo15b2o6b2o8b2o7b2o
22bo18bo14b2o11b2o11b2o9b2o18bobobo2bobobo$153bo18bo2bo10bo12bo$41bo61b
o7bo9bo8bo22bo17bo3bo68bo6bo$65bo11bo8bo16bo7bo9bo8bo18bo37bo12bo12bo
10bo$41bobobo56bo7bo9bo8bo19bo49bo25bo18bobobo2bobobo13bo$134bo14bo3b
o115bo$76bo8bo17bo7bo9bo8bo3bo15bo116bobo$39b9o28bo8bo47b2o105b18o12b
o$76b2o7b2o48bo13bo118bo$77bo5bo2bobo23bo9bo87bo11bo9bo34bo$112bo9bo52b
o3bo6bo3bo6bo3bo8bo11bo9bo$43bo67b2o8b2o40bo7bo3bo3bo6bo3bo6bo3bo8bo11b
o9bo14bobobo18bo$111bo7bobo2bo38bo7bo3bo3bo6bo3bo6bo3bo$41bobo21bo12b
o13bo70bo7bo43bo11bo23bo$65bo12bo13bo52bo7bo5bo50bo4bo6bo4bo4bo$43bo21b
o12bo13bo52bo7bo5bo15bo3bo6bo3bo6bo3bo10bo2bo8bo2bo2bo16bobobo$145bo7b
o5bo3bo7bo4bo10bo11bo14bo11bobo$43bo17bo12bo13bo60bo15bo8bo72bo$61bo3b
o8bo3bo9bo3bo56bo16bo$41bobobo15b2o11b2o12b2o13bo7bo9bo8bo14bo3bo3bo5b
o5bo81bobobo$60bo12bo13bo15bo7bo9bo8bo17bobo11bo3bo$79bo13bo8b2o6b2o8b
2o7b2o$79bo13bo55bo$78b2o12b2o8bo7bo9bo8bo$78bo11bobo2bo6bo7bo9bo8bo$
103bo7bo9bo8bo2$102bo7bo9bo8bo4bo$103bo7bo9bo8bo3bo$133b2o$135bo$112b
o9bo$112bo9bo$111b2o8b2o$111bo7bobo2bo2$344bo3b2o2$345bo3$345bo$345bo
$328b3o19b3o21b3o2$277bobobo$330bo21bo21bo$142bobobo6b2o7bobo7b2o7b2o
7b2o89bo48bo21bo21bo$152bo2bo5bobo6b2o8bobo6b2o139bo21bo21bo$146bo132b
obo$313b2o20b2o20b2o20b2o$2bo10b2o127bobobo134bo$13b2o280b2o15bo2bo18b
o2bo18bo2bo18bo2bo$obo139bo134bobobo14b2o13bo4bo16bo4bo16bo4bo16bo4bo
$309bo8bo12bo8bo12bo8bo12bo8bo$2bo139bobobo5b2obo5bob2o5b2obo135bo8bo
12bo8bo12bo8bo12bo8bo$153b2o7bobo7b2o122b2o13bo4bo16bo4bo16bo4bo16bo4b
o$2bo28bo263b2o15bo2bo18bo2bo18bo2bo18bo2bo$13b2o7b2o6bob2o5bobo2bo$o
bobo8bobo7b2o6bo7bo2bobo268b2o20b2o20b2o20b2o$14b2o6bobo6bo3$152bo8bo
9bo8bo8bo9bo6bo8bo$153bo8bo7bo8bo10bo7bo6b2o8bobo$152bobo6bo2bo6bobo6b
2o6b2o7b2o8b2o5bobo108bo13bo27bo13bo$153bobo6b2o6bobo6bo2bo7b2o7b2o6b
o8bo89b3o2bo7b3o2bo8b2o2bo10b3o2bo7b3o2bo8b2o2bo10b3o2bo$13b2o7b2o7bo
bo6bo2bo5bo2bo6bobo6bobo228b2o10bo13bo27bo13bo27bo$13bobo6bo2bo5b2o7b
2o7bobo6bo2bo5b2o242bo13bo27bo13bo27bo$14bobo6b2o8b2o7b2o6bobo6b2o8b2o
227bo2bo16bo6bo13bo20bo6bo13bo$15b2o7b2o6bobo6b2o7b2o6bobo6bobo227bo4b
o15bo20bo6bo13bo20bo6bo$295bo8bo27bo13bo27bo13bo$153bo10bo6bo10bo6bo8b
o96bo8bo27bo13bo27bo13bo$155bo6bo10bo6bo8bobo5b2o98bo4bo9b2o2bo10b3o2b
o7b3o2bo8b2o2bo10b3o2bo7b3o2bo$152b2o7b2o7bo2bo5bo2bo7bo8bo98bo2bo16b
o27bo13bo27bo$154b2o7b2o6b2o7b2o6bobo8b2o$299b2o$13bo2bo5bobo6b2o9b2o
6bobo7b2o$14bobo6bobo5bo2bo5b2o7bobo7b2o$14b2o7b2o8b2o5bo2bo5bo2bo5b2o
$13bobo6bo2bo6b2o7b2o7b2o6bo2bo278b3o$152bo8bo10bo6bo$152b2o7bo2bo7b2o
7b2o$154bo8bo6bo10bo158bo$154b2o6b2o6b2o7b2o159bo$340bo2$14b2o6bobo6b
obo6b2o8b2o7bobo5bo2bo261bob3o$13bo2bo5bobo7bobo5b2o8b2o6bobo7b2o263b
o$13bo2bo6bobo5bobo8b2o5bo2bo5bobo7b2o$14b2o7bobo6bobo7b2o5bo2bo6bobo
5bo2bo84bo5bo11bo5bo$152bo11bo7b2o7b2o150bo$154b2o7b2o5b2o7b2o152bo$152b
2o7b2o7bo11bo150bo$325bo3b2o2$326bo$14b3o8b2o2b2o25b2o7bob2o7bob2o$13b
o3bo7bo4bo8b3o24bo10bo$13bo3bo19b2o3b2o22bo10bo74bo8bo164bo$13bo3bo38b
2o8bo10bo74b2o7bobo162bo$14b3o8bo4bo6b2o3b2o9bo101bo8bo154b3o$25b2o2b
2o8b3o11bo100b2o6bobo$53bo$49b2o15bo10bo241bo$66bo10bo241bo$66bo10bo241b
o$49b2o14bob2o6b2obo$152b2o7bobo147bob3o$13b2o9b2o126bo8bo150bo$13b2o
9b2o129bo8bo$15b2o9b2o126b2o6bobo$15b2o9b2o284bo$17b2o9b2o282bo$17b2o
9b2o282bo$30b2o272bo3b2o$30b2o$305bo$64bob2o11bob2o$65bo14bo$65bo14bo
224bo$65bo14bo71bobo2bo5bo3b2o8b2o3bo122bo$152bobo2bo6b2o3bo6bo2bobo116b
3o3$65bo14bo217bo$65bo14bo217bo$18b2o5bobo37bo14bo170bo4bo41bo$251b2o
2b2o$189bobo5bobo8b2o7b2o2bo7bobobo7bo2b2o7bo49b2o$18b2o5bobo125bobo6b
obo6b2o6b2o$15bo10bo38bo14bo73bo8bo9bo7bo5bo114bo2bo$15bo10bo38bo14bo
71bo3bo6bo6bo3bo6bo6bo2bo4bobobo5b2o2bo8bo10bo11bo58bo4bo$15bo10bo38b
o14bo73bo6bo3bo7bo4bo3bo4bo111bo8bo$64bob2o10b2obo72bo8bo9bo7bo5bo111b
o8bo$197bobo8b2o7b2o2bo7bobobo7bo2b2o7bo47bo4bo$251bo4bo45bo2bo$15bo10b
o224b2o2b2o$15bo10bo276b2o$15bo10bo$13b2obo7b2obo3$153bobo5b2o8bo2bo$
153bo8bo8b2obo$152bob2o5bob2o6bob2o8bo2bo4bobo$152b2o8bobo6bo2bo10b2o
bob2o$91b3o3b3o12bob2o$90bo9bo12bo$90bo9bo12bo$19bo2bo2bo10bo2bo2bo2b
o12bo2bo2bo25bo9bo12bo$237bo$200bobo11bo2bo7bo2bo6bo$19bo5bo10bo8bo12b
o5bo2bo107bobo10b2o45bo139b2o5b2o$90bo9bo12bo39bobo6b2o177bobo9b2obo3b
ob2o$90bo9bo12bo9bo28bo3bo4bo3bo8bo2bo8bo2bo10b2o12b2o9bobo9bo44bo3bo
8b2o8b2o9b3o7bo2b2o7bobo13bo2bobo2bo12b2o5b2o$19bo2bo2bo10bo8bo12bo2b
o5bo22bo9bo12bo9bo30bo9bo8bo11bo11bo13bo10bo13bo58b2o8b2o9bo2bo6bobob
o42bo3bo3bo3bo$91b3o3b3o14b3o3b3o31bo9bo8bo11bo11bo13bo10bo13bo45bo3b
o32bo18bobo$123bo30bo9bo8bo11bo11bo13bo10bo13bo81b2o7bo13bobo29bo3bo3b
o3bo$36bo2bo2bo2bo15bo2bo2bo214bobobo8bo10bo19bo2b2o2$286bo8bo10bo$154b
o9bo8bo11bo11bo13bo10bo13bo$154bo9bo8bo11bo11bo13bo10bo13bo49bo$154bo
