Crystal Programming

[Extrementhusiast]

While reading some of the topics here, I ended up thinking: how would one get very long delays in stable circuitry? One solution that I thought of was the usual P2N crystal. However, it turns out that there is a whole lot more that this can do than I first thought.

There are many catalyses that cleanly destroy the head of the crystal (although, depending on the catalysis, it may take more than one glider to fully clean up), allowing it to be broken down, e.g.:

Code: Select all

x = 123, y = 114, rule = B3/S23
16b2o$9b2o5b2o$9b2o3$11b2o17b2o8b2o$11b2o17bo9b2o$5b2o21bobo$5b2o21b2o
$46b2o$46b2o$42b2o$42b2o4$47b2o$5bo41b2o$5b3o$8bo$7b2o11$2o$2o2$23bo$
22b2o$5b2o15bobo2b2o$5b2o20bobo$b2o26bo$b2o23bob2o$19b2o5b2o14b2o$18bo
bo21b2o$7b2o9bo17b2o$7b2o8b2o17b2o$56bobo$57b2o$38b2o17bo$31b2o5b2o$
31b2o40$89b2o$88bobo$88bo$87b2o17$120bobo$121b2o$121bo2$120b2o$120b2o!

There are also catalyses that destroy the head of the crystal, but leave some out-of-the-way debris behind, e.g.:

Code: Select all

x = 123, y = 114, rule = B3/S23
16b2o$9b2o5b2o$9b2o3$11b2o17b2o8b2o$11b2o17bo9b2o$5b2o21bobo$5b2o21b2o
$46b2o$46b2o$42b2o$42b2o4$47b2o$5bo41b2o$5b3o$8bo$7b2o11$2o$2o2$23bo$
22b2o$5b2o15bobo2b2o$5b2o20bobo$b2o26bo$b2o23bob2o$19b2o5b2o14b2o$18bo
bo21b2o$7b2o9bo17b2o$7b2o8b2o17b2o$56bobo$57b2o$38b2o17bo$31b2o5b2o$
31b2o45$89b2o$90bo$87b3o$87bo12$120bobo$121b2o$121bo2$120b2o$120b2o!

The usual two-eater weld can create a sideways glider while destroying the head:

Code: Select all

x = 123, y = 114, rule = B3/S23
16b2o$9b2o5b2o$9b2o3$11b2o17b2o8b2o$11b2o17bo9b2o$5b2o21bobo$5b2o21b2o
$46b2o$46b2o$42b2o$42b2o4$47b2o$5bo41b2o$5b3o$8bo$7b2o11$2o$2o2$23bo$
22b2o$5b2o15bobo2b2o$5b2o20bobo$b2o26bo$b2o23bob2o$19b2o5b2o14b2o$18bo
bo21b2o$7b2o9bo17b2o$7b2o8b2o17b2o$56bobo$57b2o$38b2o17bo$31b2o5b2o$
31b2o30$80b2o$80bobo$82bo$82b2o$84bo$82b3o$81bo$81b2o23$120bobo$121b2o
$121bo2$120b2o$120b2o!

Eating one of the accessible blinkers in the intermediate traffic light creates some debris and allows the head to keep growing:

Code: Select all

x = 123, y = 114, rule = B3/S23
16b2o$9b2o5b2o$9b2o3$11b2o17b2o8b2o$11b2o17bo9b2o$5b2o21bobo$5b2o21b2o
$46b2o$46b2o$42b2o$42b2o4$47b2o$5bo41b2o$5b3o$8bo$7b2o11$2o$2o59bo$59b
3o$23bo34bo$22b2o34b2o$5b2o15bobo2b2o$5b2o20bobo$b2o26bo$b2o23bob2o$
19b2o5b2o14b2o$18bobo21b2o$7b2o9bo17b2o$7b2o8b2o17b2o$56bobo$57b2o$38b
2o17bo$31b2o5b2o$31b2o44$89b2o$90bo$87b3o$87bo13$120bobo$121b2o$121bo
2$120b2o$120b2o!

