Recursive filter stacker

[EvinZL]

Apparently, nobody has created a pattern with growth rate related to f_w (basically the Ackermann function), even though APG's post on the tetrational diehard (and tetrational Turing machine) mentions it as the logical next step after sawmill.

Anyways, as the first step, here is a self-activating spartan recursive filter

Code: Select all

x = 316, y = 287, rule = B3/S23
157bo$156bobo$156b2o12$140b2o$133b2o5b2o$133b2o3$135b2o17b2o8b2o$135b
2o17bo9b2o$129b2o21bobo$129b2o21b2o$170b2o$170b2o$166b2o$166b2o3$134b
2o$134b2o35b2o$129bo41b2o$129b3o$132bo$131b2o5b2o$138b2o10$124b2o19bo$
124b2o19b3o$148bo$147b2o4bo$152bobo$129b2o20bo2bo$129b2o21b2o$125b2o$
125b2o$166b2o$166b2o$131b2o27b2o$131b2o27b2o3$162b2o$155b2o5b2o$155b2o
17$148b2o$148b2o7b2o$134bo22b2o$134b3o$137bo59bo$136b2o58bobo$197b2o$
141bo16b2o$140bobo15b2o$140bo2bo$123b2o16b2o$123b2o6b2o$118b2o12bo27b
2o$112b2o4b2o12bobo20b2o3b2o$112b2o19b2o20b2o51bo$124b2o80b3o$124b2o
79bo$205b2o$194b2o$144b2o48b2o$144b2o$181b2o$111b2o67bobo7b2o$111b2o
26b2o39b2o8b2o$139b2o45bo8bo$186b3o5bobo$130b2o49bo7bo4bobo$130b2o48bo
bo5b2o5bo$120bo59bobo19bo$119bobo59bo9bo9bobo105bo$118bo2bo68bobo7bo2b
o104bo$119b2o13b2o50b2o2b2o9b2o106b2o$134b2o50b2o2$115b2o$114bobo66b2o
$114bo68bobo$113b2o9b2o58bo$125bo$122b3o$122bo62b2o$185bobo$163b2o21bo
$156b2o5b2o$156b2o3$158b2o27b2o$158b2o27b2o$152b2o$152b2o$193b2o$179b
2o12b2o$179b2o8b2o$189b2o2$174b2o$174b2o106b2o$2b2o190b2o86bobo$3bo
190b2o87bo$3o50b2o$o52b2o$47bo187b2o3b2o$47b3o113b2o69bo2bo2bobo$50bo
112bo71b2o4b2o$38b2o9b2o110bobo63b2o$39bo121b2o63bobo$39bobo180b2o3bo$
40b2o179bobo7b2o5b2o$159bo62bo8b2o5bo21bo$59b2o97bobo75bobo21b3o$44b2o
13b2o97bo2bo74b2o25bo$43bo2bo112b2o71b2o6b2o20b2o$44bobo100b2o83bobo5b
2o$45bo101b2o84bo$55b2o$55b2o180b2o5b2o$236bo2bo4b2o$152b2o83b2o19bo$
36b2o114b2o103bobo$36b2o110b2o45b2o60b2o$148b2o44bo2bo$166b2o21b2o3bob
o36bo43bo$165bobo21b2o4bo36bobo41bobo$154b2o9bo17b2o47bo2bo40b2o$154b
2o8b2o17b2o48b2o$49b2o$49b2o195b2o$37b2o146b2o59bobo$37b2o4b2o133b2o5b
2o46bo14bo$43b2o133b2o51b3o14b2o$48b2o180bo$48b2o180b2o72bo$302b3o$
301bo$301b2o9b2o$312bo$310bobo$310b2o2$291b2o$291b2o13b2o$305bo2bo$
305bobo$306bo$209b2o3b2o79b2o$208bo2bobo2bo78b2o$203bo5b2o3b2o5bo$182b
o19bobo15bobo$182b3o18bo17bo92b2o$185bo48b2o78b2o$173b2o9b2o48b2o$174b
o$174bobo$175b2o57bo$233bobo$194b2o37bobo65b2o$179b2o13b2o38bo66b2o$
178bo2bo131b2o$179bobo125b2o4b2o$180bo126b2o$190b2o110b2o$190b2o110b2o
$198b2o$198b2o$171b2o84bo$171b2o83bobo$203b2o51b2o$203b2o3$224b2o$184b
2o38b2o$184b2o6b2o20b2o$172b2o17bobo20b2o3b2o$172b2o4b2o11bo27b2o$178b
2o10b2o$183b2o15b2o$183b2o14bo2bo$199bobo15b2o$200bo16b2o2$195b2o40bo$
196bo39bobo$193b3o41b2o$193bo22b2o$207b2o7b2o24b2o$207b2o32bo2bo31b2o$
241bo2bo31b2o$242b2o4$284bo$283bobo$284b2o11$294b2o$272bo21b2o$271bobo
$272bo3$158bo105b2o$156b3o105bobo15b2o$155bo109bo16b2o$155b2o9b2o51b2o
$166bo52b2o$164bobo134bo$164b2o134bobo$214b2o84b2o$145b2o67b2o$145b2o
13b2o127b2o3b2o$159bo2bo126bobo2bobo$159bobo128bo4bo$160bo$149b2o52b2o
20b2o52b2o$149b2o47b2o3b2o20bobo51b2o$198b2o27bo28bo$227b2o26bobo$168b
2o47b2o37b2o$168b2o46bo2bo$200b2o15bobo41b2o$200b2o16bo42b2o2$222b2o
60b2o$222bo61bobo$155b2o66b3o59bo$155b2o44b2o22bo$167b2o32b2o7b2o$140b
2o19b2o4b2o41b2o57b2o13b2o$140bobo18b2o106b2o13bobo$141bo14b2o127bo$
156b2o3$281b2o$280bobo$281bo!