9bo8bo11bo11bo13bo10bo13bo58b2o9b2o8b3o$152b2obo6b2obo5b2obo8b2obo8b2o
bo10b2obo7b2obo10b2obo57b2o9b2o10b2o6bobobo$319bo6bo2b2o9bo2bo9bo3bo$
316bo2bo18bo2bo33b2o5b2o$327bo$17bo2bo2bo2bo2bo6bo2bo2bo2bo2bo277bobo
bo7bo2bo12b2o3bo13bo3bo3bo3bo$340bo2bo31b2o5b2o2$17bo11bo6bo11bo308b2o
14bo3bo3bo3bo$152bo51bo11bo11bo$157b2o10b3o6b3o7b3o13bobo9b2o10b2o9b2o
3bo5b2o$17bo11bo6bo11bo10b2o2b2o2b2o83bo2bo3bo12bo5b3o10bo14bo10bo11b
o10b2o5bo3b2o73bo2b2o$59bo8bo83bo16b3o9bo9bo$117b2o3b2o48bo8bo6b3o136b
o$17bo2bo2bo2bo2bo6bo11bo68b2o3b2o78b2o9bobo9b2o99bobobo32bo2bo$59bo8b
o50bobo79b3o9b3o9b3o98bo2b2o32bo2bo$59b2o2b2o2b2o292b2o4b2o$36bo2bo2b
o2bo2bo70bobo117bobo2bo5b2o$117b2o3b2o80bo11bo11bo11b2o5bo2bobo$117b2o
3b2o80b2o10b2o10b2o131b2o4b2o$205bo11bo11bo133bo2bo$363bo2bo4$18b2o2b
2o2b2o9b2o2b2o2b2o2b2o8b2o2b2o2b2o2b2o$18bo8bo9bo12bo8bo12bo$340b3o2b
2o$89bo2bo253bo$18bo8bo9bo12bo8bo12bo265bo$18bo8bo9bo12bo8bo12bo84bo2b
o5bo5bo2bo14bo2bo2bo5bo2bo2bo129bo$89bo2bo245bo7bo$346bo$18bo8bo9bo12b
o8bo12bo11bo2bo69bo2bo2bo5bo2bo2bo14bo8bo8bo137bo$18b2o2b2o2b2o9b2o2b
2o2b2o2b2o8bo12bo20bobo185bobobo52bo$293bo8bo12b3o2b2o10b3o2b2o9b3o2b
2o$84bo2bo5bobo64bo11bo17bo2bo2bo5bo2bo2bo72bo39bo32bo$59bo12bo17bobo
5bo2bo191bob6obo10bo16bo$59b2o2b2o2b2o2b2o208bobobo7bob6obo10bo16bo$90b
obo64bo2bo2bo5bo2bo2bo14bo8bo8bo104bo7bo8bo23bo$98bo2bo183bo10bo2bo21b
o32bo$321bo32bo$93bo2bo60bo2bo5bo5bo2bo14bo2bo2bo5bo2bo2bo72bobobo27b
o16bo$313b2o2b3o10b2o2b3o9b2o2b3o$346bo$93bo2bo96bo11bo132bo$338bo$338b
o7bo$190bo2bo2bo5bo2bo2bo137bo$346bo$338bo$18bo2bo2bo51bo2bo2bo107bo2b
o5bo5bo2bo129b2o2b3o3$18bo5bo51bo5bo2$23bobobobobobobobobobobobobobob
obobobobobobobobobobobobobo$18bo2bo2bo51bo2bo2bo73bo2bo2bo2bo5bo2bo2b
o10bo2bo2bo5bo2bo2bo11bo2bo2bo5bo2bo2bo$23bo53bo$281bobobo35bobo6b2o13b
2o8b2o8bobo6bobo$23bo53bo78bo8bo2bo2bo5bo10bo5bo2bo2bo5bo11bo5bo2bo2b
o5bo57b2o9bo2bo$281bo11bo2bo9b2o$23bo53bo242bo2bo5bobo12b2o8bobo7bo2b
o7b2o$156bo8bo5bo2bo2bo10bo2bo2bo5bo2bo2bo11bo2bo2bo5bo2bo2bo44bobobo
$23bo53bo215bobo9bobo$281bo3bo8bobo9bobo13b2o7b2o13b2o7bobo6b2o7b2o$23b
o53bo78bo2bo2bo2bo8bo16bo11bo17bo11bo$18bo2bo2bo51bo2bo2bo198bobobo$23b
obobobobobobobobobobobobobobobobobobobobobobobobobobobo242b2o7b2o14b2o
8b2o7bobo6bobo$168bo2bo2bo2bo10bo2bo2bo2bo2bo2bo2bo11bo2bo2bo5bo2bo2b
o$18bo5bo51bo5bo$294b2o9bo2bo$168bo8bo10bo17bo11bo5bo2bo2bo5bo56bo2bo
9b2o$18bo2bo2bo51bo2bo2bo$345b2o7b2o7b2o$168bo8bo10bo17bo11bo2bo2bo5b
o2bo2bo56b2o10b2o13bo2bo5bobo$295b2o10b2o$344bobo6b2o8b2o$168bo2bo2bo
2bo10bo2bo2bo2bo2bo2bo2bo114bobo6b2o2$344bobo6b2o7bobo$322b2o7b2o$295b
2o8b2o$18bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2b
o2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo172b2o12b2o35b2o7bobo6b2o$
320b2o7b2o2$18bo101bo172bobo9bobo$153b2o3bo4bo3bo3bo3bo3bo3bo3bo3bo3b
o3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo4bo3b2o32bobo9bobo$154b2o5b
o3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3b
o5b2o$18bo101bo3$18bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo
2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo3$153b2o3bo5bo5b
o5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo3b2o$154b2o5bo5bo5bo5bo5bo
5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5b2o5$18b2o2b2o2b2o2b2o2b2o2b2o2b2o2b
2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o
2b2o2b2o$18bo104bo$153b2o3b2ob2o3b2ob2o3b2ob2o3b2ob2o3b2ob2o3b2ob2o3b
2ob2o3b2ob2o3b2ob2o3b2ob2o3b2ob2o3b2ob2o3b2ob2o3b2o17bobobo$294bobo$18b
o104bo157bo3bo7b2o3bo$18b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b
2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o30bo107b
o35bo$281bobobo15bo$301bo3b2o$153bo109bo17bo3bo17bobo$153b2o107b2o$154b
o107bo18bobobo$18bo99bo$19b3o3b3o3b3o3b3o3b3o3b3o3b3o3b3o3b3o3b3o3b3o
3b3o3b3o3b3o3b3o3b3o3b3o$18bo99bo$18bo99bo3$260bo20bobobo7bobo$155bo103b
2o32b2o$156bo102bo21bo3bo10bo$156bo139bo$281bobobo$155bo104bo33bo$285b
o8bo$296b2o$86bo2bo2bo2bo58b2o2bobob2o2bobob2o2bobob2o2bobob2o2bobob2o
2bobob2o2bobob2o2bobob2o2bobob2o2bobob2o2bobob2o2bobob2o2bobob2o21bob
obo9bobo3$83bo2bo8bo2bo55bo104bo$262bo2$80bo2bo14bo55bo107bo$259bo$295b
o8bo6bo2bo$77bo2bo17bo55bo121bo4bobobo$293b2o7b2o7bobo$259bo14bobo8bo
7b2o7b2o7bobo$74bo2bo17bo2bo55bo107bo$276bo4bobobo7bo8bo8bo$262bo$71b
o2bo17bo2bo58bo104bo16bo4bo11bo8bo8bo2$274bobobo2bobobo7b2o7b2o7bobo$
68bo2bo17bo2bo61b2o2bobob2o2bobob2o2bobob2o2bobob2o2bobob2o2bobob2o2b
obob2o2bobob2o2bobob2o2bobob2o2bobob2o2bobob2o2bobob2o33b2o7b2o7bobo$
302bobo$295bo15bo2bo$65bo2bo17bo2bo65bo104bo2$156bo$62bo2bo17bo2bo69b
o102bo$155bo103b2o$260bo$59bo2bo17bo2bo3$56bo2bo17bo2bo3$53bo2bo17bo2b
o3$50bo2bo17bo2bo3$47bo2bo17bo2bo3$44bo2bo17bo2bo3$41bo2bo17bo2bo3$41b
o17bo2bo3$41bo14bo2bo3$41bo2bo8bo2bo3$44bo2bo2bo2bo!