Eating both of the accessible blinkers in the intermediate traffic light (with a ship) produces a really weird result: the crystal keeps growing, and after the head is destroyed, it eventually reforms and starts growing again! The head must be destroyed again to progress forward:

Code: Select all

x = 123, y = 114, rule = B3/S23
16b2o$9b2o5b2o$9b2o3$11b2o17b2o8b2o$11b2o17bo9b2o$5b2o21bobo$5b2o21b2o
$46b2o$46b2o$42b2o$42b2o4$47b2o$5bo41b2o$5b3o$8bo$7b2o11$2o$2o2$23bo$
22b2o$5b2o15bobo2b2o$5b2o20bobo$b2o26bo$b2o23bob2o38bo$19b2o5b2o14b2o
22b3o$18bobo21b2o21bo$7b2o9bo17b2o27b2o$7b2o8b2o17b2o$56bobo$57b2o$38b
2o17bo$31b2o5b2o$31b2o18$62b2o$63bo$60b3o$60bo21$87b2o$87bobo$88b2o16$
120bobo$121b2o$121bo2$120b2o$120b2o!

This allows for using the debris from one run-up to influence the next:

Code: Select all

x = 123, y = 114, rule = B3/S23
16b2o$9b2o5b2o$9b2o3$11b2o17b2o8b2o$11b2o17bo9b2o$5b2o21bobo$5b2o21b2o
$46b2o$46b2o$42b2o$42b2o4$47b2o$5bo41b2o$5b3o$8bo$7b2o11$2o$2o2$23bo$
22b2o$5b2o15bobo2b2o$5b2o20bobo$b2o26bo$b2o23bob2o$19b2o5b2o14b2o27bo$
18bobo21b2o25b3o$7b2o9bo17b2o30bo$7b2o8b2o17b2o30b2o$56bobo$57b2o$38b
2o17bo$31b2o5b2o$31b2o6$58b2o$58b2o13$66b2o$67bo$64b3o$64bo19$87b2o$
87bobo$88b2o16$120bobo$121b2o$121bo2$120b2o$120b2o!

[dvgrn]

Did you find anything new about re-starting a crystal once it's in its decay mode? There are various old high-period guns that do this; I don't remember if they all use the same mechanism or not.

This pattern uses an Fx119 variant to regenerate a new honeyfarm target periodically, but it probably makes more sense to use catalysts to change a decay-mode reaction back into a growth-mode block (or equivalent).

[Extrementhusiast]

Did you find anything new about re-starting a crystal once it's in its decay mode? There are various old high-period guns that do this; I don't remember if they all use the same mechanism or not.

You mean like this?

Code: Select all

x = 218, y = 195, rule = B3/S23
15b2o$15b2o4$16bo$15bobo$14bo3bo$15b3o$13b2o3b2o5$35bo3bo$23b2o9bo5bo
9b2o$23b2o9bo15b2o$34b2o3bo$8b2o26b3o$6bo3bo$2o3bo5bo24b3o$2o2b2obo3bo
22b2o3bo$5bo5bo22bo15b2o$6bo3bo23bo5bo9b2o$8b2o25bo3bo18$26b2o$25bobo$
25bo$24b2o85$186bo11b2o$185bobo10b2o$177bo3b2o2bobo$163bo12bobo2bo2b2o
b2o$163b3o10bobo3bobo$166bo10bob4o2bob2o$165b2o12bo3bobob2o$178bo3bobo
$177bo3bobo$177b2o3bo4$190b2o$154bo35b2o$153bobo49b2o$154bo49bo2bo$
205b2obo$149b2o57bo$145bo3b2o57b2o$146b2o45b2o18b2o$145b2o47bo18bo$
165b2o24b3o21bo$165b2o11b2o11bo2b3o14b5o$178bo14bo2bo13bo$179b3o10b2o
2bobo12b3o$181bo15b2o15bo$211b4o$206b2o3bo3b2o$206b2o4b3o2bo$214bob2o$
214bo$213b2o3$205b2o$205bo$206b3o$208bo4$180bo$178b3o$177bo$177b2o7$
167b2o$166bobo5b2o$166bo7b2o$165b2o2$179bo$175b2obobo$174bobobobo$171b
o2bobobobob2o$171b4ob2o2bo2bo$175bo4b2o$173bobo$173b2o!

Both examples that I've seen otherwise use a two-glider collision: the p2700 in DRH-oscillators.rle uses a direct honeyfarm collision, while the p9200 in guns2j-20090906 uses an interchange.

This pattern uses an Fx119 variant to regenerate a new honeyfarm target periodically, but it probably makes more sense to use catalysts to change a decay-mode reaction back into a growth-mode block (or equivalent).

