The "recursive filter" one is easy, since it was a POTY 2015 nominee; links lead to this post among others.GUYTU6J wrote: ↑February 12th, 2022, 8:07 amThis question sounds more like one from Book rather than GUYTU6J (as the latter has many previously unanswered questions), but what patterns can be demonstrated as examples for the quadratic filter, exponential filter and recursive filter?
For the quadratic and exponential filters, probably a series of quotes from the original emails is the best source:
On 6 Jun 2006, Gabriel Nivasch wrote:Subject: More orders of growth
Can we build a pattern like this?
A gun (located at X) is capable of firing block-pulling salvos to the NE.Code: Select all
#C sketch x = 182, y = 162, rule = B3/S23 175bobobobo2$179bobo2$177bo3bo2$175bo5bo2$173bo2$171bo9$161b2o$161b2o 7$153b2o$153b2o7$145b2o$145b2o7$137b2o$137b2o7$129b2o$129b2o7$121b2o$ 121b2o7$113b2o$113b2o14$2bo$obo$b2o4$86b3o$88bo$87bo7$87b3o$89bo$88bo 22$42bo7bo2$43bo5bo2$44bo3bo2$45bobo2$46bo2$45bobo2$44bo3bo2$43bo5bo2$ 42bo7bo22$80bo$78bobo$79b2o!
The gun fires a salvo each time it gets an input glider from the NW. And
each time a block is pulled all the way back home, a SE-ward glider is
emitted.
The infinite line of blocks is laid by a corder-puffer.
This device would fire its n-th output glider after receiving its
(c*n^2)-th input glider, for some constant c.
How would this thing be called? A "quadratic filter"?
If we connect k quadratic filters in series, and run the output into a
stifled breeder (a pattern that activates an additional glider gun each
time it receives an input), then we would get population growth asymptotic
to t^(1 + 2^-k).
And if a caber tosser provides the input to the first quadratic filter,
then we'd get population growth asymptotic to t*(log t)^(2^-k).
On 10 June 2006, Gabriel Nivasch wrote:Subject: Quadratic filter
I wrote:
> Can we build a pattern like this?
C'mon, even I can do it!
So here's a quadratic filter. (This thing is probably not optimized.)
Here's a pattern that grows like t^(5/4):Code: Select all
#C Quadratic filter. Base period is 60. #C n-th output glider is released when (n^2)-th input glider is received. #C Gabriel Nivasch, June 11, 2006. x = 525, y = 524, rule = B3/S23 341bo$331b3o5b2ob4o$331b3o4b2ob3ob2o$330b2o7bob3obo$331b2o4b4o3bo$336b 3ob2o$321b2o13b5o$321b2o16bo6$334bo19bo$313b2o18bobo16b2ob2o$313b2o17b o2bo$333b2o17b2o$352bo$337b2o15bo3bo$337b2o11bo3bo3$305b2o38bo10bo$ 305b2o3b2o32bobo6b3o6b2o$309b3o4b2o3bo22bobo14b3o4b2o3bo$308bo6bo2b2ob o23bo14bo6bo2b2obo$308b4o2b5o2bo38b4o2b5o2bo$309b3o3b3o43b3o3b3o$316b 3o49b3o$317b2o35b2o13b2o$318bo35b2o14bo5$349bo$348bobo$349bo2$311b3o 37bo2b2o8bo$327bo22b2o2b3o5bo2bo$326b3o20b3o2b2o6bo3bo2b3o$311b3o11bob obo20b2o2b2o5bo4bo2b3o$314bo9b3ob3o31b2o3bo$312bo49b2o$312bo11b3obo36b 2o$303b2o19b5o$303b2o18b2o2b2o$323b2obo65b2o$323b2o37b2o27b3o$323bo2bo bo33b2o26bob2o$324bo2bobo45bo13bo$328bo4b3o39bo12bo3b2o3bo$336bo38bo 11bo$332bo3bo51bobo$301b2o29b2o3b2o51bo$299bo4bo26bo2bobo2bo34bo13bobo 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48b3o16b3o110b2o30bobobo2bo88bo3bo$139bo6bobo3b2o80b2o21b3o36b2o90b3o$ 137b2ob2o3bo3bo2b2o80b2o22bo49b2o$137bo6bobo2bo14bobo87bo2bo49bo2bo$ 137bo3bo25bo50b2o33bo6bo36bo8b2o2bo4b3o67bo$138b3o4b3o15bo2bo51b2o33bo 6bo35b2o9b2o2bo71b2o$146bo15bobo88b3o4bo34bo2bo9b4o30b3o$126b3o32bo 104bo28bobo$129bo30b3o102b3o28b2o41b2o$124b2o4bo15bo2bo12bo101b2ob2o 56b3o10bo$109b3o15bo3bo14bo2bo13b2o23b2o74bobob2o35bo21bo11bob4o$117b 2o4bo4bo2bo16b2o12bo24b3o73b3o2b3o32b2o35b5o$114bob3o4bo3bo3bo29bo2bo 21bob2o39b2o31bo6bo34bo2bo2b2o$123b3obob2o31bobo6bo13bo42bobo31bob5o 35bo2bo2b2o12bo2bo$127bo36bo6bo12bo3b2o3bo35bo31b2ob4o35bo20b2obo14bob o$101b2o20b4o44bo11bo78bo25b3o10b4o19bo2bo14bobo$101b2o5b2obo11b2o59bo bo76bo24bo2bo9bobo2bo11b2o5bobo15bo$108bo2bo74bo100bo4bo7b2o4b2o10b2o 5b3o14bobo$109b3o58bo13bobo4bo95b3o2bo9bo39b2o$102bo65b2ob2o113bo5bo 50bo$97bo4bo81b4o97b7o$96bobo2bobo67bobo12b2o97bo$95bo3bobobo65bo3bo 26b2o83bo$93b2o2b3o4bo64bo2b2o26b2o70b2o12b2o60b5o$93bo3bobo70b3o99b2o 36b2o16bo9b2o6b2o5b2o$99b2o70bo138b2o14b2ob2o7b2o6bo7bo$94bob2o4bo120b 2o100b2ob3o14bo7b2o$107bo13b2o99bobo45bo17bo36b5o14bo6b2o$108bo6b3o3b 2o71b2o28bo41bobo2bo15bobo36b3o20bo$106bo2bo5bobo16bo59b2o11bo57b5o2bo 14bob2o36bo4bo11bo4bo$94bo11bo2bo4bo2bo16b2o71b2o56bo3bobo17b2o40bobo 11bob2o$92bobo12b2o6b3o14b5o45b2o22b2obo60bo16b3o42bo$93b2o20bo21bo44b 2o21b2o2bo78bo13b2o$116bo14bo5b2o65b3ob4o72bo2bo14b2o40b2o$115bobo16b 2ob3o48b2o13b2o2bobo2bo70bo6bo52bo2bo19bo$116b2o11b2o2b2obobo49b2o13b 3obobobo25b2o44bo6bo53b2o18b2ob2o$116bo13b2o2bo2bo65bob3ob2o26bobo29bo 13b3o4bo73b2o$134b2o20b3o43bobo2b4o26bo32bo95b3o$130bob2o25bo43bo3bo 61bob3o88bo3bo$130bo23b2o4bo13b2o27bo3bo64b2o89bo3bo$139b3o15bo3bo12b 2o14b2o12bo2bo154bob3o$147b2o4bo4bo2bo28b2o118b3o36b2o12b2o$144bob3o4b o3bo3bo112b2ob3o33bo35b2o12bobo$153b3obob2o116b4o3b2o22b2o4bo49bo$157b o116bo5bo3b2o25bo3bo37b2o9b2o$153b4o48b2o67bobo30bo4bo2bo36bo2bo8b3o$ 138b2obo11b2o21b2o97bob2o28bo3bo3bo36bobo8b2obo$138bo2bo34b2o96b3o30b 3obob2o38bo9b5o$139b3o40b2o91bo2b2o31bo$182b2o91bo2bo28b4o$200b2o73bo 31b2o8bo7bo$199bo2bo66b2o4bo2bo37bobo5b3o$170b2o26b2o2bo4b3o4b2o53bobo 4b2o37bo2bo2b4ob2o$170b2o27b2o2bo65bo51bo2b3o$200b4o8bo3bo101bo2b2o2bo $211bo104bobob2o$210bo7bo98bo$151b2o61bo4bo141b2o$151b2o11b2o43bo4bobo bo123b3o16b2o$164b2o43bo8bo18bo$209bob2o4bo19b2o100b2o$209b3ob2obo19b 2obo98bo$110bo99b2ob3o19b2o2bo99bob4o$108bobo69b3o51b3ob4o98b5o$109b2o 69bo2bo49b2o2bobo2bo81bobo2bo$143b2o34bo4bo48b3obobobo82bob4o23b2o$ 143b2o34b3o2bo48bob3ob2o86bo14bobo8b2o$178bo5bo47bobo2b4o60b2o21b3ob2o 12bobo$177b7o49bo3bo63bobo20b2o3bo13bo$177bo55bo3bo63bo40bobo$132b2o 18b2o23bo42b2o12bo2bo104b2o$131bobo18b2o10b2o12b2o40b2o121bo$132bo31b 2o$324b2o19b2o$212b2ob2o128b2o$118b2o60bo31bob3o3b2o13b2o84b2o$117bobo 26b2o31bobo30bo4b3obo88b3o8b2o$119bo26b2o31bob2o30bobo3bobo87bo3bo$ 181b2o30bobobo2bo88bo3bo$156b2o21b3o36b2o90b3o$156b2o22bo49b2o$176bo2b o49bo2bo$140b2o33bo6bo36bo8b2o2bo4b3o67bo$85b2o53b2o33bo6bo35b2o9b2o2b o71b2o$85b2o88b3o4bo34bo2bo9b4o30b3o$2bo185bo28bobo$obo68b2o114b3o28b 2o41b2o$b2o68b2o113b2ob2o56b3o10bo$87b2o97bobob2o35bo21bo11bob4o$185b 3o2b3o32b2o35b5o$151b2o31bo6bo34bo2bo2b2o$150bobo31bob5o35bo2bo2b2o12b o2bo$151bo31b2ob4o35bo20b2obo14bobo$83b2o3b2o94bo25b3o10b4o19bo2bo14bo bo$84b5o39b2o55bo24bo2bo9bobo2bo11b2o5bobo15bo$72bo11b2ob2o39b2o79bo4b o7b2o4b2o10b2o5b3o14bobo$71b3o10b2ob2o120b3o2bo9bo39b2o$70b5o10b3o120b o5bo50bo$69b2o3b2o131b7o$207bo$122b2o83bo$122b2o70b2o12b2o60b5o$71b3o 120b2o36b2o16bo9b2o6b2o5b2o$71b3o158b2o14b2ob2o7b2o6bo7bo$82bo62b2o 100b2ob3o14bo7b2o$70bo11bobo3bo55bobo45bo17bo36b5o14bo6b2o$69bobo10b2o 3b3o26b2o28bo41bobo2bo15bobo36b3o20bo$68bo3bo13b5o25b2o69b5o2bo14bob2o 36bo4bo11bo4bo$69b3o13bobobobo95bo3bobo17b2o40bobo11bob2o$67b2o3b2o4bo 6b2o3b2o100bo16b3o42bo$76bobo131bo13b2o$77b2o127bo2bo14b2o40b2o$88bo 21b2o93bo6bo52bo2bo19bo$87bobo20b2o47b2o44bo6bo53b2o18b2ob2o$87bo71bob o29bo13b3o4bo73b2o$88bo2bo67bo32bo95b3o$91bo99bob3o88bo3bo$90bo103b2o 89bo3bo$91b3o10b2o178bob3o$93bo10b2o126b3o36b2o12b2o$70b2o124b2ob3o33b o35b2o12bobo$70b2o127b4o3b2o22b2o4bo49bo$196bo5bo3b2o25bo3bo37b2o9b2o$ 196bobo30bo4bo2bo36bo2bo8b3o$44b2o47bo4b2o97bob2o28bo3bo3bo36bobo8b2ob o$44bobo44bobo4b2o96b3o30b3obob2o38bo9b5o$31bobo13bo44b2o103bo2b2o31bo $30bo2bo2b2o6bo2bo7b2o140bo2bo28b4o$21b2o6b2o5bobo8bo7b2o140bo31b2o8bo 7bo$21b2o4b2o3bo3bo3bo3bobo144b2o4bo2bo37bobo5b3o$29b2o5b3ob2o2b2o145b obo4b2o37bo2bo2b4ob2o$30bo2bo3b2o152bo51bo2b3o$31bobo206bo2b2o2bo$238b obob2o$239bo$47bo235b2o$45bobo216b3o16b2o$41b2o3b2o$40bobo218b2o$42bo 65bo151bo$31bo74bobo152bob4o$30b4o73b2o153b5o$18b2o9b2obobo6bobo202bob o2bo$18b2o8b3obo2bo3bo3bo202bob4o23b2o$29b2obobo4bo209bo14bobo8b2o$30b 4o4bo4bo179b2o21b3ob2o12bobo$31bo7bo183bobo20b2o3bo13bo$39bo3bo7b2o 170bo40bobo$41bobo7bobo66b2o142b2o$53bo66bobo142bo$53b2o7bo44bobo13bo$ 60bobo43bo2bo2b2o6bo2bo7b2o113b2o19b2o$61b2o34b2o6b2o5bobo8bo7b2o134b 2o$97b2o4b2o3bo3bo3bo3bobo120b2o$43b2o60b2o5b3ob2o2b2o110b3o8b2o$43bo 2bo59bo2bo3b2o116bo3bo$107bobo121bo3bo$47bo184b3o2$45b2o$44bo11b3o170b o$58bo58b2o108b2o$57bo58bobo$41b2o3b2o70bo$41b2o3b2o59bo$42b5o59b4o$ 43bobo48b2o9b2obobo6bobo$94b2o8b3obo2bo3bo3bo$43b3o59b2obobo4bo$57bo 48b4o4bo4bo$57b2o48bo7bo$56bobo56bo3bo7b2o$117bobo7bobo$41b2o86bo$42bo 86b2o$39b3o$39bo10b2o$49b2o$51bo$59b2o$60bo$60bobo10bo$61b2o9b4o$26b2o 43b2ob4o5b2o$26b2o14bo27b3ob2o3bo3bo2bo$42b2o5bo21b2ob2o3bo7bo$41bobo 3b3o22b5o3bo6bo6b2o$46bo26bo3b3o7bo6b2o$46b2o35bo2bo$83b2o2$65b2o4bo$ 26bo37b2o3b2o$25b3o5b2o31bo3b2o$24b5o4b2o$23b2o3b2o$41b2o3b2o$37b2o3b 5o26b2o9bo$28b2o6b2o4b2ob2o25b4o7bobo$30bo7bo3b2ob2o20bobo2bo2b3o5b2ob o$27bo15b3o20bo2bo2b2o9b2ob2o3b2o$27bo2bo26b2o6b2o9bo6b2obo4b2o$26b2ob 2o26b2o4b2o3bo8bo5bobo$27b2o36b2o10bo6bo$66bo2bo$41b3o23bobo$25b2o3b2o 9b3o$25b2o3b2o8bo3bo$26b5o8bo5bo$27bobo10bo3bo$41b3o$27b3o6$27b2o$27b 2o2$41b2o$41b2o!