Updates:
- Changed FWKnightships' p8 as I have a preference for 2o$b2o! over 2o$obo!
- May13's p5s and p12s, and my extension of May13's second p5
- Added FWKnightship's p8 and extra-sparky p9
- Added May13's 2c/2o

Now stop targeting me, our benevolent guardian and several innocent users. I would appreciate it if you did not doubt everything I did.

[confocaloid]

[...]
I feel it shouldn't be called a photon because the rule is range-3. Photons in this case should be reserved for spaceships with a simplified speed of 3c/1o (which do not exist in Factorio).

Instead, since c is the terminal velocity for orthogonal spaceships, I would just call this a plain old 2c/2o spaceship.
[...]

You did not answer the question. The quote you posted has only a claim, without proof.

H. H. P. M. P. Cole already proved this.

Where I can read this? You did not link to the place where that was proven.

[toroidalet]

First, the factual issue at hand. Please read all of this first, and do not use this post to confirm that you are right, no matter how right you are:

There was not a proper proof that movement faster than one diagonal cell per generation was impossible. Indeed, it briefly is (look at the block corner):

Code: Select all

x = 6, y = 7, rule = R3,C0,S2,B3,N+
5b2o2$2b2o$2b2o2$o!

However, it is fairly easy to show that one cell per generation is the orthogonal speed limit. Consider any cell to be born on the first empty row. Since by definition it is on the first empty row, the only cells that could have been on are the 3 cells directly behind it:

Code: Select all

x = 34, y = 8, rule = LifeHistory
5.D$5.D$5.D$2B3DB3DB5.C8.5BA4B$5.A10.C$5.A6.6C$5.A10.C$15.C!
#C [[ VIEWONLY ]]

Finally, the fuse example was a little irrelevant. There are fuses at c diagonal in Life, but no way to move, even for a single generation, at that speed. Or consider B6/S6,9 with the following neighborhood:

Code: Select all

0,0,0,0,0,1,0,0,0,0,0
0,0,0,0,0,0,0,0,0,0,0
0,0,0,0,0,0,0,0,0,0,0
0,0,0,0,0,0,0,0,0,0,0
0,0,0,0,2,2,2,0,0,0,0
1,0,0,0,2,0,2,0,0,0,1
0,0,0,0,2,2,2,0,0,0,0
0,0,0,0,0,0,0,0,0,0,0
0,0,0,0,0,0,0,0,0,0,0
0,0,0,0,0,0,0,0,0,0,0
0,0,0,0,0,1,0,0,0,0,0

It almost certainly has fuses far faster than the vacuum speed limit.

There. I hope we can now all agree that c orthogonal is the maximum and c/2 diagonal is theoretically possible.

EDIT by dvgrn: In response to a post report by a non-participant in the disagreement, I've moved to a new dedicated thread the second part of this post, which was a bit too long to stay here, since it's not about Factorio -- but it is very very much worth reading by everyone involved in recent public disagreements.

[Disaster16439]

Also, is it possible to make a rule with the same rules as Factorio but with the neighborhood below?

Code: Select all

bobobo$o2bo2bo$3bo$3ob3o$3bo$o2bo2bo$bobobo!

It seems like that version is terribly explosive. However, rules like R3,C0,S0-1,B4,N@552447E224AA are stable(b4 allows rules to expand out of the bounding box). However, it is pretty much impossible to get a balance.

[HerscheltheHerschel]

86M:

Code: Select all

x = 11, y = 15, rule = R3,C0,S2,B3,N+
2bobobo2bo$bobo3b2o3$8b2o$2o6b2o$2o$4bo$4bob2o2$3b2obo$6bo$9b2o$b2o6b
2o$b2o!

113M:

Code: Select all

x = 15, y = 19, rule = R3,C0,S2,B3,N+
4bo$bobo$bo2bo$2b3o4$11bo2bo3$12bobo2$2o$2o4$4b2o$4b2o!

131M:

Code: Select all

x = 15, y = 19, rule = R3,C0,S2,B3,N+
4bo$bobo$bo2bo$2b3o4$11bo2bo3$12bobo2$2o$2o4$4b2o5b2o$4b2o5b2o!

A way to turn factorials pulling pseudo-factorial and factorials pulling dot into a factorial:

Code: Select all

x = 17, y = 16, rule = R3,C0,S2,B3,N+
4bo2b3o2$3bo2$4bo2b3o5b2o$15b2o5$4bo2b3o2$2obo2$4bo2b3o5b2o$15b2o!

Inflated domino pulling block:

Code: Select all

x = 10, y = 2, rule = R3,C0,S2,B3,N+
4o4b2o$4o4b2o!

144M:

Code: Select all

x = 17, y = 22, rule = R3,C2,S2,B3,N+
4bo$bobo$bo2bo$2b3o4$11bo2bo3$12bobo2$2o$2o2$15b2o$15b2o2$4b2o3$4b2o!

[b-engine]

Clean fuse and failed splitter that may prove Factorio Turing complete:

Code: Select all

x = 128, y = 118, rule = R3,C2,S2,B3,N+
87b2o$87b2o4$89b2o$89b2o4$87b2o$87b2o4$89b2o$89b2o4$87b2o$87b2o4$89b2o
$89b2o4$87b2o$87b2o4$89b2o$89b2o4$87b2o$87b2o4$89b2o$89b2o4$87b2o$87b
2o4$89b2o$89b2o4$87b2o$87b2o4$89b2o$89b2o4$87b2o$87b2o4$89b2o$89b2o4$
87b2o$87b2o4$89b2o$89b2o4$87b2o$87b2o2$92b2o$92b2o4$90b2o$90b2o4$92b2o
$92b2o4$90b2o$90b2o5$16b2o8b2o8b2o8b2o8b2o8b2o8b2o8b2o8b2o8b2o8b2o8b2o
$o2b3o10b2o8b2o8b2o8b2o8b2o8b2o8b2o8b2o8b2o8b2o8b2o8b2o$11b2o8b2o8b2o
8b2o8b2o8b2o8b2o8b2o8b2o8b2o8b2o8b2o$11b2o8b2o8b2o8b2o8b2o8b2o8b2o8b2o
8b2o8b2o8b2o8b2o!

[H. H. P. M. P. Cole]

FACTORIO STATUS REPORT: 2023

Since Factorio's debut in early October 2023, numerous patterns have been discovered, and it's all thanks to you all who have helped me along the way.

I will reveal the reason why I posted the OP: The rule's true purpose is to be a non-Moore LtL rule which is notable.

PRE-FORUM HISTORY

In June 2023 I discovered this rule, and thought it was interesting. I found all the objects which have a 4x4 predecessor by hand using my own RLE of 4x4 configurations.

Subsequently I created my own program (in the OP) to find new objects. This included the first few p3s, p4s, and p6s. Sadly, it couldn't find spaceships, but I found numerous c/1o ships by hand. The larger oscillators and SLs were found mostly by hand. All the prime forms I have discovered are in the OP.

POST-FORUM HISTORY

Since the OP, Arie Paap and b3s23love have contributed to many of the Catagolue hauls, FWKnightship in oscillator technology, AlephAlpha in creating the wonderful factoriosrc (sadly I can't get it to work), and Haycat2009 for exchanging numerous PMs with me on Factorio.

Finally, I have though that if John Conway had found this instead of Life, he would probably have liked it better, because of the very mathematical structure of the small patterns, and the fact that there are more interesting theorems in this rule than in Life (footnote 1).

THEOREMS AND CONJECTURES SO FAR

All 1xn soups stay 1xn.
- The only known 1D object is the factorialship.
- All 1xn soups with kinks in them stay 1xn and preserve the kinks (like May13's second p5 and my extension thereof)
- There are only four 1D infinite still-lifes:

Code: Select all

x = 23, y = 16, rule = R3,C2,S2,B3,N+:T24,24
obobobobobobobobobobobo5$o2bo2bo2bo2bo2bo2bo2bo5$2o2b2o2b2o2b2o2b2o2b
2o5$3o3b3o3b3o3b3o!

All 2xn soups stay 2xn.
- There are only five known periods/speeds possible in 2xn: p1, p2, p4, c/1o, and 2c/2o.
- There are only four known width-2 still-lifes.

Permutation of columns in a 4x4 soup is permissible provided the soup never escapes its bounding box. (This includes objects too.)
- All 2xn objects have greater than or equal to 2 expanded forms.
- All 3xn objects have greater than or equal to 2 expanded forms provided the object never escapes the 3xn height constraint. If the object has C2 or D2- symmetry, only 1 expanded form is guaranteed.

All known p2 oscillators have a constant population.

The orthogonal speed limit is c/1o.
- All reduced-speed c/1o ships have the line-of-three frontend.
The diagonal speed limit is conjectured to be c/2d.

Factorio can emulate R3,C2,S2,B3,NW0000000000000000010001110111000100000000000000000 using 1x3 metacells with one cell in them, and B3/S2V using 3x3 metacells with one cell in them.