The input glider stream is marked by the 4-cell spark, and the output is the same lane on the other side. This pattern also contains a boat and eater that redirects the first output glider (which comes after the block pull reaches the end around 4 times) back to the circuitry that will construct the next one.

The reaction creating the new block is slightly messy, but it still is possible to achieve a O(t α(t)) population growth rate. Here is a corresponding pattern that produces an output p256 glider stream in a safe direction. There will be O(α(t)) such output streams active at time t.

Code: Select all

x = 316, y = 287, rule = B3/S23
157bo$156bobo$156b2o12$140b2o$133b2o5b2o$133b2o3$135b2o17b2o8b2o$135b
2o17bo9b2o$129b2o21bobo$129b2o21b2o$170b2o$170b2o$166b2o$166b2o3$134b
2o$134b2o35b2o$129bo41b2o$129b3o$132bo$131b2o5b2o$138b2o10$124b2o19bo$
124b2o19b3o$148bo$147b2o4bo$152bobo$129b2o20bo2bo$129b2o21b2o$125b2o$
125b2o$166b2o$166b2o$131b2o27b2o$131b2o27b2o3$162b2o$155b2o5b2o$155b2o
17$148b2o$148b2o7b2o$134bo22b2o$134b3o$137bo59bo$136b2o58bobo$197b2o$
141bo16b2o$140bobo15b2o$140bo2bo$123b2o16b2o$123b2o6b2o$118b2o12bo27b
2o$112b2o4b2o12bobo20b2o3b2o$112b2o19b2o20b2o51bo$124b2o80b3o$124b2o
79bo$205b2o$194b2o$144b2o48b2o$144b2o$181b2o$111b2o67bobo7b2o$111b2o
26b2o39b2o8b2o$139b2o45bo8bo$186b3o5bobo$130b2o49bo7bo4bobo$130b2o48bo
bo5b2o5bo$120bo59bobo19bo$119bobo59bo9bo9bobo105bo$118bo2bo68bobo7bo2b
o104bo$119b2o13b2o50b2o2b2o9b2o106b2o$134b2o50b2o2$115b2o$114bobo66b2o
$114bo68bobo$113b2o9b2o58bo$125bo$122b3o$122bo62b2o$185bobo$163b2o21bo
$156b2o5b2o$156b2o3$158b2o27b2o$158b2o27b2o$152b2o$152b2o$193b2o$179b
2o12b2o$179b2o8b2o$189b2o2$174b2o$174b2o106b2o$2b2o190b2o86bobo$3bo
190b2o87bo$3o50b2o$o52b2o$47bo187b2o3b2o$47b3o113b2o69bo2bo2bobo$50bo
112bo71b2o4b2o$38b2o9b2o110bobo63b2o$39bo121b2o63bobo$39bobo180b2o3bo$