And here's a pattern that grows like t*(log t)^(1/4):Code: Select all
x = 866, y = 1279, rule = B3/S23 488bo$486b2ob2o2$486b2o$486bo$471b2o15bo3bo$471b2o11bo3bo3$490bo$487b 3o2$471bo$463b2o6bobo13b3o$463b2o6bobo13b3o$472bo12b2ob2o$471b2o12bo$ 471b2o12b3o2$490b2o$490bo3b2o$455b2o32bo6bo7b3o$455b2o18bo11b5o3bo5b3o $474b3o13bo3bo6b3o$474bo2bobo7bo2bo11bo$465bo11b3o8b2o27bo$464bobo12bo 36bobo$463b2ob2o47b2ob2o$466b2o50b2o$460b2o25bo24b2o$462bo2b3o18bobo 25bo2b3o$460b2obo22bobo11b3o9b2obo$462bo2bo21bo26bo2bo$462bo51bo$463b 2o34bo15b2o$498bobo$464bo34bo16bo$462b2ob2o47b2ob2o$463bo51bo$466bo51b o$464bo51bo3$470bo$463bo3bo2bobo2bo$453b2o8b5ob2o4bo$453b2o9bobo4bo3bo 2$471b3o38b2o$472bo39b2o$536b3o$529bo$527b3o5b2o$445b2o81bo4b4o$445b2o 81b2ob3ob2o$529bobo$504b2o10b2o$504b2o10b2o2$455b2o$453b2ob2o27b2o$ 453b2ob2o8b2o16b3o$453b3o10b2o15bob2o$470bo11bo$468b2ob2o8bo3b2o3bo5b 2o10b2o$468b2obobo6bo15b2o10b2o16b2o$468b2o3bo7bobo40bo$470bo2bo9bo38b 2o4b2o4bo$470b3o8bobo4bo33bo6b2o3bo$522bo2b2o2b3o2bo$481b4o38bob2o$ 483b2o17bo$488b2o12b2o40bo$488b2o11b2obo39bo$500b2o2bo31bo5bo$499b3ob 4o27bobo6bo$498b2o2bobo2bo29bo2bo3bo$498b3obobobo28b2obobo2bo$410bo87b ob3ob2o29b2obo$408b2ob2o84bobo2b4o$498bo3bo63b3o$408b2o88bo3bo56bo$ 408bo76b2o12bo2bo54b3o5b2o$393b2o15bo3bo70b2o71bo4b4o$393b2o11bo3bo 147b2ob3ob2o$559bobo$465bobo78b2o$412bo53b2o32b2o44b2o$409b3o54bo$537b 2o$393bo83b2o57bo10bo$385b2o6bobo13b3o65b2o58b2o4bo3b3o$385b2o6bobo13b 3o83b2o45b2o4b2o$394bo12b2ob2o82bo2bo43bo3bo2b2o$393b2o12bo85b2o2bo4b 3o4b2o31b4obo$393b2o12b3o84b2o2bo44b3o10b2o$495b4o8bo3bo42bo$412b2o92b o45b2o4b2o4bo$412bo3b2o87bo7bo38bo6b2o3bo$377b2o32bo6bo7b3o80bo4bo37bo 2b2o2b3o2bo$377b2o18bo11b5o3bo5b3o78bo4bobobo27b3o9bob2o$396b3o13bo3bo 6b3o78bo8bo18bo10bo$396bo2bobo7bo2bo11bo79bob2o4bo19b2o9b2obo$387bo11b 3o8b2o27bo64b3ob2obo19b2obo9b3o4b2o$386bobo12bo36bobo64b2ob3o19b2o2bo 10bo$385b2ob2o47b2ob2o87b3ob4o$388b2o50b2o86b2o2bobo2bo11bo8b2o31bobo$ 382b2o25bo24b2o92b3obobobo12bo2bo5b2o34bo$384bo2b3o18bobo25bo2b3o86bob 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55b5o29b2o19bobo$375b3o10b2o15bob2o140bo19bo27bo6b3o11bo$392bo11bo144b o13bo5b2o46b3o$390b2ob2o8bo3b2o3bo5b2o10b2o117bo5bobo8b2ob3o47bo$390b 2obobo6bo15b2o10b2o16b2o105bobo3b2o2b2obobo49b2o$390b2o3bo7bobo40bo 109bo5b2o2bo2bo33b3o13bo$392bo2bo9bo38b2o4b2o4bo109b2o35b3o12bo2bo$ 392b3o8bobo4bo33bo6b2o3bo83b2o20bob2o38b2o13bobo$444bo2b2o2b3o2bo83b2o 5b3o12bo43bo14bo$403b4o38bob2o98bo2b2o52bo2b2o$405b2o17bo123b3o52bo3bo $410b2o12b2o40bo30bobo49bo54bo2bo$410b2o11b2obo39bo31b2o36bo3b3o61b3o$ 422b2o2bo31bo5bo33b3o34b3ob2obo$421b3ob4o27bobo6bo34b2o31b3o2bo3b2o$ 420b2o2bobo2bo29bo2bo3bo32bobo30b2ob2obo$420b3obobobo28b2obobo2bo34bo 31b2o2bo98bobo$332bo87bob3ob2o29b2obo74b2ob2o95bobo4b3obo$330b2ob2o84b obo2b4o188b2o16bo5bo4bob2o$420bo3bo63b3o64bo4b2o54b2o16bo2bo2bo4b2o$ 330b2o88bo3bo56bo64b2o6bobo3b2o72bo2bo2bo$330bo76b2o12bo2bo54b3o5b2o 57b3o4b2ob2o15b2o61bo4bo$315b2o15bo3bo70b2o71bo4b4o56bo2bo4bo2b2o17bo 48b2o16bo2bo$315b2o11bo3bo147b2ob3ob2o57b2o5b2obo15bo2bo48b2o17b2o$ 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$381bob2o63bo$381b3o61bo2bo$382bo63b3o31b2o$479bo2bo$479bo2bo$480b2o4$ 439b3o$378bobo$379b2o59bo$379bo9bo48b2ob2o$387b2ob2o46b2ob2o$387b2ob2o 46b2ob2o$373bobo10b2o3b2o$374b2o$374bo$439b3o$387bobobo47bobo12b2o$ 388b3o47bo3bo11b2o$388b3o48bobo$368b2o70bo10b2o6bobo11b2o$368b3o13bobo 5bobo56bobo8bo8b2obo$367bob2o16bo3bo45b2o3b2o7bob2o7bo8b2o2bo$367b3o8b o8bo3bo45b3ob3o7bobo5bo2bo8b3o$368bo8b3o4bo2bo3bo2bo41bob2ob2obo6bo8b 3o10b2obo$376bo4bo3b3o3b3o42b3o3b3o29b2o$377b2o2bo55bo5bo31bo2b3o$377b 3o74b2o$376b2o6bobo67b2o$375b3o5bo61b2o3bo27bobo$376b2o5bo61b3o28b3ob 3o$383bo2bo57bob2o$376bo6b3o58b3o4bo$374b2ob2o66bo5bo$479bo$373bo3bobo 89b2o7bobo$375bo3bo88bobo$369b2o4bo2b2o3b2o60bobo2b2obo5bobo8bo7b3o$ 368b3o5b3o3b3o59bo5bo2bo4bo20bo$368b2obo5bo4b2obo58bo6b3o4bo$369b3o11b 3o58bo2bo10bo2bo13b2o5b2o$370bo13bo59b3o11b3o13b3o5b3o$474b2obo3bob2o$ 475b3o3b3o$476bo5bo2$461b2o7b2o$460b2ob2o4b3o$460b2ob2o4b2obo$460b2ob 2o5b3o$462bo8bo$412b2o$412b2o$464b2o$464b2o$455bobo$454bo$454bo$454bo 2bo$454b3o3$374bobo$377bo82b3o$373bo3bo27b2o47b2o4bo2b2o3b2o$377bo28bo 46b3o5b3o3b3o$374bo2bo28bobo44b2obo5bo4b2obo$375b3o29b2o45b3o11b3o$ 455bo13bo2$419b2o$419bobo9b2o$409b2o9b2o9b2o$408bo2bo33b3o$408bo2bo32b ob2o$382bobo24b2o33b2ob2o$385bo59bo12b2o$381bo3b2obo58bo9b3o$388bo68b 3o$382bo5bo58bo9b3o$383bo3bo65bo3b2obo$384b3o64b2o5b3o$444bo7b2o5bo$ 443bobo$386bobo53b2ob2o$389bo52bo3bo11bo$385bo3bo52bo3bo9b2o$389bo67b 2o$386bo2bo52bo3bo$387b3o52bo3bo$443b3o$444bo2$440b2o5b2o15b2o$405b2o 32b3o5b3o4bo9b3o$406bo32b2obo3bob2o3bobo7bob2o$406bobo31b3o3b3o7bo6b3o $407b2o32bo5bo8bo7bo$454bo$452b2o$359bobo57b2o$362bo56bobo9b2o15bobo6b 2o$358bo3bo46b2o9b2o9b2o14bo6b2obo$358bo3bo45bo2bo35bo6bo$362bo45bo2bo 35bo2bo3bo$359bo2bo46b2o36b3o4bo3bo$360b3o4bo86bo$365bobo8bo76b2obo$ 366b2o7bobo74b3o2bo$375bobo75b2ob2o$375b3o69b2o4bo2b2o3b2o$362bo12b3o 68b3o5b3o3b3o$360bobo12b3o68b2obo5bo4b2obo$361b2o11b2ob2o68b3o11b3o$ 375b3o70bo13bo$376bo2$356bobo14bobobobo$355bo16bo7bo$355bo16bo7bo$355b o2bo13bo2bobo2bo$355b3o14b3o3b3o2$366bo$365bobo37b2o$364b2ob2o37bo$ 364b2o5b2o33bobo$364b2o4b3o34b2o$363b3o4b2obo$371b3o$372bo46b2o$419bob o9b2o$364bo55b2o9b2o$363b4o90bobo$356bobo4bo3bo2bobo87bo$359bo4bo2bo5b o82bo3bo$359bo4b3o6bo82bo3bo$356bo2bo10bo2bo78bo7bo$357b3o11b3o77bo5bo 2bo$444bo6b3o4b3o$442b2ob2o$442b2ob2o$441b2o3b2o9bo$456bo$456b3o2$442b obobo$443b3o$443b3o2$439bobo5bobo14bobo$442bo3bo7bo8bo$438bo3bo3bo7b2o 7bo$438bo3bo3bo2bo5b2o6bo2bo$405b2o35bo3b3o6bo7b3o$406bo32bo2bo10bo$ 406bobo31b3o10bo$407b2o$456b3o$356b2o89b2o5b5o$356b3o60b2o25b3o4b2o$ 356b3o60bobo9b2o13b2obo3b3o$356b3o61b2o9bo2bo12b3o3b3o$355bob2o74bo14b o5bo$355b3o3bo64bobo23bo$356bo5b2o7bo57bo22bo4bo$361b2o7bobo56bo28bo$ 369b2ob2o52bo2bo16bobo4bo6bobo$369bo3bo53b3o19bo4bo2bo5bo$356bo12bo3bo 75bo4b3o6bo$357b2o87bo2bo10bo2bo$356b2o11bo3bo59b3o6bo4b3o11b3o$369bo 3bo68bobo$370b3o61bo7b2o$371bo60b2ob2o$432b2ob2o$350b2o15b2o5b2o56b2ob 2o10bo$349b3o14b3o5b3o70bobo$349b2obo13b2obo3bob2o70b2o$350b3o14b3o3b 3o$351bo16bo5bo58b3o$361bo71bobo$359b2ob2o68bo3bo$362b2o69bobo$358bo6b obo37b2o27bo10b2o6bobo$361bo6bo37bo38bobo8bo$358bobo7bo37bobo22b2o3b2o 7bob2o7bo$359bo5bo2bo38b2o22b3ob3o7bobo5bo2bo$366b3o61bob2ob2obo6bo8b 3o$430b3o3b3o$358b2o20bo38b2o10bo5bo$358bob2o19b2o36bobo26b2o$358bo3bo 17b2o38b2o26b2o$353b2o3b2o2bo4b2o45bobo22b2o3bo$353b3o3b3o5b3o43bo25b 3o$352bob2o4bo5bob2o43bo24bob2o$352b3o11b3o44bo2bo21b3o4bo$353bo13bo 45b3o23bo5bo4$439bobo2b2obo5bobo$438bo5bo2bo4bo$438bo6b3o4bo$438bo2bo 10bo2bo$365bo72b3o11b3o$366b2o66bo$365b2o67bobo$434b2o3$386bobo$385bo 37b3o$385bo3bo11bo21bo2bo$385bo3bo11bo25bo$385bo15bo21bo2bo$385bo2bo 34b5o$385b3o3bo8bobo21b5o$392bo6b2ob2o21b2obo$390b3o6bo3bo20bob2o$350b o72b2obo$351b2o71b2o23bo$350b2o6bobo12bo27bo23bo23bobo$337b2o18bo14bob o12bo13bo47b2o$336b3o18bo3bo23b3o12bobo$336b3o18bo3bo22bo15b3o$336b2ob o17bo12bo5bo7bo15b3o$337b3o17bo2bo9bo5bo$338bo18b3o11bo3bo3bobo14bobo 5bobo$382bo16bo3bo$382bo16bo3bo$363b2o7b3o4bo2bo13bo2bo3bo2bo22bo29bo$ 363b2o7b3o5b3o14b3o3b3o22b2o29bobo$428bobo28b2o$422bo$335bo36b3o46bobo $336b2o21b2o11b3o16bo29bobo$335b2o21bo2bo10b3o15b3o4b2o22b3o38b2o$358b o2bo27bo2bo4b3o21b3o41bo$345bo5bobo4bo9bobo5bobo17bob2o21b3o38bo2bo$ 330bo13bobo7bo4bo11bo3bo12bobo5b3o21b2ob2o38bobo$331b2o11bobo7bo16bo3b o12bo8bo23b3o43bobo$330b2o12b3o4bo2bo4bo3bo4bo2bo3bo2bo43bo47bo$344b3o 5b3o14b3o3b3o92bo$344b3o12b2o58bobobobo41bo2bo$343b2ob2o35bobo2b2obo5b obo18bo7bo8bo32b3o$344b3o35bo5bo2bo4bo21bo7bo6b2o$345bo36bo6b3o4bo21bo 2bobo2bo6b3o$323b2o44b2o11bo2bo10bo2bo18b3o3b3o6b2o$322b3o9bo7bobobobo 20b3o10b3o11b3o$322b2obo7bobo5bo7bo18bob2o56bobo22b2o$323b3o6bo8bo7bo 12b3o3b3o60bo21b3o3bo$324bo7bo8bo2bobo2bo12b3o4bo61bo20bob2o2b3o$334bo 6b3o3b3o12b2obo62bo2bo20b3o5b2o$335b2o24bo67b3o21bo7bo$359b2o2bobo97bo $330b2o6bobo14bobo2bo3bo4bobo86bo4bo$331bob2o6bo12bo5bo2bo4bo71bo16bo$ 334bo6bo12bo6b3o4bo70bobo11bobo6bo4bobo$334bo3bo2bo12bo2bo10bo2bo66b2o b2o9bo5bo2bo4bo$330bo3bo4b3o12b3o11b3o67b2o5b2o5bo6b3o4bo$334bo103b2o 4b3o5bo2bo10bo2bo$332bob2o101b3o4b2obo4b3o11b3o$331bo2b3o108b3o$331b2o b2o110bo$326b2o3b2o2bo4b2o$326b3o3b3o5b3o95bo$325bob2o4bo5bob2o94b4o$ 325b3o11b3o88bobo4bo3bo2bobo$326bo13bo92bo4bo2bo5bo$433bo4b3o6bo$430bo 2bo10bo2bo$431b3o11b3o!
