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