# Talk:Infinite growth

## Fastest?

"quadratic growth is the fastest possible growth rate"

I don't believe this is correct. Is there some reason you can't have a factory that produces MMM breeders? --Axaj 02:33, 20 October 2009 (UTC)

Quadratic is the fastest possible because patterns can't possibly expand at a speed faster than c. Thus, if the bounding box is x-by-y to begin with, after k generations it is at most (x+2k)-by-(y+2k), which has area xy+2k(x+y)+4k^2, which is quadratic in k. Since the area of the bounding box is an upper bound on the number of alive cells in the pattern, the number of alive cells can't grow any faster than quadratically. Nathaniel 03:28, 20 October 2009 (UTC)
Okay, I see now. Thanks! --Axaj 15:03, 25 October 2009 (UTC)

## Only 4 classes

I would think that all linear growth patterns are MM(rake) MS(puffer) SM(gun) or SS(replicator) Can anyone think of some linear grower that isn't in any of these 4 classes? --Turtleguy1134 (talk) 21:37, 31 December 2014 (UTC)

E.g. slide factories like blockstacker don't neatly fit in this system. It's sort of "SmS"; the engine and the output are stationary, but there's a moving intermediate. --Tropylium (talk) 21:09, 26 May 2015 (UTC)

## Nonlinear

This is a weird pattern.

```x = 1261, y = 639, rule = B3/S23
1225b2o\$1221b4ob2o\$1221b6o\$1222b4o2\$1237b2o\$1235b2ob2o\$1221bo9bo3b4o\$
1220bo11bo3b2o\$1220b3o7bo2bo\$1232bo3b2o\$1231bo3b4o\$1235b2ob2o\$1203bo
18b2o13b2o\$1202bo17bo4bo\$1202b3o21bo\$1220bo5bo\$1221b6o\$1207b2o\$1206b2o
\$1208bo2\$1205bo40b2o\$1205b2o35b4ob2o\$1204bobo18b2o15b6o\$1224b2o17b4o9b
o2bo\$1226bo33bo\$1256bo3bo\$1211bo36bo3bo4b4o\$1211b2o8b4o23bo4b2o\$1210bo
bo7bo3bo18b2o7b3o\$1224bo17b2o9b2o\$1220bo2bo20bo7bo4b4o\$1256bo3bo\$1217b
3o14b2o24bo\$1217b3o13b4o19bo2bo\$1216bo3bo12b2ob2o\$1218b2o6bo2bo5b2o6b
6o\$1215bo10bo3bo11bo5bo\$1211bo3b2ob2o5bo4b2o16bo\$1210bobo5b2o6bo3bo11b
o4bo\$1209bo3b2o2bo2bo5bo2bo5b2o7b2o\$1217bo2bo12b2ob2o\$1210bo5bo3bo12b
4o\$1212b7o15b2o2\$1223b6o\$1222bo5bo\$1228bo\$1214bo2bo4bo4bo\$1218bo5b2o\$
1214bo3bo\$1215b4o433\$26b3o3b3o\$25bo2bo3bo2bo\$28bo3bo\$28bo3bo\$25bobo5bo
bo2\$29b3o\$29b3o\$28bobobo4\$23bo4b2o7b3o\$22b3o12bo2bo\$22bob2o11bo\$23b3o
11bo3bo\$23b3o4bobo4bo3bo\$23b3o4b2o5bo\$23b2o6bo6bobo3\$6bo5bo\$5b3o3b3o\$
5bob2ob2obo22bo5bo\$6b3ob3o22b3o3b3o\$6b2o3b2o21b2obo3bob2o\$34b3o5b3o\$9b
o25b2o5b2o\$8bobo\$7bo3bo27bo\$9bo28b3o\$37bo3bo\$46b3o\$bo44bo2bo\$3o12b3o6b
obo10b2ob2o4bo\$ob2o10bo2bo6b2o13bo6bo3bo\$b3o13bo7bo3b3o14bo3bo\$b3o9bo
3bo11bo2bo13bo\$b3o5bo3bo3bo11bo17bobo\$b2o4bobo7bo11bo\$8b2o4bobo13bobo
3bo4b3o\$34b2obob2o\$34b2obob2o3bo5b3o\$34b2o5b2obo4bo2bo\$36bo2bo3b2o7bo\$
38b2o4bo7bo\$41bo2bo4bobo\$41bo2bo\$29b2o9bo3bo\$28b2o9bo\$30bo9bo2bo\$41bo\$
18bobo\$18b2o\$19bo3b2o\$22b2o\$15bo8bo\$13bobo\$14b2o43\$142b2o\$138b4ob2o\$
138b6o\$139b4o2\$154b2o\$152b2ob2o\$138bo9bo3b4o\$137bo11bo3b2o\$137b3o7bo2b
o\$149bo3b2o\$148bo3b4o\$152b2ob2o\$120bo18b2o13b2o\$119bo17bo4bo\$119b3o21b
o\$137bo5bo\$138b6o\$124b2o\$123b2o\$125bo2\$122bo40b2o\$122b2o35b4ob2o\$121bo
bo18b2o15b6o\$141b2o17b4o9bo2bo\$143bo33bo\$173bo3bo\$128bo36bo3bo4b4o\$
128b2o8b4o23bo4b2o\$127bobo7bo3bo18b2o7b3o\$141bo17b2o9b2o\$137bo2bo20bo
7bo4b4o\$173bo3bo\$134b3o14b2o24bo\$134b3o13b4o19bo2bo\$133bo3bo12b2ob2o\$
135b2o6bo2bo5b2o6b6o\$132bo10bo3bo11bo5bo\$128bo3b2ob2o5bo4b2o16bo\$127bo
bo5b2o6bo3bo11bo4bo\$126bo3b2o2bo2bo5bo2bo5b2o7b2o\$134bo2bo12b2ob2o\$
127bo5bo3bo12b4o\$129b7o15b2o2\$140b6o\$139bo5bo\$145bo\$131bo2bo4bo4bo\$
135bo5b2o\$131bo3bo\$132b4o!
```

