But is exponential possible?
No, a finite pattern's building box cannot expand faster then the speed of light in any life-like cellular automaton.
Therefore no pattern can grow in population faster then the filled X*Y building box in the rule B12345678/S012345678.
Therefore the upper limit for the population of a pattern that fits in an X*Y building box is X*Y+t*2(X+Y)+t^2*4 a quadratic polynomial.
You can check the formula by running solid rectangles in that rule.
There is another explanation here:
http://www.conwaylife.com/wiki/Talk:Infinite_growth
EDIT:
Define "creating other objects."
You could say the LWSS creates a tail spark, so is a LWSS gun a breeder?
For the same reason you can say this puffer is a breeder:
Code: Select all
x = 139, y = 190, rule = B3/S23
41bo13bo$40b3o11b3o$40bob2o4bo5bob2o14bo13bo$41b3o3b3o5b3o13b3o11b3o$
41b2o3b2o2bo4b2o13b2obo5bo4b2obo$48b3o19b3o5b3o3b3o$71b2o4bo2b2o3b2o$
77b3o2$54b3o$53bo2bo$56bo14b3o$56bo14bo2bo$53bobo15bo$45b2o24bo$45b2o
25bobo$81b2o$39bo41b2o$38b3o7bo$37b2obo5b2ob2o37bo$37b3o6b2ob2o28bo7b
3o$38b2o6b2ob2o26b2ob2o5bob2o$48b2o4bo5bo16b2ob2o6b3o$53b3o3b3o15b2ob
2o6b2o$52b2obo3bob2o4bo5bo4b2o$52b3o5b3o3b3o3b3o$53b2o5b2o3b2obo3bob2o
$65b3o5b3o$46b2o9bo8b2o5b2o$47b2o7b3o$46bo8bo3bo10bo9b2o$55bo3bo9b3o7b
2o$22b3o11b3o29bo3bo8bo$21bo2bo10bo2bo12b2o2bo3bo8bo3bo$24bo4b3o6bo13b
2obo3bo29b3o11b3o$24bo4bo2bo5bo12bo3b2ob2o8bo3bo2b2o12bo2bo10bo2bo$21b
obo4bo3bo2bobo18bobo9bo3bob2o13bo6b3o4bo$28bobob2o23bo10b2ob2o3bo12bo
5bo2bo4bo$29b2ob2o35bobo18bobo2bo3bo4bobo$30b3o37bo23b2obobo$23bo70b2o
b2o$22b3o70b3o$21b2obo6bo72bo$21b3o6b2o26bo44b3o$22b2o7bo24b2ob2o35bo
6bob2o$28bo27b2ob2o8bo26b2o6b3o$26b4obo18bo6b3o7b2ob2o24bo7b2o$27bo2bo
18b3o15b2ob2o27bo$28b3o18bob2o15b3o6bo18bob4o$50b3o23b3o18bo2bo$38b3o
9b3o22b2obo18b3o$3bo13bo19bo2bo9b2o23b3o$2b3o11b3o21bo34b3o9b3o$b2obo
5bo4b2obo21bo35b2o9bo2bo$b3o5b3o3b3o19bobo47bo$2b2o5bob2o3b2o69bo$88bo
bo18b3o11b3o$35bo7b3o3b3o56bo2bo10bo2bo$36b2o5bo2bobo2bo59bo4b3o6bo$
12bo22b2o6bo7bo24b3o3b3o7bo18bo4bo2bo5bo$10b2o4b3o24bo7bo24bo2bobo2bo
5b2o16bobo4bo3bo2bobo$16bo2bo24bobobobo25bo7bo6b2o22bobob2o$13bo2bo59b