Code: Select all
x = 891, y = 1279, rule = B3/S23 513bo$511b2ob2o2$511b2o$511bo$496b2o15bo3bo$496b2o11bo3bo3$515bo$512b 3o2$496bo$488b2o6bobo13b3o$488b2o6bobo13b3o$497bo12b2ob2o$496b2o12bo$ 496b2o12b3o2$515b2o$515bo3b2o$480b2o32bo6bo7b3o$480b2o18bo11b5o3bo5b3o $499b3o13bo3bo6b3o$499bo2bobo7bo2bo11bo$490bo11b3o8b2o27bo$489bobo12bo 36bobo$488b2ob2o47b2ob2o$491b2o50b2o$485b2o25bo24b2o$487bo2b3o18bobo 25bo2b3o$485b2obo22bobo11b3o9b2obo$487bo2bo21bo26bo2bo$487bo51bo$488b 2o34bo15b2o$523bobo$489bo34bo16bo$487b2ob2o47b2ob2o$488bo51bo$491bo51b o$489bo51bo3$495bo$488bo3bo2bobo2bo$478b2o8b5ob2o4bo$478b2o9bobo4bo3bo 2$496b3o38b2o$497bo39b2o$561b3o$554bo$552b3o5b2o$470b2o81bo4b4o$470b2o 81b2ob3ob2o$554bobo$529b2o10b2o$529b2o10b2o2$480b2o$478b2ob2o27b2o$ 478b2ob2o8b2o16b3o$478b3o10b2o15bob2o$495bo11bo$493b2ob2o8bo3b2o3bo5b 2o10b2o$493b2obobo6bo15b2o10b2o16b2o$493b2o3bo7bobo40bo$495bo2bo9bo38b 2o4b2o4bo$495b3o8bobo4bo33bo6b2o3bo$547bo2b2o2b3o2bo$506b4o38bob2o$ 508b2o17bo$513b2o12b2o40bo$513b2o11b2obo39bo$525b2o2bo31bo5bo$524b3ob 4o27bobo6bo$523b2o2bobo2bo29bo2bo3bo$523b3obobobo28b2obobo2bo$435bo87b ob3ob2o29b2obo$433b2ob2o84bobo2b4o$523bo3bo63b3o$433b2o88bo3bo56bo$ 433bo76b2o12bo2bo54b3o5b2o$418b2o15bo3bo70b2o71bo4b4o$418b2o11bo3bo 147b2ob3ob2o$584bobo$490bobo78b2o$437bo53b2o32b2o44b2o$434b3o54bo$562b 2o$418bo83b2o57bo10bo$410b2o6bobo13b3o65b2o58b2o4bo3b3o$410b2o6bobo13b 3o83b2o45b2o4b2o$419bo12b2ob2o82bo2bo43bo3bo2b2o$418b2o12bo85b2o2bo4b 3o4b2o31b4obo$418b2o12b3o84b2o2bo44b3o10b2o$520b4o8bo3bo42bo$437b2o92b o45b2o4b2o4bo$437bo3b2o87bo7bo38bo6b2o3bo$402b2o32bo6bo7b3o80bo4bo37bo 2b2o2b3o2bo$402b2o18bo11b5o3bo5b3o78bo4bobobo27b3o9bob2o$421b3o13bo3bo 6b3o78bo8bo18bo10bo$421bo2bobo7bo2bo11bo79bob2o4bo19b2o9b2obo$412bo11b 3o8b2o27bo64b3ob2obo19b2obo9b3o4b2o$411bobo12bo36bobo64b2ob3o19b2o2bo 10bo$410b2ob2o47b2ob2o87b3ob4o$413b2o50b2o86b2o2bobo2bo11bo8b2o31bobo$ 407b2o25bo24b2o92b3obobobo12bo2bo5b2o34bo$409bo2b3o18bobo25bo2b3o86bob 3ob2o13b2o39bo2bo$407b2obo22bobo11b3o9b2obo89bobo2b4o13bo39bobo$409bo 2bo21bo26bo2bo88bo3bo14bo26b3o11bo$409bo51bo91bo3bo14b3o37b3o$410b2o 34bo15b2o76b2o12bo2bo15bo40bo$445bobo92b2o73b2o$411bo34bo16bo134b3o13b o$409b2ob2o47b2ob2o125b2o5b3o12bo2bo$410bo51bo69b2ob2o54b2o6b2o13bobo$ 413bo51bo66bob3o3b2o13b2o44bo14bo$411bo51bo42bobo23bo4b3obo57bo2b2o$ 507b2o24bobo3bobo46bo9bo3bo$507bo25bobobo2bo47bo10bo2bo$417bo120b2o51b o7b3o$410bo3bo2bobo2bo127b2o35bo6b2o$400b2o8b5ob2o4bo126bo2bo38b4o$ 400b2o9bobo4bo3bo116bo8b2o2bo4b3o26bo3bo$538b2o9b2o2bo35bo16bo$418b3o 38b2o76bo2bo9b4o32bobo16bobo$419bo39b2o76bobo47bo9b3o4b2ob2o2b2o$483b 3o52b2o56b4o4b5o2b2o$476bo118b2o2b2o3bo$474b3o5b2o63bo48bob2o6bo17b3o$ 392b2o81bo4b4o61b2o50b3o4b3o15bo$392b2o81b2ob3ob2o62bo2bo2b2o44bo5b3o 14b2o$476bobo67bo2bo2b2o65bo2bo$451b2o10b2o80bo73bobo$451b2o10b2o78b4o 74bo$543bobo2bo57bob2o11b2o23bobo$402b2o128bo9b2o4b2o41bo15b2o12bobo 25bo$400b2ob2o27b2o98b2o10bo46b2o27b2o23bo2bo$400b2ob2o8b2o16b3o97bobo 55b5o29b2o19bobo$400b3o10b2o15bob2o140bo19bo27bo6b3o11bo$417bo11bo144b o13bo5b2o46b3o$415b2ob2o8bo3b2o3bo5b2o10b2o117bo5bobo8b2ob3o47bo$415b 2obobo6bo15b2o10b2o16b2o105bobo3b2o2b2obobo49b2o$415b2o3bo7bobo40bo 109bo5b2o2bo2bo33b3o13bo$417bo2bo9bo38b2o4b2o4bo109b2o35b3o12bo2bo$ 417b3o8bobo4bo33bo6b2o3bo83b2o20bob2o38b2o13bobo$469bo2b2o2b3o2bo83b2o 5b3o12bo43bo14bo$428b4o38bob2o98bo2b2o52bo2b2o$430b2o17bo123b3o52bo3bo $435b2o12b2o40bo30bobo49bo54bo2bo$435b2o11b2obo39bo31b2o36bo3b3o61b3o$ 447b2o2bo31bo5bo33b3o34b3ob2obo$446b3ob4o27bobo6bo34b2o31b3o2bo3b2o$ 445b2o2bobo2bo29bo2bo3bo32bobo30b2ob2obo$445b3obobobo28b2obobo2bo34bo 31b2o2bo98bobo$357bo87bob3ob2o29b2obo74b2ob2o95bobo4b3obo$355b2ob2o84b obo2b4o188b2o16bo5bo4bob2o$445bo3bo63b3o64bo4b2o54b2o16bo2bo2bo4b2o$ 355b2o88bo3bo56bo64b2o6bobo3b2o72bo2bo2bo$355bo76b2o12bo2bo54b3o5b2o 57b3o4b2ob2o15b2o61bo4bo$340b2o15bo3bo70b2o71bo4b4o56bo2bo4bo2b2o17bo 48b2o16bo2bo$340b2o11bo3bo147b2ob3ob2o57b2o5b2obo15bo2bo48b2o17b2o$ 506bobo70bobo14b4ob2o$412bobo78b2o84b2o22bo$359bo53b2o32b2o44b2o84bobo 12bo2b3o3bo29b2o$356b3o54bo145bo19bobo11b3obo2bo2bo29b2o$484b2o73b2o 19b2o11b3o4b2o19bo$340bo83b2o57bo10bo63bobo33bobob2o21b2o$332b2o6bobo 13b3o65b2o58b2o4bo3b3o98bob2o20b5o17b2o33b3o$332b2o6bobo13b3o83b2o45b 2o4b2o98bo8bo19bo16b2o33b3o$341bo12b2ob2o82bo2bo43bo3bo2b2o107bo13bo5b 2o51bo$340b2o12bo85b2o2bo4b3o4b2o31b4obo109bo5bobo8b2ob3o40bo7b2o$340b 2o12b3o84b2o2bo44b3o10b2o39b2o64bobo3b2o2b2obobo41bo7bo$442b4o8bo3bo 42bo41bobo65bo5b2o2bo2bo38bo3bo8bo$359b2o92bo45b2o4b2o4bo32bo3bo72b2o 39bobo$359bo3b2o87bo7bo38bo6b2o3bo35b2o68bob2o42bo$324b2o32bo6bo7b3o 80bo4bo37bo2b2o2b3o2bo35bobo52b3o12bo15b2o$324b2o18bo11b5o3bo5b3o78bo 4bobobo27b3o9bob2o98bo2b2o26b2o42b2o$343b3o13bo3bo6b3o78bo8bo18bo10bo 28b2o82b3o71b2o$343bo2bobo7bo2bo11bo79bob2o4bo19b2o9b2obo25b2o83bo72bo $334bo11b3o8b2o27bo64b3ob2obo19b2obo9b3o4b2o177bo$333bobo12bo36bobo64b 2ob3o19b2o2bo10bo183bobo$332b2ob2o47b2ob2o87b3ob4o149bo45bo$335b2o50b 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2bo10bo2bo$456b3o11b3o!
On 15 June 2006, Gabriel Nivasch wrote:Subject: More orders of growth II
Here's a quadratic filter that, unlike the previous one, lays a new block
only when the previous one is consumed.
This allows us to get sublinear population growths, like t^(2^-k) and (log
t)^(2^-k) for all k.
If we attach a regular glider gun (say a p1260 gun) to the filter's input,Code: Select all
#C Quadratic filter. The n-th output glider is emitted in response to #C the Theta(n^2)-th input glider. #C Underlying period is 90. The timing between adjacent input gliders #C should be at least 1260. #C Gabriel Nivasch, June 15, 2006. x = 444, y = 415, rule = B3/S23 222bo$221bobo$221bobo$222bo2$217b2o7b2o$216bo2bo5bo2bo$217b2o7b2o$192b 3o$192b3o27bo$193bo27bobo$193bo27bobo$193bo28bo$192bobo3$192bobo$193bo $193bo$193bo$180bo11b3o$179b3o10b3o3$179b3o2$179bobo$179bobo2$179b3o3$ 179b3o$175bo4bo$174bobo$162b2o9bo3b2o6b2o$162b2o9bo3b2o5bobo$173bo3b2o 7bo10bo$174bobo19b3o$175bo19b2obo$180b2o13b3o$179bobo14b2o$157b3o21bo 48b2o$158bo71bo$158bo61b2o6bobo$157b3o59bobo5b3o$209b2o7bo6b3o$157b3o 49b2o7bo2bo2bo2bo$157b3o58bo6b2o$219bobo$157b3o60b2o$158bo$158bo$157b 3o$153bo$152bobo$140b2o10b2obo7bo$140b2o10b2ob2o6b2o$152b2obo6bobo$ 152bobo$153bo$136bo$136bo$135b3o19b3o$159bo$158bo$135b3o34bo$136bo35b 2o$136bo34bobo$136bo$136bo$135b3o3$135b3o$130bo5bo$130bobo3bo80b2o$ 118b2o11bobo83b2o$118b2o11bo2bo5b3o$131bobo8bo$130bobo8bo$130bo$197bo$ 113b3o80b3o$196bob2o9bo8bo$112bo3bo18b2o60b3o2bo5b2o7b3o$112bo3bo17bob 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we get a sawtooth pattern similar in concept to Dean's "parabolic
sawtooth". This is no good for our purposes. We need to use a sparser gun
as glider source, like a sqrtgun or a caber tosser.
To get population growth of t^(2^-k), we have to attach k-1 quadratic
filters in series to a sqrtgun. For example, here is growth of t^(1/4).
This uses one of Dean's sqrtguns, with some output filtering to only let
out gliders that are mutually congruent mod 90.