Observe:

Code: Select all

x = 28, y = 13, rule = R3,C2,S2,B3,N+
b2o6bo2bo5bo5bo2bo3$o2bo5bo2bo2bo5bo2bo2bo3$obo9bo11bo3$bobo5bo2bo2bo
5bo2bo2bo3$9bo2bo5bo5bo2bo!

Soups of around 25% density will tend to evolve as amorphous ‘plasma blobs’ for a long time. This will be named as the Durnak effect, after its discoverer.

iC1 soups tend to have a greater density of ash than C1 soups of the same size. This will be named as the Cole effect, after its discoverer.

(Sidenote: notice the various times the number 4 crops up. To be precise, the Durnak effect density is approximately 25.12271774%, which is the greater real root of 286 x^2 (1-x)^10=1. This, by sheer coincidence, is approximately 1/4.)

PATTERN COLLECTION AND TODO LIST

Please improve the intro if you can!

Code: Select all

# Factorio pattern collection 2.0
# 1/1/24
# H. H. P. M. P. Cole
# =================================
# Factorio is a range-3 cellular automaton that operates
# on the Cross neighbourhood. Each of the cells is affected
# by its three orthogonal neighbours on each side.
# The rulestring in HROT notation is R3,C2,S2,B3,N+.
# =================================
# In this collection, only ‘prime forms’ are compiled –
# those which partial or complete empty columns or rows
# cannot be trivially removed from the oscillator without
# changing its mechanics.
# =================================
# The orthogonal speed limit has been proven to be c/1o.
# The diagonal speed limit is conjectured to be c/2d by
# Haycat2009, but such a spaceship with such a speed
# is currently unknown.
# =================================
# CREDITS
# Rule discovered by H. H. P. M. P. Cole
# Pattern collection created by H. H. P. M. P. Cole
# With contributions by:
# H. H. P. M. P. Cole, FWKnightship, May13, wildmyron, Haycat2009,
# lemon41625, b3s23love, C28, AlephAlpha, and the anonymous C4_4 hauler
# Periods and speeds known:
# p1, p2, p3, p4, p5, p6, p8, p9, p10, p12, p24, p72, p18n
# c/1o, 2c/2o, 4c/4o, c/2o, c/3o, 2c/3o, c/3d
# =================================
x = 693, y = 319, rule = R3,C2,S2,B3,N+
223bobobo52bo3bo$462bo6bo$171bo12bo12bo10bo18bo52bo3bo65bo12bo9bo11bo
6bo7bo8bo13bobobo19bo3bo12bo2bo50bo5bo16bo6bo$45bo11bo8bo15bo7bo9bo8b
o61bo12bo12bo10bo41bo8bo8bo81bo12bo9bo11bo6bo7bo8bo37bo3bo10b2o4b2o17b
obobo26bo5bo16bo6bo30bobobo$45bo11bo8bo15bo7bo9bo8bo41bo19bo12bo12bo10b
o14bobobo2bobobo15bo8bo8bo11bobobo2bobobo38bobobo88bo23bo3bo10b8o43bo
bo2bo5bo2bobo6bobo2bo6bo2bobo38bo$21bobobo19bo11bo8bo15b2o6b2o8b2o7b2o
22bo17bo96bobo8b2o7bo80b3o11b3o5b3o11b3o2b3o7bob2o2b2obo52bo2b2o2bo21b
o21bobo11bobo6bobo12bobo25bo$133bo17b2o14bo12bo12bo10bo18bo6bo20bo5bo
26bo2bo17bo3bo20bo18bobo12b2o5b2o13b2o2b2o10b2o2b2o15bobobo36bo2bo46b
2o11b2o8b2o12b2o39bo$21bo61bo7bo9bo8bo22bo33bo3bo8bo3bo8bo3bo6bo3bo40b
o8bo46bo3bo38bo3bo9bo3bo3bo3bo57bobobo11bobo36bobobo2bobobo15b2o11b2o
8bo3bo6bo3bo26bobobo$45bo11bo8bo16bo7bo9bo8bo18bo22bo14b2o11b2o11b2o9b
2o17bobobo2bobobo13bo11bo7bo15bo2bobobo13bo3bo20bobobo15bo12bo9bo13b4o
9bo2bo2bo2bo54bo2bo48bobo5bobo12bobobo2bobobo37bobobo$21bobobo56bo7bo
9bo8bo19bo22bo2bo10bo12bo59bobobo52bobobo38bobobo77b9o2bo3bo8bo7bo10b
4o19bo6bo18bo4bo5bo4bo6bo16bo$30bobobo79bo14bo3bo17bo3bo95bo5bo11bo80b
o12bo9bo11bo6bo70bo4bo44bob2o9b2obo7bobo3b4o3bobo24b9o2bo3bo5b2o$56bo
8bo17bo7bo9bo8bo3bo15bo36bo12bo12bo10bo14b18o2bo3bo25bo6b18o2bo3bo4bo
3bo18b9o2bo3bo41bo2b2o2bo10bo2bo25bobobo11bobo12bob2obo18bobobo2bobob
o14b2o13b2o6b2o14b2o45bobo$19b9o2bo3bo21bo8bo47b2o64bo25bo63bo37bo77b
obo2bobo9bo4bo39bo3bo51bobobo28bo16bo34bobobo6bo2bo$56b2o7b2o48bo13bo
109bobobo52bobobo38bobobo6bo12bo9bo13bo2bo9bo3b2o3bo13bobobo17b2ob3ob
2o65bo3bo15bobob4obobo$30bobobo22bo5bo2bobo23bo9bo166bo80bo12bo9bo10b
2o6b2o6bo8bo35bo3bo3bo9bob2obo14b18o2bo3bo6b5o5b5o7bobo12bobo25bobobo
17b3o$92bo9bo123bobobo52bo3bo19bo22bobobo49bo8bo6bo8bo17bo36bo2bo49bo
7bo15bo2b2o2bo54bo$23bo67b2o8b2o40bo163bo77b2ob2ob2o52bo7bo9b2o2b2o34b
obobo10bo5bo58bo$91bo7bobo2bo38bo46bo11bo9bo17bo52bo3bo46bo49bo8bo29b
obobo18bo5bo12b2o69bo2b2ob6ob2o2bo$21bobo21bo12bo13bo70bo11bo3bo6bo3b
o6bo3bo8bo11bo9bo235bobo39bobobo19bo13bo8b3o10b3o26bobobo$45bo12bo13b
o52bo7bo5bo11bo3bo3bo6bo3bo6bo3bo8bo11bo9bo13bobobo52bobobo42bobobo49b
2obo2bob2o6bo8bo17bo19bobobo62bobobo5bobobo7bo5bo4bo5bo$23bo21bo12bo13b
o52bo7bo5bo11bo3bo3bo6bo3bo6bo3bo218bo8bo36bo5bo7bobo6bobo22bo19bo3bo
5bo3bo14bo2bo36bo$125bo7bo5bo3bo7bo43bo11bo18bo60bo42bo54bo6bo8bo6bo14b
obobo32bobo6bobo43b2o2bo3bo2b2o16b2o$23bo17bo12bo13bo60bo15bo44bo4bo6b
o4bo4bo233bo5bo9bo2b2o2bo20bobobo19b4o7b4o11b2o2b2o2b2o29bobobo$41bo3b
o8bo3bo9bo3bo56bo16bo8bo3bo6bo3bo6bo3bo10bo2bo8bo2bo2bo15bobobo56bo42b
obobo50bo6bo7b2o6b2o36bo5bo9b2o4b2o44bo2bobo3bobo2bo11b2obo2bob2o$21b
obobo15b2o11b2o12b2o13bo7bo9bo8bo14bo3bo3bo5bo5bo5bo4bo10bo11bo14bo11b
obo176bo6bo69bo6bo24bo19bo5bobo5bo10bo10bo$40bo12bo13bo15bo7bo9bo8bo17b
obo11bo3bo7bo249b2o40bob3obo7bo10bo48b3o16b2o8b2o$59bo13bo8b2o6b2o8b2o
7b2o293b2o39bo2b3o2bo8bo6bo20bobobo25b3o16bo10bo$59bo13bo55bo274b2o111b
o7bo11b2o3b6o3b2o$58b2o12b2o8bo7bo9bo8bo338bobo67bobobobo13b3o8b3o$58b
o11bobo2bo6bo7bo9bo8bo350bobo6bobo46bo2bo2bo16bo6bo$83bo7bo9bo8bo334b
o7bo62bob2o3b2obo12bo4b2o4bo$445bo7bo6bo10bo43bo5bo5bo$82bo7bo9bo8bo4b