o7bo31b2ob2o$8bo7bo30bo29bobobobo33b3o$7bo3b2o4bobo26b3o8b2o51bo$7bo
37b2ob2o7bobo20bo28b3o$8bo36b2ob2o8b2o9b2o8b3o26b2obo6bo$18b3o3b3o19bo
bo19bobo7b2ob2o25b3o6b2o$bo9bo5bo2bo3bo2bo19bo20b2o8b2ob2o26b2o7bo$3o
6b3o8bo3bo54bobo33bo$ob2o5bo10bo3bo55bo32b4obo$b3o5bobo5bobo5bobo17b2o
b2o7b2o43bo5bo5bo2bo$b2o7b2o28bo3bo5bo5bo2bo41b3o3b3o5b3o$21b3o17b2o2b
o3bo7b2o10b2o7b2ob2o17b2obo3bob2o14b3o$21b3o16b2o4b3o19bo2bo5bo5bo3bo
12b3o5b3o14bo2bo$21bobo22bobo20b2o7bo3bo2b2o14b2o5b2o15bo$22bo24bo31b
3o4b2o37bo$22bo24bo31bobo23bo20bobo$8bo71bo23b3o$8b2o20bo49bo22bo3bo$
7bobo10bo3bo4b3o71bo3bo$20b2ob2o4bob2o64bo$21bobo6b3o63b3o4bo3bo11b3o$
13bo16b2o63b2obo4bo3bo11bo$13b2o7bo72b3o5b2ob2o12bo$12bobo7bo73b2o6bob
o$22bo82bo$45bo68b3o$18bo27b2o66bo$18b2o25b2o35bo32bo$17bobo60b2o$81b
2o$15bo93b3o$14b3o6bo85bo$14bob2o5b2o32b2o51bo$15b3o4bobo22b2o8bobo$
15b3o29b2o9b2o9b2o48b3o11b3o$15b2o51bobo8b2o23b3o11bo2bo10bo2bo$68b2o
9b2o23bo16bo4b3o6bo$105bo15bo4bo2bo5bo$118bobo4bo6bobo$47bobo7b2o71bo$
47bobo6bo2bo64bo4bo$46bo10b2o10b2o7bobo43bo$46b3o19bo2bo6bobo39bo5bo$
42b2o3b3obo17b2o10bo37b3o3b3o$42b2o6b2o27b3o36b2obo3b3o$50b2o24bob3o3b
2o20b2o10b3o4b2o$38bo37b2o6b2o20b2o11b2o5b5o$38b2o36b2o34bo15b3o$37bob
o71b3o$110b2obo4bo6bo$89b3o18b3o4b3o5bo$89bo20b3o4bob2o6bo7b3o$90bo19b
3o5b3o6b2o6bo2bo$111b2o5b2o6b2o7bo$126bo8bo$115bo20bobo$114b3o$113bo3b
o3$93bo13bo5b2ob2o$46b2o5bo38b3o11b3o6bo12b3o$46b2o5b2o2b2o33bob2o4bo
5bob2o18bo$52bobo2bobo20b2o11b3o3b3o5b3o19bo$58b2o9b2o9b2o11b2o3b2o2bo
4b2o4bo3bo$68bobo3b3o23b3o9bobobobo$68b2o4bo38b5o5b3o$75bo37b2ob2o5bo$
114bobo7bo$106b3o5b3o$105bo2bo$108bo9b3o$108bo9bo$105bobo11bo$97b2o$
97b2o23bo$121b3o$91bo24b2o3bob2o$90b3o7bo15b3o3b3o$89b2obo5b2ob2o19b3o
$89b3o6b2ob2o19b2o$90b2o6b2ob2o$100b2o4$69b2o32b3o$70b2o31bo$69bo28b2o
4bo4bo$58b2o39b2o7b3o$57bo3bo36bo9bob2o$46b2o8bo5bo7bo38b3o$46b2o8bo3b
ob2o4bobo38b2o$56bo5bo3b2o12b2o21b2o$57bo3bo4b2o12b2o22b2o$58b2o6b2o
35bo$68bobo$70bo4$84b2o$85b2o$84bo5$77bo$77b2o$76bobo6$69b2o$70b2o$69b
o$58b2o$57bo3bo$46b2o8bo5bo7bo$46b2o8bo3bob2o4bobo$56bo5bo3b2o12b2o$
57bo3bo4b2o12b2o$58b2o6b2o$68bobo$70bo!