40b2o179bobo7b2o5b2o$159bo62bo8b2o5bo21bo$59b2o97bobo75bobo21b3o$44b2o
13b2o97bo2bo74b2o25bo$43bo2bo112b2o71b2o6b2o20b2o$44bobo100b2o83bobo5b
2o$45bo101b2o84bo$55b2o$55b2o180b2o5b2o$236bo2bo4b2o$152b2o83b2o19bo$
36b2o114b2o103bobo$36b2o110b2o45b2o60b2o$148b2o44bo2bo$189b2o3bobo36bo
43bo$189b2o4bo36bobo41bobo$154b2o27b2o47bo2bo40b2o$154b2o27b2o48b2o$
49b2o$49b2o195b2o$37b2o146b2o59bobo$37b2o4b2o133b2o5b2o46bo14bo$43b2o
133b2o51b3o14b2o$48b2o180bo$48b2o180b2o72bo$302b3o$301bo$301b2o9b2o$
312bo$310bobo$310b2o2$291b2o$291b2o13b2o$305bo2bo$305bobo$306bo$209b2o
3b2o79b2o$208bo2bobo2bo78b2o$203bo5b2o3b2o5bo$182bo19bobo15bobo$182b3o
18bo17bo92b2o$185bo48b2o78b2o$173b2o9b2o48b2o$174bo$174bobo$125bo49b2o
57bo$125b3o105bobo$128bo65b2o37bobo65b2o$116b2o9b2o50b2o13b2o38bo66b2o
$117bo60bo2bo131b2o$117bobo59bobo125b2o4b2o$118b2o60bo126b2o$190b2o
110b2o$137b2o51b2o110b2o$122b2o13b2o59b2o$121bo2bo73b2o$122bobo46b2o
84bo$123bo47b2o83bobo$133b2o68b2o51b2o$133b2o68b2o3$114b2o108b2o$114b
2o68b2o38b2o$184b2o6b2o20b2o$172b2o17bobo20b2o3b2o$172b2o4b2o11bo27b2o
$178b2o10b2o$183b2o15b2o$127b2o54b2o14bo2bo$127b2o70bobo15b2o$115b2o
83bo16b2o$115b2o4b2o$121b2o72b2o40bo$126b2o68bo39bobo$126b2o65b3o41b2o
$193bo22b2o$207b2o7b2o24b2o$207b2o32bo2bo31b2o$241bo2bo31b2o$242b2o4$
284bo$283bobo$284b2o11$294b2o$272bo21b2o$271bobo$272bo3$158bo105b2o$
156b3o105bobo15b2o$155bo109bo16b2o$155b2o9b2o51b2o$166bo52b2o$164bobo
134bo$164b2o134bobo$214b2o84b2o$145b2o67b2o$145b2o13b2o127b2o3b2o$159b
o2bo126bobo2bobo$159bobo128bo4bo$160bo$149b2o52b2o20b2o52b2o$149b2o47b
2o3b2o20bobo51b2o$198b2o27bo28bo$227b2o26bobo$168b2o47b2o37b2o$168b2o
46bo2bo$200b2o15bobo41b2o$200b2o16bo42b2o2$222b2o60b2o$222bo61bobo$
155b2o66b3o59bo$155b2o44b2o22bo$167b2o32b2o7b2o$140b2o19b2o4b2o41b2o
57b2o13b2o$140bobo18b2o106b2o13bobo$141bo14b2o127bo$156b2o3$281b2o$
280bobo$281bo!

[Anivec]