And if we use a caber tosser as glider source and attach k quadraticCode: Select all
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13b3o73b3o75b2o3b2o3bo12b3o4b2o$149bob2o11b5o150b2o3b2o3bo13bobo$141b 5o5b2obo8bobobobo154b2o3bo14b2o$140bob3obo5bo2bo7b2o3b2o69bo5b2o79bobo $141bo3bo6bo2bo82bobo4b2o80bo$142b3o9bo83b2obo$143bo19b2o61b2o10b2ob2o $144b2o17b2o33bo27b2o10b2obo$144bobo15bo33bobo39bobo$144bobo15b3o32b2o 40bo$145bo20bo$152b5o5b5o$151bob3obo6b2o64b2o9b2o$142b2obob2o3bo3bo73b obo7bobo$142bo5bo4b3o65b2o2b2o6bo8bo5bo$143bo3bo6bo6b2o3b2o53b2obo2bo 2bo2bo13bobo$144b3o15b5o58b2o6bo13b2obo4b2o$162b2ob2o63bobo14b2ob2o3b 2o$162b2ob2o63b2o15b2obo$153b2o8b3o81bobo$153b2o93bo4$145b2o$145b2o16b 2o$163b2o18$295bo$293bobo$284bo7bobo$283b2o6bo2bo11b2o161b2o162bo$282b 2o4b2o2bobo11b2o159bo2bo161bobo$272b2o7b3o4b2o3bobo170bo7b5o153bobo$ 272b2o8b2o4b2o5bo170bo6bo5bo153bo$283b2o181bo7b2o3bo$284bo172b3o7bo2bo 7bo149b2o7b2o$296bo159b2ob2o8b2o156bo2bo5bo2bo$297bo158b2ob2o38bo128b 2o7b2o$286bo8b3o158b5o37b4o$284bobo168b2o3b2o19b2o14b2obobo130bo$277b 2o4bobo195bo2bo11b3obo2bo2b2o124bobo$277b2o3bo2bo187b5o7bo11b2obobo3b 2o124bobo$283bobo171b2o13bo5bo6bo12b4o131bo$284bobo169b5o11bo3b2o7bo7b o5bo$286bo169bo6b2o8bo7bo2bo9bo$293b2o163b3o3bo16b2o9b3o$293b2o165bo3b obo9bo$458b2o5b2o8b4o$281bobo174b2o14b2ob4o5b2o$280bo2bo3b2o184b3ob2o 3bo3bo2bo$271b2o6b2o5b3ob2o2b2o178b2ob2o3bo7bo$271b2o4b2o3bo3bo3bo3bob o156b2o3b2o15b5o3bo6bo10bo$279b2o5bobo8bo155bobobobo16bo3b3o7bo8bobo$ 280bo2bo2b2o6bo2bo7b2o147b5o5bobo19bo2bo5b2o3b2o$281bobo13bo7b2o148b3o 7b2o19b2o7bobo$294bobo159bo8bo31bo$294b2o201b2o$270bo201bo$270bobo202b o$253b2o18b2o44bo4b2o146bo14bo2bo15bob2o7bo2bo86bo2bo$251bo3bo17b2o4b 2o36bobo4b2o149bo15bo13bo3bo11bo41b4o44bo$245b2o3bo5bo16b2o4b2o37b2o 154bob3o8bo3bo10bo4b2o8bo3bo40bo3bo40bo3bo$245b2o2b2obo3bo8bo4bobo183b 2o14b4o2bo9b4o13b2o11b4o44bo41b4o$250bo5bo9bo3bo185b2o19bo24bo2bo56bo 2bo$251bo3bo5bo2b3o198bo155b8o$253b2o209b2o155bob4obo$453b2o8b2o4b2o5b o144b8o$453b2o7b3o4b2o3bobo130b2o$261bo201b2o4b2o2bobo11b2o119b2o$261b obo200b2o6bo2bo11b2o118bo$250b2o12b2o199bo7bobo$250b2o12b2o208bobo$ 264b2o210bo125b2o$261bobo5b2o332b2o$261bo7b2o331bo3$265b2o343bo4bo$ 253b2o9bobo341b2ob4ob2o$253b3o10bo343bo4bo$244b2o9b2obo11bo69bo235b2o$ 244bo5bo4bo2bo10b2o70bo233bobo$249bo5b2obo9b2o4b2o62b2o5b2o230bo$245bo 3bo3b3o11b3o4b2o2b2o58b3o4b3o$247bo5b2o13b2o4b2o2b2o51bo7bo7b2obo251b 3o$269b2o17bo40bobo15bo2bo5b2o243bo3bo$270bo15bobo33b2o4bobo9b3o4b2obo 5b2o242bo5bo$287b2o33b2o3bo2bo8b2obo2b3o252b2obob2o$328bobo7bo3bo2b2o$ 269b2o58bobo6bo2bo244b2o$269bo2bo58bo8b2o243bobo15bo$587bo14bobo$273bo 328bobo$336b2o265bo$271b2o63b3o241bo$270bo11b3o42b2o9b2obo238b2o21b2o$ 284bo42bo5bo4bo2bo237bobo21b2o$283bo48bo5b2obo$267b2o3b2o54bo3bo3b3o7b 2o$267b2o3b2o56bo5b2o8b2o147b2o91bobo2bobo$268b5o204b2o16b2o87b2obo2bo 2bo2bob2o$269bobo205b2o109bobo2bobo2$269b3o58b2o9b2o210b3o$283bo46bobo 7bobo152b3o57bo$283b2o36b2o2b2o6bo8bo5bo136b2o8b3o56bo$282bobo36b2obo 2bo2bo2bo13bobo127bo7b2o7bo3bo83bo$325b2o6bo13b2obo126bo15bo5bo81b3o$ 267b2o61bobo14b2ob2o3b2o119bobo7bo7bo3bo81b5o$268bo61b2o15b2obo4b2o 118b2ob2o5bobo7b3o81b2o3b2o$265b3o79bobo124bo5bo4bobo$265bo82bo128bo8b o78bo$379bo94b2o3b2o84b2o$378bobo183bobo14b3o$370b2o5bo3b2o100b2obob2o 6bobo82b3o$254bo108bo5bo2bo4bo3b2o3b2o87b4o4bo5bo5bo2bo$252bobo107bobo 5b2o5bo3b2o3b2o87bo2b2o4bo3bo4bob2o$242b2o6b2o12b2o84b2o9bo3b2o11bobo 95bob2o5b3o69b2o23b2o$241bo3bo4b2o12b2o18bo15bo49b2o9bo3b2o3bo8bo116bo 61b2o22b2o$240bo5bo3b2o31b2o13bobo60bo3b2o2b2o106b2o14b2obo60bo$230b2o 8bo3bob2o4bobo28bobo5b2o4bobo17bo44bobo4bobo106bo16bo$230b2o8bo5bo7bo 36b2o3bo2bo16b2o45bo200bo2b2o4b2o2bo$241bo3bo51bobo15b2o4b2o240bo3b3o 2b3o3bo$242b2o54bobo13b3o4b2o2b2o145b2obob2o16b2o3b2o62bo2b2o4b2o2bo$ 300bo4bobo7b2o4b2o2b2o51bo7bo85bo5bo9b2o6b5o$305b2o9b2o59b4o5bobo84bo 3bo10b2o6b2ob2o30b2o$306bo10bo54b2o2bo2b2o8b2o4b2o77b3o19b2ob2o29bobo$ 247b2o11b2o110b2o2b2o11b2o4b2o100b3o32bo$245bo2bo12b2o106b2o10bo7b2o$ 244bo7b2o6bo107b3o10bo4bobo171b3o$236b2o6bo6bo2bo45b2o8b2o35bo21b2o10b o4bo172bo3bo$236b2o6bo7b2o46b2o8b2o4b3o28b3o13b2o7b2o184bo5bo$245bo2bo 58b2o6b5o30bo11bobo7b2o184bo5bo$247b2o57b3o5bo3bobo28b2o11bo135b2o61bo $253bo53b2o6bo3b2o40b2o112b2o21b2o43b3o13bo3bo$253b2o55b2o41bo121b2o 68bo14b3o$241bobo8bobo55b2o41bo190bo16bo$241bo3bo106bo$231b2o12bo10b2o $231b2o8bo4bo7bo2bo7bo41bo7bo183bo35bo25b2o$245bo7bo7b2o3bo39b4o5bobo 31b2o3b2o144bo34b2o24b2o$241bo3bo7bo6bo5bo34b2o2bo2b2o8b2o4b2o23bo5bo 142b3o33bobo$241bobo9bo7b5o35b2o2b2o11b2o4b2o$254bo2bo32b2o6b2o10bo7b 2o30bo3bo188b2o3bo2bo3b2o$256b2o32b2o5b3o10bo4bobo33b3o189b5o4b5o$298b 2o10bo4bo227b2o3bo2bo3b2o$301b2o184bo$301b2o184b3o$490bo17b3o$349b2o 138b2o19bo$350bo158bo$347b3o190bo$347bo144bo46b3o$492bo45b5o$491bobo 43b2o3b2o$490b2ob2o43b5o$489bo5bo26b2o14bo3bo$492bo30b2o14bobo$489b2o 3b2o26bo17bo$527b2o$527b2o$524b2o14b2o$512b2o9b3o14b2o$513b2o9b2o$512b o4b2o8b2o5b2o$489b2o25bobo8b2o5bobo$490bo25bo19bo$487b3o25b2o19b2o$ 487bo$397b2o$395bo3bo$394bo5bo101bo$381b2o10b2obo3bo8b2o90b2o$379bo3bo 10bo5bo8b2o90bobo$373b2o3bo5bo10bo3bo$373b2o2b2obo3bo12b2o$378bo5bo$ 379bo3bo$381b2o$395b3o$395bo$396bo9bo121b2o$405bobo97b2o21b2o$393bobo 8bob2o10b2o85bo2bo$393bo2bo6b2ob2o10b2o70bo$396b2o6bob2o82b2o17bo19bo$ 394bo3b2o5bobo81bobo36b3o$370bo25b2o8bo100b2o18bo3bo$370b3o13b2o5bo2bo 109bo22bo$373bo11bobo5bobo130bo5bo$372b2o11bo140bo5bo$384b2o117b2o3b2o 5b2o10bo3bo$503b2o3b2o5b2o11b3o$497b2o5b5o3bo$497bobo5bobo4b2o4bo5b2o$ 374b3o122bo11bobo3b3o3b2o$499b2o4b3o8bo3bo4bo$374bobo141bo$373b5o81b2o 54bo5bo$372b2o3b2o80b2o21b2o31bo5bo$372b2o3b2o103b2o32bo3bo$508bo8b3o$ 507bobo17bo$506bo3bo15b3o$507b3o16b3o$482bo22b2o3b2o$372b2o108bo41b2o 3b2o$373bo85bo7b2o12bobo40b2o3b2o$370b3o85b3o7b2o10b2ob2o$370bo86b5o5b o11bo5bo$456b2o3b2o19bo35b2o7bo$474b2o3b2o3b2o32b2o6bobo$474b2o52b2o$ 461b2o65b2o$463bo14b3o46b3o$460bo16b2obo45bobo$460bo2bo6bo6b2o29b2o16b 2o$459b2ob2o5b3o6b2o28b2o$460b2o6b5o6bobo$467b2o3b2o5bo2b2o2$458b2o3b 2o$458b2o3b2o$459b5o5b3o$460bobo6b3o$478b5o$460b3o14bob3obo$469b2o7bo 3bo$469b2o8b3o$480bo3$461b2o$461b2o16b2o$479b2o!