Or even this oscillator:
Code: Select all
x = 402, y = 145, rule = B3/S23
349bo$347b3o$346bo$346b2o$151bobo30b2o$151bo3bo28bobo157bo$135bo19bo
23b2o4b3o12bo142bobo$100bo32b4o14bo4bo4b2o12b4o2bo4b3o8b4o4bo136bo3bo$
98b3o31bobob2o4bo12bo5b2o12b3ob2o4b3o8b4o5bo137b3o$97bo29b2o2bo2bob3o
5b2obo3bo3bo28bobo9bo2bo9b2o130b2o3b2o$97b2o9b2o17b2o3bobob2o5b4obo2bo
bo30b2o10b4o9b2o$74bo33b2o23b4o6b2o2b2o39bo8b4o122b2o$74b3o58bo27b2o8b
2o12bo12bo93bo29bo$77bo85b2o8b2o12b3o101b4o29bobo6bobo$65b2o9b2o95b2o
115b4o16bo14b2o5bo2bo4bo$65b2o106bo11b2o96b2o5bo2bo8b2o5bobo19b2o5b2o$
92b2o3b2o54b2o9b2o6bobo10bobo95b2o5b4o14bo3b2o15b2o3bo9bo$92bo5bo54b2o
7bob2o6bob2o9bo105b4o3b2obobo4bo3b2o17b2o11bo$162bo131bo2bo3b2o5bo3b2o
18bo2bo$93bo3bo51bo12bo17bo117bo10bobo3b2o16bobo18b2o$94b3o34b2o16b2o
11bo2bo7b2o5bobo98b2o15bo2bo8bo4bobo37bo$64b3o11b3o50b2o15bobo12b2o8b
2o5b2o98bobo34bo37bobo10bo$63b2ob2o9bo3bo25b5o92b2o73b3o35b2o37b2o9bob
o$63b2ob2o8bo5bo23bob3obo79b3o2bo5bo3bo71b2o86b2obo7b2o$63b5o8bo5bo24b
o3bo76bo3bo9bo5bo73b2o7bo61b2o12b2ob2o6bobo$62b2o3b2o10bo28b3o75bobo4b
o8bo3bob2o2b2o67b3o6bo61b2o13b2obob3o6bo$77bo3bo27bo21bo52b2o16bo5bo3b
2o76b3o2b3o56bo12bobo2bo2bo2bo2bo7b2o$78b3o17bo30b2ob2o7b2o41b2o17bo3b
o87bo72bo4b2o6bo7b2o$64b2o13bo16bobo43b2o40b2o18b2o75b2o13bo81bobo$63b
5o29b2o29bo5bo6bo37b2o5bobo92b2o95b2o$63bo47bo66bobo7bo120b2o$65b3o12b
3o10bo17bo16b2obob2o43bo99b2o24bo4b2o42b2o10bobo$67bo12b3o9b3o15bobo
63b3o99bo19b2ob5o6b2o39b2o10b2o$65b2o12bo3bo7b5o13b2ob2o46b2o13bo93bo
6bobo18bo4b2o2bo5b3o5b2o44bo$65b2o6bobo14b2o3b2o6b2o3bo5bo19b2o24bo4bo
9b2o92bobo4b2o18bo8b2o5b2o6b2o40b2o$73b2o3b2o3b2o6b5o7b2o6bo21bobo15bo
6bobo4bobo61b2o39bobo23bo7bo4b2o43b2o6b2o22b2o$74bo16bo3bo12b2o3b2o19b
o16bobo4b2o5b2o5b3o54b2o26b2o11bo2bo22bo12b2o41bob2o30bo$60b2o3b2o25bo
bo38b2o17bobo17b3o33b2o16b2o10bo4bo13b2o11bobo14b2o8bo54bo16bo7bo6bobo
$60bobobobo3b2o19b3o39b3o3b2o11bo2bo52b2o8b2o5b3o10bo4bobo23bobo14bobo
9b2o52bo15b4o5bobo4b2o$61b5o4b2o18b2o5bo14bo21b2o3b2o11bobo63b2o6b2o
10bo7b2o21bo16bo65bo2bo7b2o2bo2b2o8b2o$62b3o26bo4bo15bo19bo18bobo11bo