Anyways, as the first step, here is a self-activating spartan recursive filter

Code: Select all

x = 316, y = 287, rule = B3/S23
157bo$156bobo$156b2o12$140b2o$133b2o5b2o$133b2o3$135b2o17b2o8b2o$135b
2o17bo9b2o$129b2o21bobo$129b2o21b2o$170b2o$170b2o$166b2o$166b2o3$134b
2o$134b2o35b2o$129bo41b2o$129b3o$132bo$131b2o5b2o$138b2o10$124b2o19bo$
124b2o19b3o$148bo$147b2o4bo$152bobo$129b2o20bo2bo$129b2o21b2o$125b2o$
125b2o$166b2o$166b2o$131b2o27b2o$131b2o27b2o3$162b2o$155b2o5b2o$155b2o
17$148b2o$148b2o7b2o$134bo22b2o$134b3o$137bo59bo$136b2o58bobo$197b2o$
141bo16b2o$140bobo15b2o$140bo2bo$123b2o16b2o$123b2o6b2o$118b2o12bo27b
2o$112b2o4b2o12bobo20b2o3b2o$112b2o19b2o20b2o51bo$124b2o80b3o$124b2o
79bo$205b2o$194b2o$144b2o48b2o$144b2o$181b2o$111b2o67bobo7b2o$111b2o
26b2o39b2o8b2o$139b2o45bo8bo$186b3o5bobo$130b2o49bo7bo4bobo$130b2o48bo
bo5b2o5bo$120bo59bobo19bo$119bobo59bo9bo9bobo105bo$118bo2bo68bobo7bo2b
o104bo$119b2o13b2o50b2o2b2o9b2o106b2o$134b2o50b2o2$115b2o$114bobo66b2o
$114bo68bobo$113b2o9b2o58bo$125bo$122b3o$122bo62b2o$185bobo$163b2o21bo
$156b2o5b2o$156b2o3$158b2o27b2o$158b2o27b2o$152b2o$152b2o$193b2o$179b
2o12b2o$179b2o8b2o$189b2o2$174b2o$174b2o106b2o$2b2o190b2o86bobo$3bo
190b2o87bo$3o50b2o$o52b2o$47bo187b2o3b2o$47b3o113b2o69bo2bo2bobo$50bo
112bo71b2o4b2o$38b2o9b2o110bobo63b2o$39bo121b2o63bobo$39bobo180b2o3bo$
40b2o179bobo7b2o5b2o$159bo62bo8b2o5bo21bo$59b2o97bobo75bobo21b3o$44b2o
13b2o97bo2bo74b2o25bo$43bo2bo112b2o71b2o6b2o20b2o$44bobo100b2o83bobo5b
2o$45bo101b2o84bo$55b2o$55b2o180b2o5b2o$236bo2bo4b2o$152b2o83b2o19bo$
36b2o114b2o103bobo$36b2o110b2o45b2o60b2o$148b2o44bo2bo$166b2o21b2o3bob
o36bo43bo$165bobo21b2o4bo36bobo41bobo$154b2o9bo17b2o47bo2bo40b2o$154b
2o8b2o17b2o48b2o$49b2o$49b2o195b2o$37b2o146b2o59bobo$37b2o4b2o133b2o5b
2o46bo14bo$43b2o133b2o51b3o14b2o$48b2o180bo$48b2o180b2o72bo$302b3o$
301bo$301b2o9b2o$312bo$310bobo$310b2o2$291b2o$291b2o13b2o$305bo2bo$
305bobo$306bo$209b2o3b2o79b2o$208bo2bobo2bo78b2o$203bo5b2o3b2o5bo$182b
o19bobo15bobo$182b3o18bo17bo92b2o$185bo48b2o78b2o$173b2o9b2o48b2o$174b
o$174bobo$175b2o57bo$233bobo$194b2o37bobo65b2o$179b2o13b2o38bo66b2o$
178bo2bo131b2o$179bobo125b2o4b2o$180bo126b2o$190b2o110b2o$190b2o110b2o
$198b2o$198b2o$171b2o84bo$171b2o83bobo$203b2o51b2o$203b2o3$224b2o$184b
2o38b2o$184b2o6b2o20b2o$172b2o17bobo20b2o3b2o$172b2o4b2o11bo27b2o$178b
2o10b2o$183b2o15b2o$183b2o14bo2bo$199bobo15b2o$200bo16b2o2$195b2o40bo$
196bo39bobo$193b3o41b2o$193bo22b2o$207b2o7b2o24b2o$207b2o32bo2bo31b2o$
241bo2bo31b2o$242b2o4$284bo$283bobo$284b2o11$294b2o$272bo21b2o$271bobo
$272bo3$158bo105b2o$156b3o105bobo15b2o$155bo109bo16b2o$155b2o9b2o51b2o
$166bo52b2o$164bobo134bo$164b2o134bobo$214b2o84b2o$145b2o67b2o$145b2o
13b2o127b2o3b2o$159bo2bo126bobo2bobo$159bobo128bo4bo$160bo$149b2o52b2o
20b2o52b2o$149b2o47b2o3b2o20bobo51b2o$198b2o27bo28bo$227b2o26bobo$168b
2o47b2o37b2o$168b2o46bo2bo$200b2o15bobo41b2o$200b2o16bo42b2o2$222b2o
60b2o$222bo61bobo$155b2o66b3o59bo$155b2o44b2o22bo$167b2o32b2o7b2o$140b
2o19b2o4b2o41b2o57b2o13b2o$140bobo18b2o106b2o13bobo$141bo14b2o127bo$
156b2o3$281b2o$280bobo$281bo!

How will the rest of the seed be activated?

[EvinZL]

How will the rest of the seed be activated?

The seed is activated by the output of the previous recursive filter (and some parts are activated by the new filter's own output)

[Anivec]

How will the rest of the seed be activated?

The seed is activated by the output of the previous recursive filter (and some parts are activated by the new filter's own output)

Can you show me how close you put them together?

[EvinZL]

Since for O(t α(t)) growth, it doesn't matter if we just produce new seeds at a linear rate, here is a completed O(t α(t)) growth pattern. (I also fixed a minor error in the original where a block is missing)