o330bo7bo11b2o53b3o21b2o$83bo7bo9bo8bo3bo65bo21bo6bo252bo6bo73b4o$113b
2o65bo21bo6bo303bo5b2ob2o5bo12bo4bo$115bo64bo21bo6bo235bo7bo6bo3bo2bo
3bo43bo3bo3bo3bo$92bo9bo342bo7bo6bo2b2o2b2o2bo43b2obo5bob2o12bo2b4o2b
o$92bo9bo83bo260bo3bo9bob2o2b2obo44bo4bobo4bo12b2obo2bob2o$91b2o8b2o77b
o5bo15bo6bo238bobo9b2obo4bob2o70bo4bo$91bo7bobo2bo78bo2bo18b2o238bo2b
obo2bo7bo2bo2bo2bo42bo3bo7bo3bo8b3obo4bob3o$184bo18b6o330bo3bo2bo3bo$
447b2ob2o9b4o2b4o46bo7bo12bo12bo$186bo274bo8bo44bo11bo10bo4bo2bo4bo$515b
o2bo5bo2bo11bo2bo4bo2bo$447bo3bo61bo15bo12bob2obo$445bobo3bobo59bo15b
o13bo2bo$461b2obo2bob2o44bo3bo3bo3bo14bo4bo$447bo3bo10bo6bo45bo2b2o3b
2o2bo10bobobo4bobobo$445bo7bo59bobo11bobo10bobob2obobo$448b3o10bo3b2o
3bo49bobo14bo3b8o3bo$462bo6bo45bo2bo5bo2bo8bo6bo2bo6bo$515bo11bo8bo16b
o$462bo6bo43bo15bo6bobo12bobo$518bo5bo15b3ob2ob3o$463bo4bo46b2o2bo3bo
2b2o8bobo12bobo$463bo4bo49bo2bo2bo12bobobobo2bobobobo$463bo4bo44bo15b
o$463b2o2b2o50b2ob2o15bo3bo2bo3bo$515bo11bo11bobobo2bobobo$464bo2bo47b
obo7bobo$464bo2bo47bo11bo2$516bo3bobo3bo10b3obo6bob3o$516bo3bobo3bo11b
ob2o2b2o2b2obo$519bo3bo$519bobobo$517bobo3bobo13bobo6bobo$515bo4bobo4b
o11bobo6bobo$515bobo7bobo$515bo11bo13bo6bo$516bo9bo11bo12bo$515bo11bo
13bo6bo$516b2o7b2o10bo14bo$515bo3bo3bo3bo9b2o12b2o$537bo2bo8bo2bo$515b
ob2o5b2obo12bo8bo$519bo3bo16bo8bo$540bo8bo$516bo3b3o3bo11bo12bo2$515b
o11bo14bo4bo$520bobo17bobo4bobo$515bobobobobobobo10bo12bo$517b2o2bo2b
2o12bo4bo2bo4bo$519bo3bo$542bo4bo$515bo2b2o3b2o2bo2$516bo9bo11bo12bo$
515bo2bo5bo2bo8bo16bo$515bo11bo8bo16bo$538bo12bo$518bobobobo14bo10bo$
516b2o7b2o9bo16bo$539bobo6bobo$536bobo2bo6bo2bobo$516bobo5bobo9bo2bo2b
o4bo2bo2bo$516bo9bo$516bo9bo11bo12bo$515bo11bo15$440bobobo104bo2bo2bo
2bo49bobobo2bobobo8b2o$277bobobo100b3o14b3o123b3o2bo97b2o6b2o$440bo58b
3o2b2o38b3o2bo8bo2b3o48bo6bo16b2o$142bobobo6b2o7bobo7b2o6b2o7b2o6b2ob
o5bob2o5b2obo62bo223bo24bo100bo$152bo2bo5bobo6b2o7bobo6b2o8b2o7bobo7b
2o165bo14bo40bobobo52bo24bo89bo2bobobo11bob2o$146bo132bobo102bo14bo97b
o24bo18bo24bo15b2o2b2o$42bo27b2o7b2o7bobo6bo2bo5bo2bo6bobo6bobo256bo14b
o44bo52bo7bo16bo18bo24bo45bo2bo14b2obo$2bo10b2o9b2o7b2o6bob2o5bobo2bo
14bobo6bo2bo5b2o7b2o7bobo6bo2bo5b2o16bobobo134bo223bo24bo10bo24bo66bo
$13b2o9bobo7b2o6bo7bo2bobo15bobo6b2o8b2o7b2o6bobo6b2o8b2o174b3o8b3o12b
3o10b3o13b3o12b2o15b2o13b2o34bobobo60bo24bo51bo4bo24bo2bobobo7b2o$obo
22b2o6bobo6bo29b2o7b2o6bobo6b2o7b2o6bobo6bobo15bo134bobobo9b2o204bo24b
obo3b2o52bo4bo39b2o6b2o$292b2o63b3o11bo2bo13bo2bo11bo2bo45bo8bo12b3o2b
2o10b3o2b2o9b3o2b2o25bobo24bobo13bo4bo47b2o$2bo139bobobo155bo10bo14bo
14bo26bo4bo11bo4bo9bo4bo72bo32bo$152bo8bo9bo8bo8bo9bo6bo8bo8bo10bo6bo
9bo6bo42bo10bo14bo14bo24bo8bo7bo8bo5bo8bo42bob6obo10bo16bo160b2o$2bo150b
o8bo7bo8bo10bo7bo6b2o8bobo8bo6bo10bo5bo8bobo30b2o8bo10bo6bo7bo14bo13b
3o8bo8bo7bo8bo5bo8bo42bob6obo10bo16bo49bo28bo5bo2b3o10b3o2bo49b2o3bo$
152bobo6bo2bo6bobo6b2o6b2o7b2o8b2o5bobo6b2o7b2o7bo2bo4bo2bo7bo30b2o27b
o49bo4bo11bo4bo9bo4bo64bo7bo8bo23bo60bo20bo47bo7bo$obobo148bobo6b2o6b
obo6bo2bo7b2o7b2o6bo8bo8b2o7b2o6b2o6b2o6bobo39b2obo11b3o2bo9b3o2bo9b3o
2bo6b3o11bo2bo13bo2bo11bo2bo48bo2bo21bo32bo130bo3b2o$13bo2bo5bobo6b2o
9b2o6bobo7b2o9b2o6bobo6bobo6b2o8b2o7bobo5bo2bo207bo14bo129bo32bo25bo28b
o74b2o$14bobo6bobo5bo2bo5b2o7bobo7b2o9bo2bo5bobo7bobo5b2o8b2o6bobo7b2o
208bo14bo21b2o15b2o13b2o66bo16bo84bo20bo$14b2o7b2o8b2o5bo2bo5bo2bo5b2o
10bo2bo6bobo5bobo8b2o5bo2bo5bobo7b2o345b2o2b3o10b2o2b3o9b2o2b3o62bo2b
3o10b3o2bo$13bobo6bo2bo6b2o7b2o7b2o6bo2bo9b2o7bobo6bobo7b2o5bo2bo6bob
o5bo2bo377bo33bobo24bobo$497bo25b2o3bobo104b2o$153bo7bo8bo10bo6bo11bo
4bo11bo5bo8bo8bo7b2o7bobo236bo24bo7bo51bo4bo39b2o6b2o$152b2o7b2o7bo2b
o7b2o7b2o5bo10bo7b2o7b2o5b2o7bobo5bo8bo238bo7bo16bo18bo24bo15bo4bo39b
2o$154bo8bo8bo6bo10bo8b2o6b2o5b2o7b2o10bo8bo7bo8bo29b3o110b3o98bo35bo
24bo15bo4bo45bo$154b2o7b2o6b2o6b2o7b2o7b2o6b2o7bo11bo7b2o6bobo6b2o6bo
bo243bo35bo24bo63b2obo$112b2o383bo32bo$13bo2bo2bo9bo2bo26bob2o228bo112b
o92b2o2b3o18bo7bo51b2o2b2o43bob2o$29bo2bo6bob2o6bob2o19b3o7b2o3b2o5bo
bobobo190bo48bobo3bobo55bo125bo13b3o2bo8bo2b3o67bo$27b2o11bo2bo6bo2bo
6bo2bo6b2o3b2o7b3o7b2o3b2o11b2o177bo21bobobobobobo80bo117b2o3b3o106b2o
$13bo5bo30bo2bo6bo2bo6b2o3b2o5b2o3b2o6bobobo9bo202bo2bo5bo2bo15bo7bo200b
o2bo2bo2bo69b2o6b2o$40bo2bo65bo185b3obo11bobo9bobo16bo3bo49bob3o227b2o
$27b2o12b2obo6b2obo6b2obo44bo42bobo2bo5bo3b2o8b2o3bo115bo11bobo11bobo
70bo$13bo2bo2bo85b2o45bobo2bo6b2o3bo6bo2bobo153bobo3b2o3b2o3bobo$118b
2o5bobo182b2o13b2o13bo7bo91bobobo9b2o3bo$298bo36bo2bobo7bobo2bo43bo61b
o$105b2o191bo11bo15bo70bo42bo11bo3bo2bo$118b2o5bobo170bo98bo$115bo10b
o133bo4bo24bo3b2o14bo15bo62bo3b2o45bobobo$115bo10bo133b2o2b2o69bo2bob
o7bobo2bo$14b3o7b2o2b2o5b2o8bob2o7bob2o55bo10bo62bobo5bo2bo5bobo8b2o7b
2o2bo7bobobo7bo2b2o7bo28bo18b2o13b2o13bo7bo41bo49bo3bo$13bo3bo6bo4bo5b
2o9bo10bo14bo10b3o7b2o58bobo6bobo6b2o6b2o154bobo3b2o3b2o3bobo$13bo3bo
19b2o7bo10bo8bob2o11b2o3b2o5b2o59bo8bo9bo7bo5bo7bo114bobo11bobo113bob
obo35bobo6b2o13b2o8b2o8bobo6bobo10b2o9b2o$13bo3bo19b2o7bo10bo14bo22b2o
55bo3bo6bo6bo3bo6bo6bo2bo6b2o5bobobo5b2o2bo8bo10bo11bo39bo19bobo9bobo
16bo3bo43bo62b2o9bo2bo76bo3bo6bo3bo$14b3o7bo4bo9b2o31bo8b2o3b2o7b2o18b
o10bo27bo6bo3bo7bo4bo3bo4bo7bo95bo20bo2bo5bo2bo15bo7bo41bo61bo2bo9b2o
$24b2o2b2o9b2o26bo15b3o11b2o16bo10bo27bo8bo9bo7bo5bo7bo100b3o14bobobo