It seems that its growth rate is best approximated by a line but it is not perfectly linear. It is choppy. Notice the tendency to form dots.

-wwei23 11:04PM 9/28/2015 NY time

I call this one the "synthesizer."

```x = 1261, y = 856, rule = B3/S23
782b3o3b3o\$782bo2bobo2bo\$782bo7bo\$782bo7bo\$783bobobobo2\$786bo\$785b3o\$
784b2ob2o\$785b3o\$785b3o\$785b3o\$779bo5bobo5b3o\$778b3o4bobo4bo2bo\$777b2o
bo5bo8bo\$777b3o11bo3bo\$777b3o11bo3bo\$777b3o15bo\$778b2o12bobo199\$1225b
2o\$1221b4ob2o\$1221b6o\$1222b4o2\$1237b2o\$1235b2ob2o\$1221bo9bo3b4o\$1220bo
11bo3b2o\$1220b3o7bo2bo\$1232bo3b2o\$1231bo3b4o\$1235b2ob2o\$1203bo18b2o13b
2o\$1202bo17bo4bo\$1202b3o21bo\$1220bo5bo\$1221b6o\$1207b2o\$1206b2o\$1208bo
2\$1205bo40b2o\$1205b2o35b4ob2o\$1204bobo18b2o15b6o\$1224b2o17b4o9bo2bo\$
1226bo33bo\$1256bo3bo\$1211bo36bo3bo4b4o\$1211b2o8b4o23bo4b2o\$1210bobo7bo
3bo18b2o7b3o\$1224bo17b2o9b2o\$1220bo2bo20bo7bo4b4o\$1256bo3bo\$1217b3o14b
2o24bo\$1217b3o13b4o19bo2bo\$1216bo3bo12b2ob2o\$1218b2o6bo2bo5b2o6b6o\$
1215bo10bo3bo11bo5bo\$1211bo3b2ob2o5bo4b2o16bo\$1210bobo5b2o6bo3bo11bo4b
o\$1209bo3b2o2bo2bo5bo2bo5b2o7b2o\$1217bo2bo12b2ob2o\$1210bo5bo3bo12b4o\$
1212b7o15b2o2\$1223b6o\$1222bo5bo\$1228bo\$1214bo2bo4bo4bo\$1218bo5b2o\$
1214bo3bo\$1215b4o433\$26b3o3b3o\$25bo2bo3bo2bo\$28bo3bo\$28bo3bo\$25bobo5bo
bo2\$29b3o\$29b3o\$28bobobo4\$23bo4b2o7b3o\$22b3o12bo2bo\$22bob2o11bo\$23b3o
11bo3bo\$23b3o4bobo4bo3bo\$23b3o4b2o5bo\$23b2o6bo6bobo3\$6bo5bo\$5b3o3b3o\$
5bob2ob2obo22bo5bo\$6b3ob3o22b3o3b3o\$6b2o3b2o21b2obo3bob2o\$34b3o5b3o\$9b
o25b2o5b2o\$8bobo\$7bo3bo27bo\$9bo28b3o\$37bo3bo\$46b3o\$bo44bo2bo\$3o12b3o6b
obo10b2ob2o4bo\$ob2o10bo2bo6b2o13bo6bo3bo\$b3o13bo7bo3b3o14bo3bo\$b3o9bo
3bo11bo2bo13bo\$b3o5bo3bo3bo11bo17bobo\$b2o4bobo7bo11bo\$8b2o4bobo13bobo
3bo4b3o\$34b2obob2o\$34b2obob2o3bo5b3o\$34b2o5b2obo4bo2bo\$36bo2bo3b2o7bo\$
38b2o4bo7bo\$41bo2bo4bobo\$41bo2bo\$29b2o9bo3bo\$28b2o9bo\$30bo9bo2bo\$41bo\$
18bobo\$18b2o\$19bo3b2o\$22b2o\$15bo8bo\$13bobo\$14b2o43\$142b2o\$138b4ob2o\$
138b6o\$139b4o2\$154b2o\$152b2ob2o\$138bo9bo3b4o\$137bo11bo3b2o\$137b3o7bo2b
o\$149bo3b2o\$148bo3b4o\$152b2ob2o\$120bo18b2o13b2o\$119bo17bo4bo\$119b3o21b
o\$137bo5bo\$138b6o\$124b2o\$123b2o\$125bo2\$122bo40b2o\$122b2o35b4ob2o\$121bo
bo18b2o15b6o\$141b2o17b4o9bo2bo\$143bo33bo\$173bo3bo\$128bo36bo3bo4b4o\$
128b2o8b4o23bo4b2o\$127bobo7bo3bo18b2o7b3o\$141bo17b2o9b2o\$137bo2bo20bo
7bo4b4o\$173bo3bo\$134b3o14b2o24bo\$134b3o13b4o19bo2bo\$133bo3bo12b2ob2o\$
135b2o6bo2bo5b2o6b6o\$132bo10bo3bo11bo5bo\$128bo3b2ob2o5bo4b2o16bo\$127bo
bo5b2o6bo3bo11bo4bo\$126bo3b2o2bo2bo5bo2bo5b2o7b2o\$134bo2bo12b2ob2o\$
127bo5bo3bo12b4o\$129b7o15b2o2\$140b6o\$139bo5bo\$145bo\$131bo2bo4bo4bo\$
135bo5b2o\$131bo3bo\$132b4o!
```