filters in series, we get growth like (log t)^(2^-k). For example, here's
growth sqrt log t:
Code: Select all
x = 505, y = 589, rule = B3/S23 287bo$279bobob2obo$279bo3b4o3b3o$279b2ob2o2bo$287bo$287b3o$268b2o17b3o $268b2o3$304bo$304bo$304bo$300b2o$260b2o38b2o$260b2o38b3o3bo$303b3o$ 304bo$304b2o$303b3o$294bo8bo$292b2ob2o8bo$252b2o38b2o9bo$252b2o40b3o6b 3o$290bo3bo$291bo3bo$290bob3o18bo$291b2o12bobob2obo$291bobo11bo3b4o3b 3o$261bo2b2o26bo12b2ob2o2bo$260bobo29b2o19bo$263bo28b3o18b3o$291b2obo 18b3o$260b2o29b5o2$259b2o$261bo$259b2ob2o$259b2o$262bo12bo$275bo$267bo 5bo$265bobo6bo21b4o$268bo2bo3bo19bo$266b2obobo2bo19bo4bo7b2ob2obo$266b 2obo25bob2o7b2o2b5o$296bo10bob3o2bo$308bo5$306b2o$306b2o2$287bo2b2o$ 286bobo$289bo2$286b2o$298b2o$285b2o11b2o$287bo$285b2ob2o$285b2o$288bo 3$290b2o$290b2o105$283bo$282bobo$282bobo$283bo2$278b2o7b2o$277bo2bo5bo 2bo$278b2o7b2o$253b3o$253b3o27bo$254bo27bobo$254bo27bobo$254bo28bo$ 253bobo3$253bobo$254bo$254bo$254bo$241bo11b3o$240b3o10b3o3$240b3o2$ 240bobo$240bobo2$240b3o3$240b3o$236bo4bo$235bobo$223b2o9bo3b2o6b2o$ 223b2o9bo3b2o5bobo$234bo3b2o7bo10bo$235bobo19b3o$236bo19b2obo$241b2o 13b3o$240bobo14b2o$218b3o21bo48b2o$219bo71bo$219bo61b2o6bobo$218b3o59b obo5b3o$270b2o7bo6b3o$218b3o49b2o7bo2bo2bo2bo$218b3o58bo6b2o$280bobo$ 218b3o60b2o$219bo$219bo$218b3o$214bo$213bobo$201b2o10b2obo7bo$201b2o 10b2ob2o6b2o$213b2obo6bobo$213bobo$214bo$197bo$197bo$196b3o19b3o$220bo $219bo$196b3o34bo$197bo35b2o$197bo34bobo$197bo$197bo$196b3o3$196b3o$ 191bo5bo$191bobo3bo80b2o$179b2o11bobo83b2o$179b2o11bo2bo5b3o$192bobo8b o$191bobo8bo$191bo$258bo$174b3o80b3o$257bob2o9bo8bo$173bo3bo18b2o60b3o 2bo5b2o7b3o$67b2o104bo3bo17bobo60b2o3b3o3bobo5b5o$68b2o127bo68bo9bobob obo$67bo106b3o88b2o9b2o3b2o$210b2o$211b2o$174b3o33bo65b2o$276b2o$173bo 3bo97bo$173bo3bo97b3o$250b2o13b2o3b2o7bo$168bo5b3o73b2o14b5o4b5o$168bo bo87bo7b2ob2o6b2o$157b2o12b2o84b3o6b2ob2o$9b2o146b2o12b2o6b2o69bo5b2ob o7b3o$9b2o160b2o7b2o67b3o4b3o15b2o3b2o$168bobo8bo68bo3bo4b2o16b5o$152b o15bo81bo24b2ob2o$152b3o92bo5bo21b2ob2o$8b3o144bo91bo5bo22b3o6b2o$8b3o 143b2o92bo3bo32b2o$7bo3bo237b3o12bo$6bo5bo113bo137bobo3bo$7bo3bo112bob o46b3o78b2o8b2o3b3o$8b3o104bo7bobo49bo79b2o11b5o$114b2o6bo2bo11b2o35bo 79bo12bobobobo2b2o$113b2o4b2o2bobo11b2o18bo30bo78b2o3b2o2b2o7b3o$103b 2o7b3o4b2o3bobo29b3o29b2o70b2o22b2ob2o$103b2o8b2o4b2o5bo28b5o27bobo70b obo21b2ob2o$7bobo104b2o38b2o3b2o99bo23b5o$7bo2bo104bo167b2o3b2o$9b2obo 114bo124bo$127b2o122b3o18b2o$9bo107bo6b2ob2o27b3o92b3o18bo$9bob2o102bo bo38b3o114b3o$10bo97b2o4bobo6bo2bo122b2o3b2o11b3o5bo8b2o$108b2o3bo2bo 7bobo27b2o5bo87b2o3b2o11bo$114bobo7bo2bo27bo4b2o106bo9bo$4b2o3b2o104bo bo7bo2bo23b3o5bobo114bobo$5b5o107bo10bo23bo99bo12bobo8bob2o$5b2ob2o8bo 107bo124bobo11bo2bo6b2ob2o$5b2ob2o6bobo231b2o4b2o10b2o6bob2o105b2o$6b 3o8b2o231b2o4b2o8bo3b2o5bobo104bo2bo$112bobo135b3o8b2o5b2o8bo105bo$ 111bo2bo3b2o131bobo6bo4bo2bo115bo$25bo76b2o6b2o5b3ob2o2b2o24b2o99b2o 11bobo116bobo$o8b2o12b3o76b2o4b2o3bo3bo3bo3bobo14bo7bobo231bobo$3o6bo 12bo87b2o5bobo8bo14bo8bo232bo$3bo6b3o8bobo87bo2bo2b2o6bo2bo7b2o3b3o$2b 2o8bo10bo88bobo13bo7b2o27b2o$125bobo38b2o214b2o3b2o$125b2o38bo216bo5bo $5bo$5bo16bo171b2o187bo3bo$4bobo15b3o98bo62bo7bo2bo186b3o$3b2ob2o17bo 97b3o59bo3b2o7bo9bobo$2bo5bo3b2o10bo101bo58bo5bo6bo7bo3bo$5bo6b2o10bo 2bo97b2o59b5o7bo7bo$2b2o3b2o4b3o12bo165bo2bo7bo4bo8b2o$14b2o9bo3bo133b 2o18b2o9b2o10bo12b2o$14bobo10bo134bobo17b2o22bo3bo176b2o$7b3o14bo5bo 130b3o20bo12bobo8bobo176bo$7bob2o13bo5bo129b3o34b2o189b3o$9b2o14bo3bo 131b3o34bo191bo$8b2o16b3o124b2o7bobo5b2o$6bobo143bobo8b2o5bobo28bo$4b 2o2bo13b2o128bo19bo27bobo$21b2o128b2o19b2o24b2o3bo$23bo104b3o67b2o3bo 9b2o$110b2o18bo67b2o3bo9b2o$109bobo17bo70bobo$95bo12b3o4b2ob3o80bo$5b 5o80bo4b4o8b3o4bo2b4o$4bob3obo79bo5b4o8b3o4b2o$5bo3bo15bo59b2o9bo2bo9b obo86b2o9b2o$6b3o15b3o58b2o9b4o10b2o85b2o9bobo$7bo16b3o68b4o8bo84bo6bo 7b3o4b2ob3o$95bo12bo82bobo12b3o4bo2b4o$22b2o3b2o77b3o75b2o3b2o3bo12b3o 4b2o$22b2o3b2o155b2o3b2o3bo13bobo$7b2o180b2o3bo14b2o$7b2o95bo5b2o79bob o$25bo77bobo4b2o80bo$24bobo76b2obo$26b2o63b2o10b2ob2o$26b2o35bo27b2o 10b2obo$25b3o33bobo39bobo$24bobo35b2o40bo$24b2o2$95b2o9b2o$95bobo7bobo $86b2o2b2o6bo8bo5bo$86b2obo2bo2bo2bo13bobo$90b2o6bo13b2obo4b2o$95bobo 14b2ob2o3b2o$95b2o15b2obo$112bobo$113bo24$160bo$158bobo$149bo7bobo$ 148b2o6bo2bo11b2o161b2o162bo$147b2o4b2o2bobo11b2o159bo2bo161bobo$137b 2o7b3o4b2o3bobo170bo7b5o153bobo$137b2o8b2o4b2o5bo170bo6bo5bo153bo$148b 2o181bo7b2o3bo$149bo172b3o7bo2bo7bo149b2o7b2o$161bo159b2ob2o8b2o156bo 2bo5bo2bo$162bo158b2ob2o38bo128b2o7b2o$151bo8b3o158b5o37b4o$149bobo 168b2o3b2o19b2o14b2obobo130bo$142b2o4bobo195bo2bo11b3obo2bo2b2o124bobo $142b2o3bo2bo187b5o7bo11b2obobo3b2o124bobo$148bobo171b2o13bo5bo6bo12b 4o131bo$149bobo169b5o11bo3b2o7bo7bo5bo$151bo169bo6b2o8bo7bo2bo9bo$158b 2o163b3o3bo16b2o9b3o$158b2o165bo3bobo9bo$323b2o5b2o8b4o$146bobo174b2o 14b2ob4o5b2o$145bo2bo3b2o184b3ob2o3bo3bo2bo$136b2o6b2o5b3ob2o2b2o178b 2ob2o3bo7bo$136b2o4b2o3bo3bo3bo3bobo156b2o3b2o15b5o3bo6bo10bo$144b2o5b obo8bo155bobobobo16bo3b3o7bo8bobo$145bo2bo2b2o6bo2bo7b2o147b5o5bobo19b o2bo5b2o3b2o$146bobo13bo7b2o148b3o7b2o19b2o7bobo$159bobo159bo8bo31bo$ 159b2o201b2o$135bo201bo$135bobo202bo$118b2o18b2o44bo4b2o146bo14bo2bo 15bob2o7bo2bo86bo2bo$116bo3bo17b2o4b2o36bobo4b2o149bo15bo13bo3bo11bo 41b4o44bo$110b2o3bo5bo16b2o4b2o37b2o154bob3o8bo3bo10bo4b2o8bo3bo40bo3b o40bo3bo$110b2o2b2obo3bo8bo4bobo183b2o14b4o2bo9b4o13b2o11b4o44bo41b4o$ 115bo5bo9bo3bo185b2o19bo24bo2bo56bo2bo$116bo3bo5bo2b3o198bo155b8o$118b 2o209b2o155bob4obo$318b2o8b2o4b2o5bo144b8o$318b2o7b3o4b2o3bobo130b2o$ 126bo201b2o4b2o2bobo11b2o119b2o$126bobo200b2o6bo2bo11b2o118bo$115b2o 12b2o199bo7bobo$115b2o12b2o208bobo$129b2o210bo125b2o$126bobo5b2o332b2o $126bo7b2o331bo3$130b2o343bo4bo$118b2o9bobo341b2ob4ob2o$118b3o10bo343b o4bo$109b2o9b2obo11bo69bo235b2o$109bo5bo4bo2bo10b2o70bo233bobo$114bo5b 2obo9b2o4b2o62b2o5b2o230bo$110bo3bo3b3o11b3o4b2o2b2o58b3o4b3o$112bo5b 2o13b2o4b2o2b2o51bo7bo7b2obo251b3o$134b2o17bo40bobo15bo2bo5b2o243bo3bo $135bo15bobo33b2o4bobo9b3o4b2obo5b2o242bo5bo$152b2o33b2o3bo2bo8b2obo2b 3o252b2obob2o$193bobo7bo3bo2b2o$134b2o58bobo6bo2bo244b2o$134bo2bo58bo 8b2o243bobo15bo$452bo14bobo$138bo328bobo$201b2o265bo$136b2o63b3o241bo$ 135bo11b3o42b2o9b2obo238b2o21b2o$149bo42bo5bo4bo2bo237bobo21b2o$148bo 48bo5b2obo$132b2o3b2o54bo3bo3b3o7b2o$132b2o3b2o56bo5b2o8b2o147b2o91bob o2bobo$133b5o204b2o16b2o87b2obo2bo2bo2bob2o$134bobo205b2o109bobo2bobo 2$134b3o58b2o9b2o210b3o$148bo46bobo7bobo152b3o57bo$148b2o36b2o2b2o6bo 8bo5bo136b2o8b3o56bo$147bobo36b2obo2bo2bo2bo13bobo127bo7b2o7bo3bo83bo$ 190b2o6bo13b2obo126bo15bo5bo81b3o$132b2o61bobo14b2ob2o3b2o119bobo7bo7b o3bo81b5o$133bo61b2o15b2obo4b2o118b2ob2o5bobo7b3o81b2o3b2o$130b3o79bob o124bo5bo4bobo$130bo82bo128bo8bo78bo$244bo94b2o3b2o84b2o$243bobo183bob o14b3o$235b2o5bo3b2o100b2obob2o6bobo82b3o$119bo108bo5bo2bo4bo3b2o3b2o 87b4o4bo5bo5bo2bo$117bobo107bobo5b2o5bo3b2o3b2o87bo2b2o4bo3bo4bob2o$ 107b2o6b2o12b2o84b2o9bo3b2o11bobo95bob2o5b3o69b2o23b2o$106bo3bo4b2o12b 2o18bo15bo49b2o9bo3b2o3bo8bo116bo61b2o22b2o$105bo5bo3b2o31b2o13bobo60b o3b2o2b2o106b2o14b2obo60bo$95b2o8bo3bob2o4bobo28bobo5b2o4bobo17bo44bob o4bobo106bo16bo$95b2o8bo5bo7bo36b2o3bo2bo16b2o45bo200bo2b2o4b2o2bo$ 106bo3bo51bobo15b2o4b2o240bo3b3o2b3o3bo$107b2o54bobo13b3o4b2o2b2o145b 2obob2o16b2o3b2o62bo2b2o4b2o2bo$165bo4bobo7b2o4b2o2b2o51bo7bo85bo5bo9b 2o6b5o$170b2o9b2o59b4o5bobo84bo3bo10b2o6b2ob2o30b2o$171bo10bo54b2o2bo 2b2o8b2o4b2o77b3o19b2ob2o29bobo$112b2o11b2o110b2o2b2o11b2o4b2o100b3o 32bo$110bo2bo12b2o106b2o10bo7b2o$109bo7b2o6bo107b3o10bo4bobo171b3o$ 101b2o6bo6bo2bo45b2o8b2o35bo21b2o10bo4bo172bo3bo$101b2o6bo7b2o46b2o8b 2o4b3o28b3o13b2o7b2o184bo5bo$110bo2bo58b2o6b5o30bo11bobo7b2o184bo5bo$ 112b2o57b3o5bo3bobo28b2o11bo135b2o61bo$118bo53b2o6bo3b2o40b2o112b2o21b 2o43b3o13bo3bo$118b2o55b2o41bo121b2o68bo14b3o$106bobo8bobo55b2o41bo 190bo16bo$106bo3bo106bo$96b2o12bo10b2o$96b2o8bo4bo7bo2bo7bo41bo7bo183b o35bo25b2o$110bo7bo7b2o3bo39b4o5bobo31b2o3b2o144bo34b2o24b2o$106bo3bo 7bo6bo5bo34b2o2bo2b2o8b2o4b2o23bo5bo142b3o33bobo$106bobo9bo7b5o35b2o2b 2o11b2o4b2o$119bo2bo32b2o6b2o10bo7b2o30bo3bo188b2o3bo2bo3b2o$121b2o32b 2o5b3o10bo4bobo33b3o189b5o4b5o$163b2o10bo4bo227b2o3bo2bo3b2o$166b2o 184bo$166b2o184b3o$355bo17b3o$214b2o138b2o19bo$215bo158bo$212b3o190bo$ 212bo144bo46b3o$357bo45b5o$356bobo43b2o3b2o$355b2ob2o43b5o$354bo5bo26b 2o14bo3bo$357bo30b2o14bobo$354b2o3b2o26bo17bo$392b2o$392b2o$389b2o14b 2o$377b2o9b3o14b2o$378b2o9b2o$377bo4b2o8b2o5b2o$354b2o25bobo8b2o5bobo$ 355bo25bo19bo$352b3o25b2o19b2o$352bo$262b2o$260bo3bo$259bo5bo101bo$ 246b2o10b2obo3bo8b2o90b2o$244bo3bo10bo5bo8b2o90bobo$238b2o3bo5bo10bo3b o$238b2o2b2obo3bo12b2o$243bo5bo$244bo3bo$246b2o$260b3o$260bo$261bo9bo 121b2o$270bobo97b2o21b2o$258bobo8bob2o10b2o85bo2bo$258bo2bo6b2ob2o10b 2o70bo$261b2o6bob2o82b2o17bo19bo$259bo3b2o5bobo81bobo36b3o$235bo25b2o 8bo100b2o18bo3bo$235b3o13b2o5bo2bo109bo22bo$238bo11bobo5bobo130bo5bo$ 237b2o11bo140bo5bo$249b2o117b2o3b2o5b2o10bo3bo$368b2o3b2o5b2o11b3o$ 362b2o5b5o3bo$362bobo5bobo4b2o4bo5b2o$239b3o122bo11bobo3b3o3b2o$364b2o 4b3o8bo3bo4bo$239bobo141bo$238b5o81b2o54bo5bo$237b2o3b2o80b2o21b2o31bo 5bo$237b2o3b2o103b2o32bo3bo$373bo8b3o$372bobo17bo$371bo3bo15b3o$372b3o 16b3o$347bo22b2o3b2o$237b2o108bo41b2o3b2o$238bo85bo7b2o12bobo40b2o3b2o $235b3o85b3o7b2o10b2ob2o$235bo86b5o5bo11bo5bo$321b2o3b2o19bo35b2o7bo$ 339b2o3b2o3b2o32b2o6bobo$339b2o52b2o$326b2o65b2o$328bo14b3o46b3o$325bo 16b2obo45bobo$325bo2bo6bo6b2o29b2o16b2o$324b2ob2o5b3o6b2o28b2o$325b2o 6b5o6bobo$332b2o3b2o5bo2b2o2$323b2o3b2o$323b2o3b2o$324b5o5b3o$325bobo 6b3o$343b5o$325b3o14bob3obo$334b2o7bo3bo$334b2o8b3o$345bo3$326b2o$326b 2o16b2o$344b2o!
On 10 June 2006, Dean Hickerson wrote:Subject: Re: More orders of growth II
Gabriel Nivasch wrote:
> Here's a quadratic filter that, unlike the previous one, lays a new block
> only when the previous one is consumed.
The quadratic filter is a great idea! I wish I'd thought of it.
The latest one reminded me of my parabolic sawtooth pattern, and I
thought it would be easy to modify that to build a smaller quadratic
filter. It wasn't. I soon realized that I'd have to replace the
glider + LWSS reaction that was used to detect when the tractor beam
had pulled the block all the way back by some more complicated circuitry.
But of course once I started thinking about it I had to build it.