bobobo59b3o93bo2bo5bobo12b2o8bobo7bo2bo7b2o73bo2bobobo22b2o25b2o$67bo
29b2o16bo10bo79bobo8b2o7b2o2bo7bobobo7bo2b2o7bo77bobo3bobo196bobo8b2o
76b2o3bo7bo2b3o14bo3b2o$46bo10bo12b2obo25b2o12b2obo7b2obo132bo4bo186b
obo9bobo79bobo9b2o49bo2bo3bo15bo7bo25bo7bo$46bo10bo9bo31b2o159b2o2b2o
32bo84bo69bobo9bobo13b2o7b2o13b2o7bobo6b2o7b2o99bo3b2o29b2o3bo$46bo10b
o240bo84bo225bo2bobobo2bobobo8b2o39b2o$45bob2o6b2obo239bo84bo$227bobo
249b2o7b2o14b2o8b2o7bobo6bobo74bo2bo3bo2bo3bo$153bobo5b2o8bo2bo28bobo
10b2o72bob3o80bob3o266b2o11b2o$153bo8bo8b2obo6bobo6b2o48bo2bo7bo2bo36b
o84bo232bo2bobobo2bo3bo22bobo9bobo$152bob2o5bob2o6bob2o5bo3bo4bo3bo8b
o2bo8bo2bo9b2o35bo188b2o9bo2bo178b2o11b2o$152b2o8bobo6bo2bo7bo9bo8bo11b
o10bo37bo189bo2bo9b2o78bobo8bobo87bo13bo$182bo9bo8bo11bo10bo15b2o9bob
o8bo28bo26bo57bo167bo3bo6bo3bo87bobo7bobo$14bob2o7bob2o6bob2o143bo9bo
8bo11bo10bo12bo10bo42bo84bo127b2o7b2o7b2o126bo5bo$15bo10bo9bo18b3o3b3o
9b2o2b2o6bo2bo2bo2bo7bo2bo2bo9bo2bo2bo2bo109bo10bo15bo26bo23bo2bo2bo20b
o2bo30bo75b2o10b2o13bo2bo5bobo158b2o5b2o$15bo10bo9bo17bo9bo7bo2b2o2bo
157bo10bo14bo30b2o3bo18bo20bo2bo2bo2bo19bo3b2o80b2o10b2o78b2o8b2o90bo
bo5bobo$15bo10bo9bo17bo9bo7bo6bo183bo51bo2bo2bo17bo8bo154bobo6b2o8b2o
21bo2bo9b2o89b2o5b2o$54bo9bo8bo4bo6bo8bo7bo5bo2bo6bo8bo24bo29bo9bo8bo
11bo10bo38bo34bo19bo18b2o10b2o18bo110bobo6b2o$73bo4bo78b2o23bo9bo8bo11b
o10bo86bobo9bobo$72bo6bo72bo2bo3bo22bo9bo8bo11bo10bo12bo10bo254bobo6b
2o7bobo$15bo10bo9bo35bo2b2o2bo5bo8bo7bo2bo5bo6bo8bo24bo27b2obo6b2obo5b
2obo8b2obo7b2obo11bo10bo49bo37b2o12b2o17bo111b2o7b2o$15bo10bo9bo9bo7b
o9bo8b2o2b2o158bo10bo14bo34bo10bob4o7b4obo41bo84b2o8b2o$15bo10bo9bo9b
o7bo9bo170b2obo7b2obo13bo27b3o68b3o87b2o12b2o35b2o7bobo6b2o$37b3o3b3o
8bo9bo20bo2bo2bo2bo10bo2bo2bo6bo8bo135bo72b2o12b2o127b2o7b2o$46bo8b3o
3b3o197b2obo46bobo9bobo215bob2o$291bo26bo43bo89bobo9bobo75bo2b2o$15bo
10bo91bo2bo2bo2bo55bo6b3o10bo11bo11bo63bo23bo2bo2bo15b2o10b2o11bo90bo
bo9bobo76bobobo$15bo10bo125b3o6b3o7b3o6b3o7b3o10bobo9b2o10b2o62bo26bo
20bo8bo13bo$15bo10bo128bo5b3o10bo30bo10bo11bo86bo2bo2bo17bo2bo2bo2bo$
14bob2o6b2obo124b3o9bo9bo5b3o7b3o103b2o44bo2bo21b2o$155bo8bo6b3o6b3o10b
o52bob2o7bo5bo54bo184bobo3bobo$36b2o2b2o2b2o7b2o2b2o2b2o9b2o2b2o2b2o2b
2o8b2o2b2o2b2o2b2o71bo9bo3bo7b2o9bobo9b2o9bo12b3o6b3ob3o31bo2bo67bo2b
o133b3o3b3o127b2o34b2o$36bo8bo7bo8bo9bo12bo8bo12bo92b3o9b3o9b3o8bobo2b
o53bo4bo65bo4bo108bobo3bobo15bo7bo122b2o3bo7bo2b3o23bo3b2o$257b3ob3o28b
o8bo61bo8bo106bo7bo15bobo3bobo10b2o108bo7bo34bo7bo$235bobo2bo7b3o6bo5b
o28bo8bo61bo8bo106bo7bo33b3o109bo3b2o38b2o3bo$36bo8bo7bo8bo9bo12bo8bo
12bo95bo11bo11bo12bo5bob2o44bo4bo65bo4bo105b3o9b3o29bo111b2o48b2o$36b
2o2b2o2b2o7bo8bo9bo12bo8bo12bo95b2o10b2o10b2o66bo2bo67bo2bo155bo$14bo
2bo2bo2bo2bo177bo11bo11bo223b2o7b2o13bo13bo34bo$152b2o3bo5b2o6bobo5bo
bo114b2o69b2o84bobo3bobo58bo125b2o20b2o$53bo8bo9bo12bo8bo12bo45b2o5bo
3b2o7b2obob2o341b3o122bobo18bobo$14bo11bo26b2o2b2o2b2o9b2o2b2o2b2o2b2o
8bo12bo414b2o122b2o20b2o$236bob2o6b2obo7b2o3b2o189bobo3bobo14bo13bo155b
o22bo$257b2o3b2o188b2o7b2o41b2o3b2o136bobo16bobo$14bo11bo67bo12bo138b
obobo225b3o9b3o12b3o3b3o138bo14bo$94b2o2b2o2b2o2b2o82bo2b2o5bo2b2o5bo
bobo5bobobo10bobobo19b3o217bo7bo16bo5bo138b2o14b2o$152bobo2bo4bo3bo4b
o2bo4bobo10bo8bo11bo7bo13b2obo8bob2o6b2o3b2o215bo7bo16b2o3b2o137bobo14b
obo$14bo11bo124bo3bo4bo2bobo7b2obob2o299bobo3bobo161b2o14b2o2$37b2o2b
2o2b2o7b2o2b2o2b2o2b2o8b2o2b2o2b2o2b2o100bo2b2o5bo2b2o5bobobo5bobobo$
14bo2bo2bo2bo2bo9bo2b2o2b2o2bo5bo2b2o2b2o2b2o2bo6bo2b2o2b2o2b2o2bo9bo
2bo87b2o8b2o8bobo7bobo$36bo10bo5bo14bo6bo14bo31bobobobo$37bo8bo7bo12b
o8bo12bo147bobo7bobo$37bo8bo7bo12bo8bo12bo10bo2bo48bobo2bo5b2o6bobo5b
obo57bo9bo$36bo10bo5bo14bo6bo14bo31b2o3b2o24b2o5bo2bobo6bobobob2o64bo
3bo$36bo10bo5bo14bo6bo14bo4bo2bo24bo3bo106bo3bo17b2o5b2o$37bo8bo7bo12b
o8bo12bo14bobo130bo9bo8b3o3b3o281bo4bo$20b2o2b2o11bo8bo7bo12bo8bo12bo
144b2o8b2o$36bo10bo5bo14bo6bo14bo4bo2bo5bobo16bo3bo420b2o$14bo2bo2bo15b
o2b2o2b2o2bo5bo2b2o2b2o2b2o2bo6bo14bo10bobo5bo2bo9b2o3b2o$14bo10bo11b
2o2b2o2b2o7b2o2b2o2b2o2b2o8bo12bo$76bo12bo11bobo408bo10bo$75bo14bo18b
o2bo9bobobobo382b2o10b2o114b2o43b2o$14bo10bobo47bo2b2o2b2o2b2o2bo60bo
2bo5bo5bo2bo7bo2bo2bo5bo2bo2bo9bo2bo2bo5bo2bo2bo119b2o7b2o145bo10bobo
10bobo20b2o2b2o82b2o3bo7bo2b3o32bo3b2o$14bobo10bo48b2o2b2o2b2o2b2o14b
o2bo234b2o3bobob2o11b2o5b2o10bo10bo11bo34bobobo36bo13bo2bo9b3o4bo2bo4b
3o21b2o82bo7bo43bo7bo$330bobo50b2o9b2o10b2o46bobo16bo5bo16bo20b2o29b2o
83bo3b2o47b2o3bo$119b2o2b2o26bo2bo2bo5bo2bo2bo7bo8bo8bo9bo5bo2bo2bo5b
o72b2o2bobo2b2o9b3o8bobo34b2o5b2o22bo11bo33bo3bo7b2o3bo15b2o3bo2bo6bo
3bo5bo132b2o57b2o$16bo10bo76bo2bo129bobo10bobobobo20bo3bo14b2o7b2o9bo
2bo42bo3bo3bo3bo9bo73bo23bo52bo6bo12bo6bo$21bo2bo2bo208bo3bo10bo3bo63b
o7bobo111bobobo15bo12b2o36bo10bo18bo12bo$119bo4bo29bo11bo10bo2bo2bo5b
o2bo2bo9bo2bo2bo5bo2bo2bo12bo3bo7bo9bo18bo3bo36b2o10bobo29bo3bo3bo3bo
8bo3b2o5bo2bobo6bo3b2o49bo3b2o24b2o20bo8bo14bo5b2o8b2o5bo85b2o29b2o$16b
2o2b2o212b2o5b2o6bobo3bobo84b2obo3bob2o33bo2bo7bo2bo40bo3bo17bobo47bo
8bo14bo5b2o8b2o5bo85bobo27bobo$43bob2o45bo2bo2bo2bo8bobo120bo9bo4bo3b
obo3bo18bobobo61bo2bobo2bo57bo2bo99bo10bo18bo12bo90b2o29b2o$101bo2bo4b
o3bo5bo4bo26bo2bo2bo5bo2bo2bo7bo8bo8bo12bo11bo220bobobo89bo6bo12bo6bo
83bo31bo$35bo22b2o2b2o10bo2bo2bo2bo26bobo120bo9bo4bo3bobo3bo22bo365bo