63b2o2b2o11b2o4b2o31b2o66b2o8b2o2b2o11b2o$63bo24b3o5b3o14bo37bo12bo5b
2o3b2o52b2o2bo2b2o8b2o4b2o106b2o10bo7b2o$88bo75b3o4b5o58b4o5bobo113b3o
10bo4bobo$83b2o87b3o41b2o17bo7bo116b2o10bo4bo$83bo26b2o21bo17bobo19bo
42b2o136b2o7b2o$84b3o14bo8b2o20b3o16b2o200bobo7b2o$60b2o17bo6bo10b2o2b
2ob3o24b5o16bo63bo60b2o74bo$61bo18b2o15b2o4b4o23b2o3b2o78bobo8bobo3bo
44bobo72b2o$58b3o18b2o20b2o28b5o71b3o5bo2bo7b2o3b2o45b3o4b3o75b2o$58bo
72bo3bo70bo3bo5bo2bo7bo3bobo21b2o22b2o4bo78bo$34bo30bo66bobo32b3o5b2o
28bo5bo43bo20b2o8bo77bobo5b2o$32b3o30b3o65bo28b2o3bo7bo30bo3bo5bo2bo
24b2o7bobo20b3o86b2o5bobo$31bo36bo93bobo3bo7b3o28b3o6b2o26bobo6b2o118b
3o12bo$31b2o9b2o12b2o9b2o5bo88b3o12bo28b3o24bo4b2o6bo37b3o86b3o8b4o$
42b2o12b2o16b3o56b2o29b2o67bobo2bo2bo2bo2bo13bo15b2o8bo85b3o8b4o9b2o$
71bo5bo55b2o26b2o10b2o58b2obob3o6bo12bo16b2o7bo6b2o69b2o6bobo9bo2bo9b
2o$71bo4b2o83b3o9b2o58b2ob2o6bobo13b3o30bobo67bobo6b2o10b4o5bo$233b2ob
o7b2o8bobo36bo68b3o11bo8b4o4bo$80bo124b3o15b2o8bobo18b2o106b2o11bo12bo
$43bo23b2o3b2o6bo81b2o40b2ob2o3bo9bobo9bo20bo109b2o8b3o$29bo13bo24b5o
6bo82b2o40b2ob2o4b2o7bo55b2o84b3o$28b3o11bobo24b3o22bo109b5o3b2o7b2o
54bobo$27b5o9b2ob2o24bo24b2o69b2o35b2o3b2o69bo$26b2o3b2o7bo5bo6b2obob
2o16b2o3b2o11b2o69bobo100bo20b2o9b3o9b2o31b2o17b2o$27b5o11bo32bo5bo52b
o31bo99b4o18bo10bo9bo2bo30b3o17b2o$27bo3bo8b2o3b2o6bo5bo75bobo44b3o81b
2obobo6bobo6bobo5bo5bo7bo34b2obo$28bobo46bo3bo53b2o45bo82b3obo2bo3bo3b
o6b2o4b4o12bo35b3o44b2o$29bo24b2ob2o19b3o102bo82b2obobo4bo15bobob2o11b
o36bo33b3o2bo5bo3bo$42b4o10bo92bo8b2o14b2o19bo61b2o8b4o4bo4bo10bo2bob
3o11bo2bo5b2o55bo3bo9bo5bo3b2o$41b2o2bo23bo77bobo6bo2bo14bo20b2o11b2o
46bobo9bo7bo14b2obob2o14b2o5bobo52bobo4bo8bo3bob2o2b2o$27bo13b2obo22b
2o66bo10bobo7bo3bo2b2o7bobo9bo5b2o4b2o10bo47bo19bo3bo8b3ob4o24bo50b2o
16bo5bo$25b2ob2o38b2o24bobo37bo10bo2bo7bo2b2o2b3o6b2o10bobo3b2o4b3o10b
3o43b2o21bobo7bobo4bo25b2o49b2o17bo3bo$34bo7b2o37b2o12b2o37b3o9bobo16b
2obo16bobo2b2o4b2o13bo76bo83b2o18b2o$24bo5bo4bo6bo38bo13bo46b2o3bobo4b
3o8bo2bo16bo2bo6b2o7b2o81b2o78b2o5bobo$33b3o46b3o36bobo17bobo5bo15b2ob
o16bobo7bo8bobo159bobo7bo$24b2obob2o22b3o28bo36b2o18bo21b3o8b2o8bobo