The filter uses p120 logic. Here it's shown being driven by a p840 gun.
As Gabriel mentioned, the result is just another parabolic sawtooth
pattern; I'm including it because it shows the reactions involved pretty
quickly.
Next, here the filter is attached to a sqrtgun, giving populationCode: Select all
#C Inefficient parabolic sawtooth pattern #C Delete the southwest eater to see the normal output of the quadratic #C filter. x = 259, y = 218, rule = B3/S23 231bo$229b4o$228bobob2o14b2o$223bo3bo2bob3o11bo2bo$223b2o3bobob2o11bo$ 229b4o12bo12bo$218bo12bo5bo7bo11b2o$218bobo15bo9bo2bo$201b2o18b2o4b2o 7b3o9b2o$203bo17b2o5bo$193b2o9bo16b2o$193bo10bo13bobo$204bo13bo$203bo$ 201b2o26bo$229bobo$229b2o5$208b2o12bo$208b2o11bo$208b2o6b3o2b3o$208bo 7bo$207bobo7bo$207bob2o3$209bo$208b2o14b2o$224bobo$224bo5$243b2o$231b 3o8bo$34b2o11b2o36b2o18b2o120bo3bo9bo9b2o$35bo12bo37bo18bo119bobo4bo8b o10bo$217b2o4b2o16bo$217bo5b2o17bo$223b2o18b2o$225bobo$227bo$16b2o16bo $17bo15b3o$33b3o36b2o29bo5bo$72bo11b3o16b2o3b2o$31b2o3b2o6b2o3b2o32bo 3bo$31bo5bo44bo5bo16b3o$45bo3bo32bo5bo16b3o$46b3o57bo$46b3o24bo$35bo 35b2ob2o9b2o$34bo50bo$34b3o33bo5bo$14b5o127b2o$13bob3obo50b2o3b2o5b3o 62bo36bo$14bo3bo26bo5bo30b3o33b2o64bobo$15b3o15bo5bo4b3o5bo28bo3bo33bo 39b2o23b2o$16bo16bo5bo4b3o3b3o106bo$34bo3bo41b2o3b2o20b3o21b2o12b3o$ 35b3o4b2o3b2o57bo3bo20bo13b3o$42bo5bo24bo31bo5bo32bo3bo$5b2o7bo57bo32b o5bo31bo5bo$6bo7bo57b3o20bobo46bo3bo$13bobo79b2o48b3o$12b2ob2o79bo$11b o5bo99b3o11b3o23b2o3b2o$14bo23b2o7b2o23b2o3b2o26b2o9bo3bo9b2ob2o22b2o 3b2o$11b2o3b2o20bo8bo24bo5bo27bo8bo5bo8b2ob2o23b5o$5bo33b3o6b3o31bo20b 3o9bo5bo8b5o24bobo$4b3o27b2o5bo8bo4b2o16bo3bo4b2o19bo25b2o3b2o$4b3o21b o6bo19bo18b3o82b3o$29bo5bobo5bo9bobo62b2o$2b2o3b2o18b3o6b2o4bobo8b2o 63bo$2bo5bo32bob2o$40b2ob2o$13bo27bob2o70b3o$13b2o9bo17bobo70b3o$4bo 14b3ob2o2b2o14bo30bo39bo3bo22b2o3b2o$5bo13b4o5bo36bo8b2o66b5o$3b3o17b 2o36b2o2b2ob3o42b2o3b2o22b2ob2o15bo$61bo5b4o13b4o54b2ob2o14b3o$65b2o 16bo7b2o38b2o3b2o5b3o14b5o$83bo3b2o3bo38bobobobo21b2o3b2o$o5bo77bo2bo 36bobo5b5o$o5bo117b2o7b3o$bo3bo119bo8bo6b2o$2b3o137bo$113b2o24b3o$114b o24bo$111b3o$34bo76bo49bo$34b3o124b2o$37bo95bo$36b2o87bo2bo4b2o$26bo 93bo3b2o3bo$25b2o42b2o49b2o7bo$70bo54b4o$25bo44bobo5bo$3b2o3b2o14bobo 44b2o3b4o$3b2o3b2o14bo2bo8bo5bo32bobob2o9b2o42bo$4b5o3bo12bo2bo7bo5bo 31bo2bob3o9bo42bobo$5bobo4b2o23bo3bo33bobob2o53b2o$11bobo11bo12b3o35b 4o$5b3o17b2o51bo2$172bo$172bobo$175b2o6b2o$8bo43b2o107bo13b2o4bo3bo$7b obo42bo108b2o12b2o3bo5bo$6bo3bo161bobo4b2obo3bo9bo$7b3o28bo133bo7bo5bo 8b2o$5b2o3b2o26b2o14b2o125bo3bo$54bo32b2o94b2o$45b2o5bobo33bo56b2o19b 2o$44b3o5b2o92bo19bo$32bo8bob2o101bobo8b2o5bobo$32bobo6bo2bo102b2o7b3o 5b2o$20b2o11bobo5bob2o108bob2o$20bo12bo2bo7b3o106bo2bo$33bobo9b2o106bo b2o$32bobo121b3o$32bo124b2o$9bo$8b2o46b2o$57bo2$47b2o99b2o$47bo8bo91bo $55b2obo45bo$58bo45bobo$58bo45b2o$55bo2bo77b2o$56b2o79b2o$136bo$28bobo $28bo3bo$18b2o12bo10b2o64b2o$18bo14bo7bo2bo65bo$32bo7bo11b2o56bobo5bo 10bo32b2o$28bo3bo7bo12bo57b2o5b2o9b2o15b2o15bo$28bobo9bo78b2o7bobo4bo 9bobo15bobo6bobo$41bo2bo17b2o55b3o13bobo7bo18b2o5bo2bo$43b2o16bobo55b 2o15bobo5b2o24b2o17bo$60b3o55b2o16bo2bo28b2o3bo14bobo$34bo25b2o56bo17b obo31b2o16b2obo$34bobo26b2o70bobo3b2o28bo2bo2bobo8b2ob2o4bo$17b2o18b2o 4b2o17b3o70bo5bobo28bobo2b2o9b2obo4b2o$19bo17b2o5bo98bo34bo9bobo$20bo 16b2o104b2o11b2o31bo$9bo10bo8bo4bobo26bo92bo$9b2o9bo9bo3bo27b2o$19bo8b 3o125bo2bo$17b2o136bo2bo$155bobo$156bo2$156b2o$156bo27bo$183b2o$167bo 14b2o8b2o$165bobo13b3o9bo$158b2o4bobo15b2o$158bo4bo2bo16b2o$33b3o5b2o 19b2o100bobo17bo$35bo6bo19bo102bobo$24bo9bo7bobo7bo7bobo104bo$23bobo 17b2o7bobo5b2o$11b2o10b2obo8bobo17b2o$11bo11b2ob2o6bo2bo17b2o$23b2obo 6b2o20b2o$23bobo5b2o3bo15bobo$24bo8b2o17bo$34bo2bo5b2o86b2o$35bobo5bob o85bo$45bo25b2o$45b2o25bo$72bobo6bo$73b2o6b4o23b2o30b2o$82b4o7bo10b4o 5bo26bo$82bo2bo6bobo9b3ob2o2b2o$82b4o4b2o3bo13bo$81b4o5b2o3bo$81bo8b2o 3bo$92bobo8b2o20b2o$67b2o24bo9bobo6b3o10bo$67bo37bo8bo11b3o$105b2o6bo 14bo$67bo2bo$66bo2bo$66bobo9bo$67bo10b2o$105b2o$67b2o35bobo14b2o$67bo 26bo11bo13b2o$94bobo25bo$80b2o15b2o9b2o$80bo16b2o9bo25b2o$77b2o18b2o6b 2o27bo2bo$69bo6b3o15bobo7b3o17bo3b3o7bo$69b2o6b2o15bo10b2o16b5o3bo6bo 7bo$80bo27bo13b2ob2o3bo7bo6b2o$80b2o26b2o11b3ob2o3bo3bo2bo$122b2ob4o5b 2o$123b4o$124bo4$19b2o$18bobo$18bo$17b2o!
growth t^(1/4):
Code: Select all
#C Population is asymptotic to (1125 t/2)^(1/4). In particular, for #C n>=4, the population in gen 90n^4 + 180n^3 + 1650n^2 + 1560n + 423 #C (when a honey farm has just been destroyed) equals 15n + 2870. x = 366, y = 309, rule = B3/S23 257b2o$256bobo$242bo12b3o$242b4o8b3o12bobo$243b4o8b3o9bo3bo$232b2o9bo 2bo9bobo2b2o4bo19bo$232bo10b4o10b2o2bo4bo19b4o$242b4o21bo17b2obo$242bo 24bo3bo12b3obobo3b2o$255b2o12bobo13b2obo5bo$255bo30b4o$287bo4$248b2o5b o$248bo5b2o$237bobo6bobo$235bo3bo6b2o6bo$227bo7bo17bobo$226b4o4bo18bo 2bo$225b2obobo4bo18bo2bo31bo$214b2o8b3obo2bo3bo3bo7b2o38b4o$214bo10b2o bobo6bobo7b2o5bo33bob2o14b2o$226b4o17b2o5b2o25b2o3bobob3o11bo2bo$227bo 20bo32bo6bob2o11bo$231b2o5bo8bobo37b4o12bo11b2o$219b2o10bo4bobo7b2obo 39bo13bo11bo$219bo17b2o65bo2bo$306b2o$247b2o12b2o$247bo4bobo7bo$252b2o 8bobo6b2o$253bo9b2o6b3o$273b2obo5b2o$273bo2bo5bo$217b2o3b2o49b2obo$ 218b5o48b3o$219b3o49b2o$220bo$213b2o$213bo19bo57b2o$233b3o51b2o2b2o2b 2o$236bo50bo3bo2bobo$235b2o56b3o19bobo$293b2o20bo3bo$302b2o3b2o10bo5b 2o$300bo2bo3bobo10bo4bo$221b3o37b2o36bo7bo11bo$261bo37bo15bo3bo$221bob o75bo15bobo$220b5o12b3o53b2o5bo2bo$211b5o3b2o3b2o10bo3bo51bobo7b2o$ 210bob3obo2b2o3b2o9bo5bo50bo$211bo3bo19b2obob2o48b3o$212b3o74bo$213bo 75b2o15bobo$304bo3bo$304bo19bo$224b2o71b2o4bo19b4o$211bo12bo72bo6bo17b 2obo5b2o$211bo13b3o76bo3bo12b3obobo3bo$210bobo5bo8bo9b2o47b3o17bobo13b 2obo$209b2ob2o2bobo18bo47bo3bo33b4o$208bo5bo2b2o105bo$211bo36bo35bo5bo 18b2o$208b2o3b2o33b3o33b2o3b2o18bo$251bo$250b2o$237b2o$236bobo4b2o$ 238bo4bo8b3o$252b3o34b2o$251bo3bo33bo$210b2o30b2obo4bo5bo33b3o$210bo 32bobo5bo3bo36bo$244bo7b3o43bo$243b2o51b2o58b2o$243b2o52b2o39b2o16bo$ 220bo22b2o93bo$219bobo$207b2o10b2obo8bobo$207bo11b2ob2o6bo2bo$219b2obo 6b2o10b2o$219bobo5b2o3bo8bo8b2o$220bo8b2o20bo$230bo2bo14b3o103bo5bo$ 231bobo14bo87b2o3b2o11b2o3b2o$336b2o3b2o$333bo3b5o14b3o$213b2o117b2o4b obo15b3o$213bo118bobo22bo$338b3o$220b2o19b2o$221bo19bo$221bobo8b2o5bob o$222b2o6bo2bo5b2o$229bo107bo$229bo106bobo$211b2o3b2o11bo105bo3bo$211b obobobo12bo2bo102b3o$212b5o15b2o100b2o3b2o17b3o$213b3o141bo3bo$214bo 141bo5bo$356bo5bo$346bobo$268bo77b2o$266b2o79bo$267b2o$211b2o$212bo97b 2o22b2o$209b3o44b2o53b2o22bo$209bo46bo53bo21b3o$245bobo6bobo75bo$243bo 3bo6b2o$243bo115b2o3b2o$242bo103bo2bo$243bo97b2o2b2o3bo4b2o2bo5bo$237b 2o4bo3bo93bo8bo4bo$236bobo6bobo98b4o10b2ob2o$236bo125bo$235b2o43b2o$ 280bo$360bo$359bobo$358bo3bo$358b5o$357b2o3b2o$235b3o120b5o$235bo123b 3o$236bo123bo2$234bo45b3o$234bobo42bo3bo$237b2o39bo5bo$223bo13b2o40bo 3bo32bobo$223b2o12b2o41b3o33b2o$34b2o11b2o36b2o18b2o127bobo5b2o36b3o 34bo19b2o23b2o$35bo12bo37bo18bo128bo7bobo92bo24bo$244bo118b3o$244b2o 32b2o85bo$279bo5b2o$276b3o6bobo$276bo8bo$16b2o16bo$17bo15b3o$33b3o36b 2o29bo5bo$72bo11b3o16b2o3b2o$31b2o3b2o6b2o3b2o32bo3bo$31bo5bo44bo5bo 16b3o$45bo3bo32bo5bo16b3o$46b3o57bo$46b3o24bo$35bo35b2ob2o9b2o204bo$ 34bo50bo205bobo$34b3o33bo5bo217b2o$14b5o127b2o132b2o12b2o$13bob3obo50b 2o3b2o5b3o62bo132bo13b2o$14bo3bo26bo5bo30b3o33b2o171bobo5b2o$15b3o15bo 5bo4b3o5bo28bo3bo33bo39b2o130bo7bobo$16bo16bo5bo4b3o3b3o106bo141bo$34b o3bo41b2o3b2o20b3o21b2o12b3o153b2o$35b3o4b2o3b2o57bo3bo20bo13b3o$42bo 5bo24bo31bo5bo32bo3bo$5b2o7bo57bo32bo5bo31bo5bo$6bo7bo57b3o20bobo46bo 3bo$13bobo79b2o48b3o$12b2ob2o79bo$11bo5bo99b3o11b3o23b2o3b2o$14bo23b2o 7b2o23b2o3b2o26b2o9bo3bo9b2ob2o22b2o3b2o$11b2o3b2o20bo8bo24bo5bo27bo8b o5bo8b2ob2o23b5o$5bo33b3o6b3o31bo20b3o9bo5bo8b5o24bobo$4b3o27b2o5bo8bo 4b2o16bo3bo4b2o19bo25b2o3b2o$4b3o21bo6bo19bo18b3o82b3o$29bo5bobo5bo9bo bo62b2o$2b2o3b2o18b3o6b2o4bobo8b2o63bo$2bo5bo32bob2o$40b2ob2o$13bo27bo b2o70b3o$13b2o9bo17bobo70b3o$4bo14b3ob2o2b2o14bo30bo39bo3bo22b2o3b2o$ 5bo13b4o5bo36bo8b2o66b5o$3b3o17b2o36b2o2b2ob3o42b2o3b2o22b2ob2o15bo$ 61bo5b4o13b4o54b2ob2o14b3o$65b2o16bo7b2o38b2o3b2o5b3o14b5o$83bo3b2o3bo 38bobobobo21b2o3b2o$o5bo77bo2bo36bobo5b5o$o5bo117b2o7b3o$bo3bo119bo8bo 6b2o$2b3o137bo$113b2o24b3o$114bo24bo$111b3o$34bo76bo49bo$34b3o124b2o$ 37bo95bo$36b2o87bo2bo4b2o$26bo93bo3b2o3bo$25b2o42b2o49b2o7bo$70bo54b4o $25bo44bobo5bo$3b2o3b2o14bobo44b2o3b4o$3b2o3b2o14bo2bo8bo5bo32bobob2o 9b2o42bo$4b5o3bo12bo2bo7bo5bo31bo2bob3o9bo42bobo$5bobo4b2o23bo3bo33bob ob2o53b2o$11bobo11bo12b3o35b4o$5b3o17b2o51bo2$172bo$172bobo$175b2o6b2o $8bo43b2o107bo13b2o4bo3bo$7bobo42bo108b2o12b2o3bo5bo$6bo3bo161bobo4b2o bo3bo9bo$7b3o28bo133bo7bo5bo8b2o$5b2o3b2o26b2o14b2o125bo3bo$54bo32b2o 94b2o$45b2o5bobo33bo56b2o19b2o$44b3o5b2o92bo19bo$32bo8bob2o101bobo8b2o 