bo25bobo$35bo8bo28b2o8b2o6b2o16bo3bo120b2o5b2o6bobo3bobo259b2o29b2o100b
o23bo$38bob2o62bo4bo3bo5b2o2b2o26bo2bo5bo5bo2bo7bo2bo2bo5bo2bo2bo9bo2b
o2bo5bo2bo2bo12bo3bo7bo9bo22bo34b3o190b3o4bo2bo4b3o21b2o99b2o23b2o$18b
2o3b2o10bo8bo10bo2bo4bo2bo169bo3bo10bo3bo49b2o11b2o190bobo10bobo20b2o
2b2o96bobo23bobo$18b2o3b2o19bo10bo10bo6bo10bo6bo18bobo124bobo10bobobo
bo39b2o2bobo2b2o12bo9bo2bo12bo2bo162b2o10b2o124b2o23b2o$20bobo16bo64b
o75bo11bo12bo5bo2bo2bo5bo72b2o18bo2bo7bo2bo14bo2bo15b2o5b2o29bo7bo101b
o10bo$39bo8bo294b2o4b2o32bo2bobo2bo9bobo5bobo$20bobo19b2obo9bo10bo6bo
10bo6bo18bobo214bo2bo31bo3bo3bo3bo7bobo5bobo9bobo3bobo$18b2o3b2o14bo8b
o6bo2bo4bo2bo36b2o14b2o2b2o52bo2bo2bo5bo2bo2bo9bo2bo2bo5bo2bo2bo105bo
2bo31b2o5b2o10bobo3bobo11bobobobo138b2o$18b2o3b2o23bo294b2o4b2o33bo5b
o13bo3bo$73b2o8b2o6bo2bo23bo2b2o2bo219bo2bo13bo3bo3bo3bo7bo9bo153bo4b
o$37b2obo17b2o2b2o10bo2bo2bo2bo10bo2bo2bo2bo14b2o4b2o51bo2bo5bo5bo2bo
149bo2bo55bo3bo$382bo9bo10bobobobo$384bo5bo11bobo3bobo$120bo2bo259bob
o3bobo9bobo5bobo29bobobo7bobo$17bo2bo2bo51bo2bo2bo300bobo5bobo9bo7bo42b
2o$111b3o269bo2bobo2bo49bo3bo10bo$96b3o10b2o3bo5bo2bo332bo$17bo5bo51b
o5bo12b2o3bo14bo181bo2b2o6bobobo6bo2b2o6bobobo12bo2bo91bobobo$94b2o3b
o9b2o3bo181bobobo6bo2b2o17bo3bo31bo2bobo2bo80bo$22bobobobobobobobobob
obobobobobobobobobobobobobobobobobobo15b2o5bo11bobo205bo12bo13bo2bo95b
o8bo$17bo2bo2bo51bo2bo2bo10b2o3b2o6bobo3bobo37b2o3bo4bo3bo3bo3bo3bo3b
o3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo4bo3b2o37bo10bo9b
obobo8bo63bo3bo8bo2bo44b2o$22bo53bo14bo5b2o6bobo44b2o5bo3bo3bo3bo3bo3b
o3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo5b2o37bo2b2o6b
obobo6bo2b2o6bobobo30b2obo3bob2o8bo3bo53bobobo9bobo$91bo3b2o7bo3b2o239b
o2bobo53bo2bo2bo$22bo53bo14bo3b2o7bo279b2o3bo6b2o3bo$92b3o9bo3b2o255b
o2bobo2bo$22bo53bo28b3o244bobo32b2o22bo2bo$399b2o$22bo53bo220b2o10b2o
9b2o$151b2o3bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo3b2o38b
o2b2o17bo3bo$22bo53bo75b2o5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5b
o5bo5b2o39bobobo6bo2b2o6bo2b2o$17bo2bo2bo51bo2bo2bo225b2o2bo8bo115bo4b
obobo$22bobobobobobobobobobobobobobobobobobobobobobobobobobobobo220b2o
10b2o9b2o$333bo7bo7bo7bo7bo7b2o6bo9bo9bo7bo9bo14bobo4bo3bo$17bo5bo51b
o5bo252bobo6b2o6b2o5bobo5b2o14b2o7b2o2bobo2b2o$336bo7bo22bo7b2o5bo26b
2o2bobo2b2o16bo4bo3bo7bo2bo12bo2bo$352bo7bo13b2o16bo7bo9bo7bo37bo12bo
$17bo2bo2bo51bo2bo2bo69b2o3b2ob2o3b2ob2o3b2ob2o3b2ob2o3b2ob2o3b2ob2o3b
2ob2o3b2ob2o3b2ob2o3b2ob2o3b2ob2o3b2ob2o3b2ob2o3b2o73b2o5bobo5bobo6b2o
6b2o13bobo51bo4bo3bo7bo18bo$335b2o5bobo5bobo6b2o6b2o13bobo74bobo2bobo
$352bo7bo13b2o16bo7bo9bo7bo15bobobo2bobobo$152bo107bo75bo7bo22bo7b2o5b
o26b2o2bobo2b2o$334bobo6b2o6b2o5bobo5b2o14b2o7b2o2bobo2b2o$17bo2bo2bo
2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo
2bo2bo2bo2bo2bo2bo2bo2bo2bo213bo7bo7bo7bo7bo7b2o6bo9bo9bo7bo9bo$151bo
109bo$151b2o107b2o$17bo101bo32bo107bo3$17bo101bo300bo$297bo2bo2bo2bo2b
o2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2b
o2bo2bo2bo2bo2bo2bo2bo22bo2$17bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2b
o2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo302bo
32bo8bo6bo2bo8bo8bo6bo2bo$258bo37b2o101b2o8bobo8bo15bo4bobobo$153bo103b
2o157bo3bo32b2o7b2o7bobo7b2o7b2o7bobo$154bo102bo38b2o101b2o7bo3b2o20b
obo8bo7b2o7b2o7bobo7b2o7b2o7bobo$154bo261bo$419bobo14bo4bobobo7bo8bo8b
o9bo8bo8bo$17b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b
2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o30bo104bo222bo8bo8b
o$17bo104bo290bobo20bo4bo11bo8bo8bo9bo8bo8bo$418bo$152b2o2bobob2o2bob
ob2o2bobob2o2bobob2o2bobob2o2bobob2o2bobob2o2bobob2o2bobob2o2bobob2o2b
obob2o2bobob2o2bobob2o163b2o3bo7bobobo2bobobo7b2o7b2o7bobo7b2o7b2o7bo
bo$17bo104bo174b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o
2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o15bo3bo34b2o7b2o7bobo
7b2o7b2o7bobo$17b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b
2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o291bo8bobo36bob
o25bobo$152bo104bo154bo42bo15bo2bo8bo15bo2bo$260bo33bo2bo100bo2bo$412b
o$152bo107bo33bo2bo100bo2bo12bo$257bo$17bo99bo$18b3o3b3o3b3o3b3o3b3o3b
3o3b3o3b3o3b3o3b3o3b3o3b3o3b3o3b3o3b3o3b3o3b3o35bo$17bo99bo$17bo99bo139b
o$152bo107bo110bo2bo86b2o$341bo3bo5bo8bobo29bo41bobobo2bo3bo7b2o6b2o10b
4o$260bo80b2o5bo3b2o17bo2bo15bobo60b2o18bobo$152bo104bo48bo4b5o7bo3bo
b4o7bo11bo28b2o7bo47bo2bo3bo13bo14b3o$306bo16bo36bobo2bo90b2obo15bo$19b
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobo186bobo4bo9bobo4bo34bo4b2o10b2o50bobo
bo2bobobo28bo$152b2o2bobob2o2bobob2o2bobob2o2bobob2o2bobob2o2bobob2o2b
obob2o2bobob2o2bobob2o2bobob2o2bobob2o2bobob2o2bobob2o48bo16bo17bo11b
o32b2obo67bob2o14bo3bobo$17bo2bobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo2bo184bo
25bo56bo44bo10bo11bo18bob4o$19bo99bo195bo7bo62bo75b2o13bobobo$17bo103b
o31bo104bo56bo16bo7bo11bo33bob2o44bobobo6bo8b2o6b2o16b2o$19bo99bo188b
o4bobo9bo4bobo31b2o4bo21b2o60b2o$17bo103bo32bo160bo16bo37bo2bobo$19bo
99bo34bo102bo48b5o4bo7b4obo3bo8bo11bo31bo7b2o$17bo103bo31bo103b2o81b2o
3bo5b2o8bo2bo18bobo$19bo99bo138bo83bo5bo3bo20bobo7bo$17bo2bobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobo2bo239bo2bo2$19bobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo!