19bo159bo$42b2obob2o3bo3bo12b2o3b2o33bo12bo17b2o21b2o8bobo8bo21b2o157b
2o$36bo5bo5bo12b2o8b3o36b2o61bo$35bo7bo3bo3bo5bo3b2o7bo3bo34b2o61b2o$
35b3o6b3o4b2o3b2o13bobo169b2o58b2o$72bo169b4o56b4o$242b2ob2o55b2ob2o$
24b2o28bo11bobo5b2o65b2o58b2o41b2o15b2o41b2o15b2o$25bo27bobo11b2o5bo
64b2ob2o55b2ob2o55b2ob2o55b2ob2o$22b3o28bobo11bo7b3o61b4o56b4o56b4o56b
4o$22bo30bo23bo62b2o58b2o58b2o58b2o$53bo67bo59bo59bo59bo$44b2o7bo2bo
63b3o3b2o52b3o3b2o52b3o3b2o52b3o3b2o38bo$35bo8b2o8b2o4bo2b2o54b5ob3o9b
3o39b5ob3o9b3o39b5ob3o9b3o39b5ob3o9b3o25bo$31b2o2b2ob3o18bo3b2o2b2o54b
3o9bo3b2o42b3o9bo3b2o31bobo8b3o9bo3b2o31bobo8b3o9bo3b2o24b3o$31b2o4b4o
18bo7b2o54b3o9bobo2b2o41b3o9bobo2b2o31b2o8b3o9bobo2b2o31b2o8b3o9bobo2b
2o$35b2o23b4o60bo9bo5bo43bo9bo5bo32bo10bo9bo5bo32bo10bo9bo5bo21b2o$21b
o101bo11bo2b2o43bo11bo2b2o43bo11bo2b2o43bo11bo2b2o22b2o$20bo114bo59bo
59bo59bo$20b3o114bo59bo59bo29bobo27bo$70bo2bo56bo2bo56bo2bo56bo2bo34b
2o20bo2bo$12bo61bo6b2o51bo6b2o51bo6b2o51bo6b2o25bo25bo6b2o$12bobo55bo
3bo4b2ob2o46bo3bo4b2ob2o46bo3bo4b2ob2o46bo3bo4b2ob2o46bo3bo4b2ob2o$2o
11bobo55b4o4b4o48b4o4b4o48b4o4b4o48b4o4b4o48b4o4b4o$2o11bo2bo63b2o58b
2o58b2o58b2o20bobo35b2o$13bobo267b2o$12bobo268bo$12bo50b2o181b2o8b2o8b
2o8b2o8b2o8b2o8b2o8b2o8b2o8b2o$63bo28bo153bobo7bobo7bobo7bobo7bobo7bob
o7bobo7bobo7bobo7bobo$55bo5bobo23b3ob2o2b2o151bo9bo9bo9bo9bo9bo9bo9bo
9bo9bo$16bo37b2o5b2o24b4o4b2o151b2o8b2o8b2o8b2o8b2o8b2o8b2o8b2o8b2o8b
2o$16bo21b2o13b2o36b2o7b2o$15bobo20b3o11b3o45b2o$14b2ob2o21b2obo9b2o3b
2o$13bo5bo20bo2bo10b2o22bo$16bo23b2obo11bo6b3o13b3o$13b2o3b2o11b2o5b3o
10bo12bo3b2o11bo$30bobo5b2o9bobo11bo3bobo10b2o$30bo19b2o14b3o31b3o$15b
o13b2o35b2o22b3o$15bo53b2o19bo9bobo$14bo53b3o20bo7b5o$56b2o40b2o3b2o$
56b2o40b2o3b2o$16b2o50b2o20b3o$16b2o27bo22b2o12b3o7bo$44b4o33bo3bo5bo
6b2o$32b2o9b2obobo6bobo22bo5bo9b2obo$32b2o8b3obo2bo3bo3bo23bo3bo10bo$
43b2obobo4bo12b2o14b3o$44b4o4bo4bo8b2o14bo2bo11b3obo$45bo7bo29b3o15bo$
53bo3bo25b2obo14bo$55bobo26bobo$85bo3$82b2o3b2o7b2o3b2o$82bobobobo9b3o
$83b5o9bo3bo$84b3o11bobo$85bo13bo4$98b2o$87b2o9b2o$87bo$88b3o$90bo!