5bobo$32bobo6bo2bo102b2o7b3o5b2o$20b2o11bobo5bob2o108bob2o$20bo12bo2bo 7b3o106bo2bo$33bobo9b2o106bob2o$32bobo121b3o$32bo124b2o$9bo$8b2o46b2o$ 57bo2$47b2o99b2o$47bo8bo91bo$55b2obo45bo$58bo45bobo$58bo45b2o$55bo2bo 77b2o$56b2o79b2o$136bo$28bobo$28bo3bo$18b2o12bo10b2o64b2o$18bo14bo7bo 2bo65bo$32bo7bo11b2o56bobo5bo10bo32b2o$28bo3bo7bo12bo57b2o5b2o9b2o15b 2o15bo$28bobo9bo78b2o7bobo4bo9bobo15bobo6bobo$41bo2bo17b2o55b3o13bobo 7bo18b2o5bo2bo$43b2o16bobo55b2o15bobo5b2o24b2o17bo$60b3o55b2o16bo2bo 28b2o3bo14bobo$34bo25b2o56bo17bobo31b2o16b2obo$34bobo26b2o70bobo3b2o 28bo2bo2bobo8b2ob2o4bo$17b2o18b2o4b2o17b3o70bo5bobo28bobo2b2o9b2obo4b 2o$19bo17b2o5bo98bo34bo9bobo$20bo16b2o104b2o11b2o31bo$9bo10bo8bo4bobo 26bo92bo$9b2o9bo9bo3bo27b2o$19bo8b3o125bo2bo$17b2o136bo2bo$155bobo$ 156bo2$156b2o$156bo27bo$183b2o$167bo14b2o8b2o$165bobo13b3o9bo$158b2o4b obo15b2o$158bo4bo2bo16b2o$33b3o5b2o19b2o100bobo17bo$35bo6bo19bo102bobo $24bo9bo7bobo7bo7bobo104bo$23bobo17b2o7bobo5b2o$11b2o10b2obo8bobo17b2o $11bo11b2ob2o6bo2bo17b2o$23b2obo6b2o20b2o$23bobo5b2o3bo15bobo$24bo8b2o 17bo$34bo2bo5b2o86b2o$35bobo5bobo85bo$45bo25b2o$45b2o25bo$72bobo6bo57b 2o$73b2o6b4o23b2o29bo$82b4o7bo10b4o5bo$82bo2bo6bobo9b3ob2o2b2o$82b4o4b 2o3bo13bo$81b4o5b2o3bo$81bo8b2o3bo$92bobo8b2o20b2o$67b2o24bo9bobo6b3o 10bo$67bo37bo8bo11b3o$105b2o6bo14bo$67bo2bo$66bo2bo$66bobo9bo$67bo10b 2o$105b2o$67b2o35bobo14b2o$67bo26bo11bo13b2o$94bobo25bo$80b2o15b2o9b2o $80bo16b2o9bo25b2o$77b2o18b2o6b2o27bo2bo$69bo6b3o15bobo7b3o17bo3b3o7bo $69b2o6b2o15bo10b2o16b5o3bo6bo7bo$80bo27bo13b2ob2o3bo7bo6b2o$80b2o26b 2o11b3ob2o3bo3bo2bo$122b2ob4o5b2o$123b4o$124bo!
Not at all coincidentally, the other messages interspersed with these in June 2006 were announcements of the release of Golly 1.0. (!)On 21 June 2006, Gabriel Nivasch wrote:Subject: Improved quadratic filter
This improved quadratic filter can accept a p90 input source.
We can add multiple blocks to the filter's loop. This has the effect ofCode: Select all
#C Quadratic filter #C n-th output glider is emitted in response to ((n^2+n)/2)-th #C input glider. #C Here shown with p90 glider source. #C Gabriel Nivasch, June 21, 2006. x = 491, y = 416, rule = B3/S23 268bo$267bobo$267bobo$268bo2$263b2o7b2o$262bo2bo5bo2bo$263b2o7b2o2$ 268bo$267bobo$238bo28bobo$237b3o28bo$236b2ob2o$235b3ob3o$235b3ob3o$ 235b3ob3o$235b3ob3o$236b2ob2o$237b3o$238bo2$242b3o$225bo$224bobo$223bo 3bo$223bo3bo$223bo3bo$223bo3bo10bo$223bo3bo10b2o$223bo3bo9bobo$224bobo $225bo2$216b2o$208bo7bo2bo$207bo3b2o7bo$207bo5bo6bo$208b5o7bo$216bo2bo $216b2o5$202b3o15b3o$202bobo17bo$202b3o16bo$202b3o$202b3o44b2o19b2o$ 202b3o45bo19bo$202bobo10b2o33bobo6bobo6bobo$202b3o11b2o33b2o5bo2bo6b2o $215bo41b2o$255b2o3bo$194b2o33b3o25b2o$194bobo34bo26bo2bo$185b3ob2o4b 3o32bo28bobo$185b4o2bo4b3o42b3o$189b2o4b3o42bo2bo$194bobo46bo$194b2o 47bo$240bobo3$181bo$181bo16b2o$180bobo16b2o$181bo16bo$181bo$181bo$181b o$180bobo$181bo11bo$181bo11b2o$192bobo46bo$172b2o64b2o2bo2bo$172bobo 32b2o29b3o4bo16b2o$163b2o2b2o6bo30bobo28b2o3b2obo16b2o$163b2obo2bo2bo 2bo32bo29b2o3b2o$167b2o6bo72b2o$172bobo73bobo$172b2o74bo$159bo$159bo2$ 159bo87bo$158bobo15b2o69b3o10b2obob2o$175bobo63b3o6bo4b3o$158b3o16bo 62bo2bo5b2o4bo4bo5bo$243bo6b3o3bo$243bo7bobo7b2ob2o$158b3o79bobo7bo3bo 8bo$250b5o$158bobo88b2o3b2o$159bo90b5o6bo$170b2o62b2o15b3o6bobo$150bo 8bo11b2o61b2o16bo6bo3bo$150b2o7bo10bo88b5o$141b2o2b2o4b2o105b2o3b2o$ 141b2o2b2o4b3o30b3o72b5o$145b2o4b2o33bo66bo6b3o$150b2o33bo64b2o9bo76bo $136bo13bo82b3o5b3o6b3o83b3o$136b3o102bo2bo6b2o82bo$139bo93bobo5bo9bo 17b2o64b2o$138b2o92b5o4bo8bobo16b2o$231b2o3b2o4bobo5b2o$112b2o40bo76b 2o3b2o$111bobo40b2o$96bobo11bo6b2o34bobo95b2obob2o$91bo4bo2bo10bo2bo2b o2bob2o113b2o22b2o68b2o3b2o$92b2o5b2o9bo6b2o2b2o15b2o3b2o91bob2o11bo5b o2b2o68b2o3b2o$87b2o8bo3b2o8bobo27bo97bo$87b2o10b2o11b2o24bo5bo107b2ob 2o75b3o$96bo2bo8bo30b2ob2o90bob3o8bo6bo15bo61b3o$96bobo10b2o29bobo91bo 11b2o21b3o61bo$108b2o31bo92bo11bobo19b5o$141bo6bo107b2o9b2o3b2o$103b2o 43b2o106bo11b5o$102bobo42bobo107b3o8bo3bo$92b2o7bo6b2o149bo9bobo63b2o$ 92b2o7bo2bo2bo2bo27b2o22b2o69b2o3b2o30bo64bo$101bo6b2o5bobo21bo21bobo 71b3o16b2o9b2o69b3o$102bobo11b2o18b3o24bo70bo3bo14b2o9bobo71bo$103b2o 11bo19bo98bobo10bo6bo7b3o4b2o$236bo10bobo12b3o4bo2bo$240b2o3b2o3bo12b 3o4b2o$240b2o3b2o3bo13bobo102b2o$99bo145b2o3bo14b2o102b2o$98bobo70b2o 63b2o9bobo$86b2o9bo3b2o8bo57bo2bo63b2o10bo117b2o$86b2o9bo3b2o5b4o4bo 37b2o4b2o6bo15bobo179b2o$97bo3b2o4b4o5bo37bobo3b2o6bo10b3o2bo3bo$98bob o6bo2bo9b2o32bo13bo19bo174b2o$99bo7b4o9b2o47bo2bo2b2o7bo4bo4b2o167b2o$ 108b4o59b2o2bo2bobo7bo5b2o$111bo64b3o5bo3bo171b2o$184bobo173b2o2$107bo 249b2o$107b3o15b2o230b2o$110bo15b2o41b2o10bo$109b2o14bo43bo10bobo171b 2o$173b2o4bo3b2o169b2o$139b3o4bobo21bo2b2o4bo3b2o3b2o$101b2o38bo4bo3bo 23bo4bo3b2o3b2o161b2o$101bobo36bo9bo18bo3bo6bobo168b2o$89bo12b3o7b2o 32bo4bo17bo11bo$86b4o3b2o8b3o6b2o36bo20bo176b2o$85b4o3b2o8b3o32b2o7bo 3bo3b2o192b2o$78b2o5bo2bo3b2obob2o2bobo32bobo7bobo5bobo25b2o$78b2o5b4o 4bobob2o2b2o33bo19bo25bobo160b2o$86b4o3bob2o38b2o19b2o14bo4b2o4b3o7b2o 150b2o$89bo81bobob2o2bo4b3o6b2o$159b2o9bo3bob3o4b3o156b2o$25bo74b2o57b 2o9bo3bob2o4bobo157b2o$25b4o71b2o68bo3b2o6b2o$9bo16b4o62bo78bobo165b2o $8bobo5b2o8bo2bo5b2o54bobo78bo166b2o$6b2o3bo14b4o5b2o53bob2o$b2o3b2o3b o4bobob2o3b4o55b2o3b2ob2o242b2o$b2o3b2o3bo5b2o3bo2bo58b2o4bob2o242b2o$ 8bobo10bo69bobo9bo$9bo8bo2bo70bo10b2o228b2o$102bobo228b2o2$16bo73b2o 238b2o$16b4o69bobo238b2o$6b2o9b4o58b2o7bo6b2o4bo$6b2o9bo2bo58b2o7bo2bo 2bo2bo2bobo224b2o$11bo5b4o67bo6b3obob2o10b2o212b2o$11bo4b4o69bobo6b2ob 2o10b2o$16bo73b2o7bob2o221b2o$100bobo221b2o$101bo$36bo284b2o$9b2o9b3o 11bobo284b2o$bo7bo2bo9bo12b2o$o3b2o7bo7bo5bo290b2o$o5bo6bo12b4o288b2o$ b5o7bo11b2obobo$9bo2bo11b3obo2bo2b2o279b2o$9b2o14b2obobo3b2o279b2o$26b 4o$27bo284b2o$312b2o2$309b2o$309b2o2$306b2o$306b2o2$303b2o$303b2o2$ 300b2o$300b2o2$297b2o$297b2o2$294b2o$294b2o2$291b2o$188b2o19b2o80b2o$ 189bo19bo$189bobo5bo9bobo78b2o$190b2o4bobo8b2o79b2o$194b2o3bo118b2o 164bo$194b2o3bo85b2o22b2o7bo2bo161bobo$194b2o3bo85b2o21bo4b2o7bo160bob o$196bobo109bo6bo6bo6b2o153bo$197bo84b2o25b6o7bo6b2o$282b2o34bo2bo157b 2o7b2o$318b2o158bo2bo5bo2bo$179b2o98b2o64bo133b2o7b2o$179bo99b2o25b2o 3b2o30b4o$170b2o5bobo127b5o22b2o5b4ob2o136bo$169bobo5b2o97b2o29b2ob2o 20bo2bo3bo3b2ob3o8b2o124bobo$154bobo11bo107b2o29b2ob2o19bo7bo3b2ob2o9b 2o124bobo$149bo4bo2bo10bo2bo136b3o12b2o6bo6bo3b5o137bo$150b2o5b2o9bo 104b2o48b2o6bo7b3o3bo$145b2o8bo3b2o8bobo101b2o39b2o16bo2bo$145b2o10b2o 11b2o143bo18b2o$154bo2bo8bo103b2o43bobo4bo$154bobo10b2o101b2o44b3ob4o 23bo$166b2o150b2obob2o14b2o7b2o$267b2o44bo4bo2bob3o11bo2bo6b2o$181bo 85b2o38bo3bobo5bobob2o11bo$181bobo122b3o3b2o6b4o12bo$184b2o78b2o39b5o 12bo5bo7bo$165bo18b2o4b2o72b2o38bobobobo16bo9bo2bo5b2o$165bobo16b2o4b 2o29bo82b2o3b2o16b3o9b2o5bobo$154b2o12b2o11bobo37b2o38b2o85bo5bobo$ 154b2o12b2o11bo34b2o4b2o37b2o57bo27b2o5b2o$168b2o46b2o4b3o82bo13bo33bo $165bobo48b2o4b2o34b2o46bobo10b3o$165bo47b2o6b2o7b2o26b2o46bobo38b2o 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226b3o80b3o45bo8bo5bo$226b3o80b3o19bo25bo8bo5bo$332bo36bo5b2o3b2o$332b o34bo3bo3b2o3b2o$224b2o142b3o$225bo81b2o3b2o55bo7b3o$222b3o83b5o10b2o 5b2o3b2o19b2o3b2o14b3o$222bo86b3o11b2o8bo24b3o17bo$310bo15b2o2bo5bo20b o3bo7b2o$314b3o3b3o3bobo2b2ob2o22bobo8b2o$316bo3b3o3bo5bobo24bo$315bo 17bo$333bo$377b2o$318b2o3b2o34b2o16b2o$319b5o35b2o$320b3o8bo$311b3o7bo 8b3o$329bo3bo$311bobo14bob3obo$310b5o14b5o$309b2o3b2o$309b2o3b2o3$312b o7b2o$310b2o8b2o2$309bo2$310bo2bo$312b2o16b2o$330b2o![\code][/quote] [quote="On 25 June 2006, Gabriel Nivasch"][b]Subject: Exponential filters[/b] Using a similar approach we can build "exponential filters". These allow us to get asymptotic population growths of the form log log ... log t. [code]#C Exponential filter #C n-th output glider is emitted in response to (5 * 2^n - 4)-th #C input glider. #C Recovery time is 1620. #C Here shown with p1620 glider source. #C Gabriel Nivasch, June 25, 2006. x = 738, y = 627, rule = S23/B3 495bo$494bobo$494bobo$495bo2$490b2o7b2o$489bo2bo5bo2bo$490b2o7b2o2$ 495bo$494bobo$494bobo$495bo13$440b3o$440bobo$440b3o$440b3o$440b3o$440b 3o$440bobo$440b3o8$441b2o$441bobo$441bo12$439b2o$440b2o$421bo17bo$421b 3o$424bo$423b2o4$463b3o$408b3o52bo$408b3o53bo$409bo15b3o$409bo15bo2bo$ 409bo15bo$408bobo14bo$426bobo2$408bobo11bo$409bo11bobo$409bo$409bo$ 408b3o6bo$404bo3b3o6b2o$403b4o9bobo$391b2o9b2obobo$391b2o8b3obo2bo$ 402b2obobo$403b4o$404bo2$387bo98b2o$386b3o97bobo$486bo2$386b3o2$386bob o$386bobo$399b3o$386b3o12bo$400bo2$386b3o$382bo4bo$381bobo10b2o$369b2o 9bo3b2o9b2o$369b2o9bo3b2o8bo$380bo3b2o$381bobo24b3o$382bo27bo$409bo2$ 364b3o$365bo142b3o$365bo142bo$364b3o142bo$425b3o$364b3o57bo2bo$364b3o 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lowering the filter's scale factor, and also lowering the recovery time.