The glider stream passes thru the LWSS stream like it wasn't there. Some escaping gliders collide with the stream, hence the name "synthesizer." Lots of different syntheses happen and a huge mess builds up. This is the other pattern but with an extra glider rake. Which is better for this one? QuickLife, or HashLife? -wwei23 11:13PM 9/25/2015 NY time -wwei23 10:43PM 9/30/2015 NY time

## KNIGHTSHIP

While cubic growth is impossible, that doesn't stop this rule from trying anyway. It is a breeder puffer.

```x = 20, y = 20, rule = B3/S234y
b2ob2ob2o4bobo2b2o\$o2b3o2bobobo4b2o\$2b3o2bobob2obo2b2o\$2obobo2b2ob2o3b
2o\$bob2o2b4obo5bo\$3ob3o6bobo3bo\$obo5bobo2b2ob4o\$o2b2o5b3ob2ob3o\$bob3ob
ob2o2bobobo\$bo4bo3b2ob2o4bo\$5ob7o3bob2o\$2o4b3obo2bob5o\$2ob6o4b4ob2o\$bo
b2o3b2o5b4o\$b2ob2ob4o2b2ob2o\$2b2obobobobo3b4o\$b3o3b2obob3ob3o\$4ob7obo
2b3o\$obo8b2obo4bo\$b4obo3bob2o2bobo!

```

-wwei23 6:46AM 6/22/2017 NY time Try the R-pentomino in this rule. -wwei23 3/10/2018 8:19 AM NY time

## Strange replicator

It doesn't go by Rule 90.

```x = 1, y = 99, rule = B23/S:T0,100
o2\$o2\$o2\$o2\$o2\$o2\$o2\$o2\$o2\$o2\$o2\$o2\$o2\$o2\$o2\$o2\$o2\$o2\$o2\$o2\$o2\$o2\$o2\$o
2\$o2\$o2\$o2\$o2\$o2\$o2\$o2\$o2\$o2\$o2\$o2\$o2\$o2\$o2\$o2\$o2\$o2\$o2\$o2\$o2\$o2\$o2\$o
2\$o2\$o2\$o!
```

-wwei23 3/9/2018 8:30 PM NY time