TODO:
- wait for the factorisrc GUI

- (IMPORTANT TO ME) enumerate all patterns up to 7 cells

- apgsearch iC1

- find a 2xn SL that is not 2o$2o!, obo$obo!, o2bo$o2bo!, or obo2bo$o2bobo! (or prove that there are none)
- find a height-1 finite object that is not the factorial (or prove that there are none)
- find a p2 with a non-constant population (or prove that there are none)
- find more periods of height-2 oscillators (or prove that there are no more)
- find more periods of oscillators in B3/S2V for emulation (or prove that there are no more)
- find a statored nontrivial p6
- find new periods (ideally prime), sparkers, and speeds

- find factorial-speed (since lightspeed is 3c for R3 Cross, I might as well use factorial-speed) spaceships from c/1o to 8c/8o
- optimize the GIANT 2c/3o ships
- find a stable eater for the factorialship

- find common evolutionary sequences in Factorio

Engineering challenge:
- find infinite growth of any kind (particularly guns)

(footnote 1) You could interpret this sentence two ways: the theorems themselves are more interesting, or there are a higher quantity of interesting theorems. Either way John Conway would probably have liked Factorio better than Life.

[confocaloid]

[...]
Finally, I have though that if John Conway had found this instead of Life, he would probably have liked it better, because of the very mathematical structure of the small patterns, and the fact that there are more interesting theorems in this rule than in Life (footnote 1).
[...]
(footnote 1) You could interpret this sentence two ways: the theorems themselves are more interesting, or there are a higher quantity of interesting theorems. Either way John Conway would probably have liked Factorio better than Life.

I don't agree with the comparison. Conway's Game of Life also has interesting associated theory (e.g. GoE, still lives, speed limits, oscillator periods, constructibility). And frankly, saying that a rule is "better than" some other rule is not a very good introduction.
Soups in CGoL are often more active, and there are reactions that move across the grid before settling. Probably this would be enough to prefer Life, even if Factorio was explored earlier.

According to Martin Gardner, Conway experimented with different rules, aiming for rules that would allow for patterns to "apparently" grow without limit, while keeping it difficult to prove that any given pattern would do so. Moreover, some "simple initial patterns" should "grow and change for a considerable period of time" before settling into a static configuration or a repeating loop. Conway later wrote that the basic motivation for Life was to create a "universal" cellular automaton.

[HerscheltheHerschel]

158M:

Code: Select all

x = 17, y = 22, rule = R3,C0,S2,B3,N+
4bo$bobo$bo2bo$2b3o4$11bo2bo3$12bobo2$2o$2o$16bo$15bo$15bo$16bo$4b2o3$
4b2o!

[squareroot12621]

THEOREMS AND CONJECTURES SO FAR
All 1xn soups stay 1xn.
…
All 2xn soups stay 2xn.

Proven.
Assume that the soup is 2 × n, laid horizontally. (The white cells are part of the soup; they can be on or off.)

Code: Select all

x = 15, y = 2, rule = B/S012345678History
15C$15C! [[ GRID GRIDMAJOR 0 ]]

Then, if we want a birth above or below the soup, it needs 3 births inside its neighborhood. Any potential birth sites in the gray areas wouldn't have any neighbors that are part of the soup, so we can discard those cells:

Code: Select all

x = 25, y = 18, rule = B/S012345678History
25F$25F$25F$25F$25F$5F15.5F$5F15.5F$5F15.5F$5.15C$5.15C$5F15.5F$5F15.
5F$5F15.5F$25F$25F$25F$25F$25F! [[ GRID GRIDMAJOR 0 ]]

We can also trivially discard the areas directly left and right of the soup, because those don't contribute to making the soup taller.
The only cells that can be born now are those up to three cells above or below the soup. However, looking at their neighborhoods, they only have one or two potential neighbors in the soup, so none of them can be born.

Code: Select all

x = 18, y = 13, rule = B/S012345678History
14.B$14.B$3.B10.B$3.B7.3BD3B$3.B10.B$3BD3B7.B$2.CE4CE5CE2C$2.CE4CE8C$
3.B4.B$5.3BD3B$8.B$8.B$8.B!

Uh oh! We've run out of potential soup-growing cells. This means that any 2 × n soup (or 1 × n, following the same argument) can only grow horizontally.

[H. H. P. M. P. Cole]

[...]
Finally, I have though that if John Conway had found this instead of Life, he would probably have liked it better, because of the very mathematical structure of the small patterns, and the fact that there are more interesting theorems in this rule than in Life (footnote 1).
[...]
(footnote 1) You could interpret this sentence two ways: the theorems themselves are more interesting, or there are a higher quantity of interesting theorems. Either way John Conway would probably have liked Factorio better than Life.

I don't agree with the comparison. Conway's Game of Life also has interesting associated theory (e.g. GoE, still lives, speed limits, oscillator periods, constructibility). And frankly, saying that a rule is "better than" some other rule is not a very good introduction.
Soups in CGoL are often more active, and there are reactions that move across the grid before settling. Probably this would be enough to prefer Life, even if Factorio was explored earlier.

Okay, let's not start another argument. To settle this as quickly as possible, your 'interesting associated theories' are also (debatably) applicable to Factorio.

A few examples: Factorio (technically) has a GoE, but we haven't found it yet. Factorio could be omniperiodic/universal. There is still some dispute regarding the diagonal speed limit.

And I never said that Factorio is 'better' than Life, I just said that John Conway might have liked it better. Of course, such arguments of 'which rule is best' are very subjective. I personally thought that the theorems in Factorio are subjectively more interesting, that's all.

[b-engine]

I'd hand searched some density 30% 16x16 soups, but none of them lives for over 100 ticks. The best I'd gone so far is 96M:

Code: Select all

x = 16, y = 16, rule = R3,C2,S2,B3,N+
b2o9b3o$o6bobob3obo$11b2o$3bo2bobo3b4o$2o3bo3bobo2b2o$5bobo4bob2o$o2b
o4b4o3bo$2bo2bobo4bo$2b2o2bo4bo2bo$o3b3o5b2o$5bo2b3o4bo$bo2bo5bo3bo$b
3o2b2o3bo2bo$obo6bo4b2o$bo2bobobobobo$10bo2bo!