For example:
To get population growth ofCode: Select all
#C Exponential filter #C n-th output glider is emitted in response to S(n)-th #C input glider, where #C S(n) ~= 7.89860 * 1.32472^n. #C #C More precisely, S(n) is given by: #C S(1)=3, S(2)=7, S(3)=12, S(4)=18, S(5)=25, S(6)=35, #C and then #C S(n) = 2*S(n-1) - S(n-2) + S(n-5) - S(n-6). #C #C The filter is shown with a p90 glider source. #C Gabriel Nivasch, June 25, 2006. x = 745, y = 636, rule = S23/B3 504bo$503bobo$503bobo$504bo2$499b2o7b2o$498bo2bo5bo2bo$499b2o7b2o2$ 504bo$503bobo$503bobo$504bo22$440b3o$440bobo$440b3o$440b3o$440b3o$440b 3o$440bobo$440b3o8$441b2o$441bobo$441bo12$439b2o$440b2o$421bo17bo$421b 3o$424bo$423b2o4$463b3o$408b3o52bo$408b3o53bo$409bo15b3o$409bo15bo2bo$ 409bo15bo$408bobo14bo$426bobo2$408bobo11bo$409bo11bobo$409bo$409bo$ 408b3o6bo$404bo3b3o6b2o$403b4o9bobo$391b2o9b2obobo$391b2o8b3obo2bo$ 402b2obobo$403b4o$404bo2$387bo98b2o$386b3o97bobo$486bo2$386b3o2$386bob o$386bobo$399b3o$386b3o12bo$400bo2$386b3o$382bo4bo$381bobo10b2o$369b2o 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11bo18b2o88bo3bo376bo2bob2obo2bo$10b2o16bo2bo84bo5bobo375b2o2bo4bo2b2o $19b2o6bo7b3o3bo73b3o372b2o9bo2bob2obo2bo$4b3o12b2o6bo6bo3b5o53bo17bob obo372b2o3b3o$3b2ob2o19bo7bo3b2ob2o9b2o39bobo17bobobo371bo5b3o$3b2ob2o 20bo2bo3bo3b2ob3o8b2o37b2o21b3o377bo3bo$3b5o22b2o5b4ob2o48b2o22bo377bo 5bo$2b2o3b2o30b4o49b2o390b2o9bo3bo$41bo46b2o4bobo8b2o376bobo10b3o$14b 2o71bobo6bo8bobo8bo368bo$14bo2bo69bo19bo7b3o$5b6o7bo6b2o59b2o19b2o5bob obo$4bo6bo6bo6b2o87bobobo$4bo4b2o7bo96b3o$5b2o7bo2bo98bo$14b2o442bo$ 458b2o$457bobo$497b2o$497b2o3$480bo2bob2obo2bo$480b4ob2ob4o$469b2o9bo 2bob2obo2bo$468bobo5bo$470bo4b3o$474bo3bo$473bob3obo$474b5o$461b3o$ 398b2o63bo$380b2o16b2o62bo$380b2o16b2o$399bo$398bobo$398bobo$380bo7b2o 9bo$379b3o6b2o45b2o$378bo3bo53b2o$377bob3obo12b2o3b2o32bo40b2o$378b5o 8bo4bobobobo73b2o$390bo6b5o$390bo7b3o$399bo59bo2bo4bo2bo$457b3o2b6o2b 3o$386b2o3b2o55bo10bo2bo4bo2bo$377b2o2bo7bo58b2o5bo$379bobo4bo5bo54bob o4bobo$381b2o4b2ob2o61bo3bo$382b2o4bobo63b3o$380bob2o5bo6bobo53b2o3b2o $380b3o6bo6b2o41b2o$397bo40bobo$440bo$375b2o3b2o$378bo12b2o7b3o$375bo 5bo9b2o6bo3bo$376b2ob2o17bo5bo$377bobo19bo3bo$378bo21b3o10bo$378bo21b 3o10b2o$412bobo40b2o$455b2o2$401b2o36b2o6b2o$378b2o21b2o34bo4bo2bo4bo$ 378b2o57bo4bo2bo4bo$437bo4bo2bo4bo$381bo44b3o10b2o6b2o$381b3o44bo4b3o$ 384bo42bo5b3o$383b2o47bo3bo$402bobo$403b2o26b2o3b2o$403bo12b3o$418bo$ 417bo$383b2o3b2o$383bobobobo$384b5o$385b3o$386bo32bo$390b2o27b2o$391b 2o21b2o4b2o12b2o$390bo23b2o4b3o11b2o$414b2o4b2o$411b2o6b2o7b2o$383b2o 25bobo6bo8bobo$384bo25bo19bo$381b3o25b2o19b2o$381bo6$394b2o$393bobo$ 395bo5$422b2o$399b2o21b2o$399b2o$407b3o$407bo$408bo3$362b2o$362b2o21b 2o$385b2o12b3o13b2o$398bo3bo12b3o$391b2o4bo5bo8b2o6b2o3b2o$391bobo3b2o bob2o7bo3bo6b3o$385bo7bo17bo3bo5bo3bo$361b3o20b3o6b2o17b2o8bobo$371b3o 9bo3bo15bo19bo$361bobo9bo8bob3obo13b2o$360b5o7bo10b5o32b3o$359b2o3b2o 35bob2o15b3o$359b2o3b2o34bo2b2o$377b2o21b4o5b2o3b2o$377b2o32b3o$364b2o 14b3o27bo3bo3b2o3b2o$364bob2o4b3o5bo18b2o3b2o5bobo5b5o$367bo13bo20bo9b o7b3o$372bobo24bo5bo15bo$362bob3o4b5o24b2ob2o$362bo7b2o3b2o24bobo$362b o7b2o3b2o25bo9b2o$402bo9b2o2$373bo8b3o$374b2o5bo3bo$361b2o3b2o12bo5bo 33b2o$363b3o10bo3b2obob2o15b2o16b2o$362bo3bo35b2o$363bobo6bo2bo$364bo 7b2o9bo$382bobo$382bobo$383bo$364b2o$364b2o16b2o$382b2o!
log ... log t,
with k logs, we attach k-1 exponential filters in series to a caber
tosser. And to get population growth of
sqrt ... sqrt log ... log t,
with j sqrts and k logs, we attach k-1 exponential filters to a caber
tosser, and *then* add j quadratic filters (the order is significant
here).
For example, here's growth log log t:
Code: Select all
x = 738, y = 774, rule = S23/B3 397b4o3b2o$396bo6bo2bob3o$396b5o2bo2bo$403bo2bo$404bo$386b2o17bobo$ 386b2o18bo3$422bo$422bo$422bo$418bo$378b2o37bo2b3o$378b2o38bo4bo$419bo 3bo$420b3o2$412bo$411b3o7bobo$410bo2bo7bobo$370b2o39b3o7bobo$370b2o39b 3o7bobo$409bob2obo6b2o$408b3o2bo$407b2ob4o$408b3obo10b4o3b2o$408b3o11b o6bo2bob3o$379bobo26b2o12b5o2bo2bo$379b3o47bo2bo$380b2o48bo$412b2o17bo bo$410bob2o18bo$378bo31b4o$378bobo30bo$378b3o$377bo$377b5o3$384bo6b3o 20bobo$384bob2o3b2o20bo3bo$384bobo5b2o18bo4bo7b3o$384bob3o23bo4bo6b4o 3b2o$384b2o26bo3bo6bo4bo3b2o$413bo2bo7b2ob2o$425b4o$427bo4$424b2o$424b 2o2$405bobo$405b3o$406b2o3$404bo11b2o$404bobo9b2o$404b3o$403bo$403b5o 4$408b2o$408b2o79$495bo$494bobo$494bobo$495bo2$490b2o7b2o$489bo2bo5bo 2bo$490b2o7b2o2$495bo$494bobo$494bobo$495bo13$440b3o$440bobo$440b3o$ 440b3o$440b3o$440b3o$440bobo$440b3o8$441b2o$441bobo$441bo12$439b2o$ 440b2o$421bo17bo$421b3o$424bo$423b2o4$463b3o$408b3o52bo$408b3o53bo$ 409bo15b3o$409bo15bo2bo$409bo15bo$408bobo14bo$426bobo2$408bobo11bo$ 409bo11bobo$409bo$409bo$408b3o6bo$404bo3b3o6b2o$403b4o9bobo$391b2o9b2o bobo$391b2o8b3obo2bo$402b2obobo$403b4o$404bo2$387bo98b2o$386b3o97bobo$ 486bo2$386b3o2$386bobo$386bobo$399b3o$386b3o12bo$400bo2$386b3o$382bo4b o$381bobo10b2o$369b2o9bo3b2o9b2o$369b2o9bo3b2o8bo$380bo3b2o$381bobo24b 3o$382bo27bo$409bo2$364b3o$365bo142b3o$365bo142bo$364b3o142bo$186bo 238b3o$186b2o176b3o57bo2bo$185bobo176b3o60bo$377b2o48bo$364b3o11b2o44b obo$365bo11bo$365bo$364b3o$360bo$359bobo$347b2o10b2obo9bo$347b2o10b2ob 2o8b2o$359b2obo8bobo$359bobo223b2o$127b2o231bo25b2o197bo2bo$127b2o214b o41bobo183bobo15bo$343bo43bo181bo3bo2b3o10bo$342b3o224bo19bo$127bo434b 2o4bo4bo7b2o2bo2bo5b2o$126b3o402b2o29b2o5bo7bobo2bo2b2o7bobo$125bo3bo 212b3o186bobo35bo3bo5b3o14bo$127bo215bo187bo39bobo22b2o$124bo5bo212bo$ 124bo5bo212bo$125bo3bo213bo11b2o219b2o7bo$126b3o213b3o9bobo211bo7bo2bo 5bo$356bo210bo3b2o7bo2bobo$567bo5bo6bo2bo$342b3o223b5o7bo3bo$337bo5bo 232bo2bo$129bo207bobo3bo232b2o$325b2o11bobo$325b2o11bo2bo254bo$129bo 208bobo8b2o243bobo$127bobo207bobo10b2o217b2o24b2o$128b2o190bo16bo11bo 217bo3bo5bo2b3o$320b3o238b2o3bo5bo9bo3bo$323bo39b3o195b2o2b2obo3bo8bo 4bobo$322b2o41bo200bo5bo16b2o$122b2o3b2o235bo202bo3bo17b2o4b2o$136bo 156bo275b2o18b2o4b2o$123bo3bo9bo154bobo291bobo$124b3o8b3o144b2o7bob2o 258b3o30bo$124b3o154bobo6b2ob2o10b2o246bo$280bo6b3obob2o10b2o17b3o227b o$143bo127b2o7bo2bo2bo2bo2bobo28bo3bo5bo91b3o186b2o$118bo8b2o12b3o127b 2o7bo6b2o4bo28bo5bo4b2o90bo2bo185b2o$118b3o6bo12bo140bobo38b2obob2o3bo bo90bo$121bo6b3o9b2o140b2o141bo$120b2o8bo295bobo17b2o$294bobo28bo120b 2o$284bo10b2o27bobo$123bo159bobo9bo28bobo105b2o$121b2ob2o14bo135b2o4bo b2o37b3o106bobo$140b3o133b2o3b2ob2o36b2o108bo185bo$120bo5bo16bo138bob 2o37bo3bo291bo$142b2o139bobo34b3o4b2o288b3o$120b2obob2o3b2o152bo35bo5b obo$292b2o137bo$133bo158b2o47b2o88b3o10b2obob2o$126b2o212bobo82b3o6bo 4b3o$125bobo153bo60bo81bo2bo5b2o4bo4bo5bo$126bo15b2obob2o129b4o3bob2o 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On 11 June 2006, Gabriel Nivasch wrote:Subject: Re: Quadratic filter
Bill Gosper wrote me:
> Hi Gabriel, did you Golly your tsqrtqsrtlgt?
That's what the pattern is called? It doesn't have a single vowel!
In this pattern you have to press the "+" key a *quadratic* number of
times in order to see the n-th gun activated.
The third gun is activated when you get to around speed 2^53. And the
fourth gun when you get to around speed 2^230.
Interestingly, Golly has a much easier time running the tsqrtsqrtlgt than
its cousin the tsqrtsqrtt.