If you're talking about in the middle of a crystal, that's apparently impossible with stable circuitry (the decay envelope is contained entirely within the growth envelope), unless if you set it up beforehand using the ship (or any other catalysis that functions similarly). If you're talking about after the complete decay of the crystal, see the previous pattern (which could likely be improved with a direct G-to-junk converter).

[Sphenocorona]

No idea where to put these, but uh, anybody want some period multiplying eaters? Now available in periods 5, 6, 12, and 13 (!):

Code: Select all

x = 177, y = 63, rule = B3/S23
115b2o3bo$o2b2obob2o106bo2bobo$4ob2ob2o104bo4bobo15b2o4b2obob2o2bo$
114b5obo16bo5b2ob2ob4o$2o31b2o71b2o10bo19bo$bo16b2o12bo2bo7b2o46b2o13b
2o6b2o3bo17b2o12b2o$o18bo13b2o8bo48bo21b2o4bo16bo13bo$2o17bobo19bobo
48bobo24b2o17bo13bo$bo18b2o19b2o50b2o42b2o12b2o$bobob2o2bo16bo72bo37bo
13bo$2ob2ob4o15bobo70bobo26b2o9bo4bo2b2obobo$26bo72bo27bo9b2o4b4ob2ob
2o$8b2o10b2o71b2o30bobo9bo$8bo10bobo70bobo30b2o11bo4b2o$9bo9bo72bo27bo
16b2o5bo$8b2o8b2o18b3o50b2o18b3o5bobo21bo$8bo29bo72bo8bo16b2o4b2o$2ob
2obobo30bo72bo12b2o11bo5bo$2obob2ob2o16b2o71b2o24bobo9bo6bobob2ob2o$
26bo4b2o66bo4b2o21bo9b2o4b2ob2obob2o$27bo3b2o67bo3b2o21b2o$28bo72bo$
26bob5o66bob5o$25bobo4bo65bobo4bo$25bobo2bo67bobo2bo$26bo3b2o67bo3b2o
2$34b2o5b2o64b2o5b2o$34b2o5b2o64b2o5b2o2$38b2o71b2o$38b2o71b2o2$43b3o
70b3o$42bo4bo67bo4bo$42b2obo15b2o52b2obo15b2o$46b3o12b2o56b3o12b2o$49b
o72bo$58b2o5b2o64b2o5b2o$58b2o5b2o64b2o5b2o2$30b2ob2obob2o102b2o3bo$
30bob2ob2ob2o103bo2bobo$141bo4bobo$141b5obo13b2o4b2obob2o$30b2o113bo
15bo5b2ob2ob3o$30b2o44b2o40b2o21b2o3bo15bo13bo$76bo42bo21b2o4bo13b2o
12b2o$74bobo42bobo24b2o13bo13bo$30b2obob2o2bo34b2o44b2o40bo13bo$30b2ob
2ob4o29bo56bo34b2o12b2o$68bobo54bobo26b2o5bo12bo$38b2o29bo56bo27bo7bo
5bob2obob2o$30b2o6bo35b2o44b2o30bobo6b2o5b2obobobo$30b2o7bo20b2o12bobo
42bobo30b2o7bo10b2obo$38b2o20b2o14bo42bo27bo14bo12b2o$38bo37b2o40b2o
26bobo12b2o12bo$30b2ob2obobo108bo28bo$30b2obob2ob2o112b2o7b2o12b2o$
152bobo7bo12bo$154bo6bo5b2obob2obo$139b2o13b2o5b2o4b2ob2ob2o$139b2o!

The low period ones are actually almost stable versions of the Quinti-snark and Sexta-snark, but the regular glider-liberating reaction unfortunately isn't actually compatible here.

[apg]

No idea where to put these, but uh, anybody want some period multiplying eaters? Now available in periods 5, 6, 12, and 13 (!):

Oh wow! This allows any even-period glider stream to form a crystallisation and decay oscillator:

Code: Select all

x = 89, y = 86, rule = LifeHistory
8.A$8.3A$11.A$10.2A$10.4B$12.3B$12.4B$.4B2.B.3B.4B$.4B.18B$2A5B2A16B$
2A5B2A16B$.B.22B$3.B2A21B$4.2A7B2.13B$4.8B6.10B$6.7B7.7B$5.10B6.8B$5.
13B2.7B2A$6.8BA12B2AB$8.4BABA15B.B$8.4B3A9B2A5B2A$8.4BA11B2A5B2A$9.
18B.4B$16.4B.3B.B2.4B$17.4B$18.4B$19.4B$20.4B$21.4B$22.4B$23.4B$24.4B
$25.4B$26.4B$27.4B$28.4B$29.4B$30.4B$31.4B$32.4B$33.4B$34.4B$35.2BAB$
36.2B2A$37.2A2B$38.4B$39.4B$40.4B$41.4B14.A$42.4B11.3A$43.4B5.B3.A$
44.4B3.3B2.2A$45.4B2.7B$46.10B$47.10B$48.10B$49.11B$50.12B$51.13B$51.
13B$51.14B$51.14B$51.14B$51.15B9.2A3.A$52.14B10.A2.A.A$51.15B8.A4.A.A
$51.17B6.5A.A$51.18B9.A$51.18B5.2AB2.A$51.19B3.B2A3B.A$52.18B4.4B.2A$
52.25B$53.14BA9B$53.15B2A7B10.2A$54.13B2A9B2.2B5.A$55.5B3.20B.BA.A$
56.4B5.18B.B2A$57.2B6.15BA4B$65.14BABA4B$66.14BA4B$67.16B.B2A$70.13B.
BA.A$70.8B2.2B5.A$71.B2A3B10.2A$71.B2A3B$72.B.B!

[dvgrn]

No idea where to put these, but uh, anybody want some period multiplying eaters? Now available in periods 5, 6, 12, and 13 (!):

Oh wow! This allows any even-period glider stream to form a crystallisation and decay oscillator...

Any even-period glider stream above p78, anyway. The traffic light doesn't quite have time to form at p78:

Code: Select all

x = 105, y = 94, rule = B3/S23
18b2o$18b2o3$22bo15bo$20bobo15b3o$20bob2o17bo$14bo8bo2b2o12bobo$8b3o2b
ob2o6b6o11bobo$6b2ob2obo2b2ob4ob2o4bo11bo$3b4o2bob2o2bo2b4o2b2ob2o$3b
6o2bo2bo2bo7b3o15b3o$12bobo$43bobo$43bobo2b3o5b2o$56b2o$43b3obo3b2o$
47bo4bo$3b2o42b2o2b2o$2bo2bo2b2o26b2o9bo$3b2o2bobo25bobo9b3o$5b2o16b2o
10bo12b2o$5bo17bo10b2o$2b2obo2bo15b3o$2bob2obobo16bo$6bobo42b2obo$3b2o
2bo43b2ob3o$b3ob2o50bo$o50b2ob3o$b3ob2o6b3o34bo2b2o$3bob2o6bo2bo32bobo
$11bo19bo16bobob2obo$17bo13b3o15bo2bob2o$11bo4bo5b2o10bo5b3o9bo$11bo
10bo10b2o6b2o8b2o$11b4o5bobo16bobo6bobo2b2o$11bo8b2o17bo8b2o2bo2bo$37b
2o14b2o$38bobo$17b2o20b2o$2o15bobo34b2o$2o15bo36bo$52bobo$52b2o3$16bo
8bobo$15bobo8b2o6bo$15bobo8b2o5bo$16bo$17b3o11bo$19bo10bo2bo$30bobo$
31bo25bo$38b2o18bo$38b2o16b3o$75bo$73b3o$72bo$72b2o12$91b2o3bo$92bo2bo
bo$77bo12bo4bobo$75bobo12b5obo$76b2o5bo10bo$82bobo5b2o3bo$82bobo5b2o4b
o$83bo11b2o2$78b2o7b2o$77bo2bo5bo2bo13b2o$78b2o7b2o14bo$101bobo$83bo
17b2o$82bobo11bo$82bobo10bobo$83bo12bo$101b2o$101bobo$88b2o13bo$87bo2b
o12b2o$88b2o!
#C [[ STOP 66 ]]

P80 works, though there's another stage where one of the gliders gets harmlessly absorbed by a spark. P82 or above seems to be safe, with all gliders participating in crystal formation. Here's p80 on the left, and a couple of p82 crystal lengths on the right:

Code: Select all

x = 426, y = 147, rule = B3/S23
163b2o132b2o$163b2o132b2o4$156b2o132b2o$156b2o132b2o6$10b2o5bo11bo5b2o
$10bo5bobo9bobo5bo$11b3obo2bo9bo2bob3o$13bob2ob2o7b2ob2obo$16bobo9bobo
$13b2o3bo9bo3b2o116bo23bobo107bo23bobo$12b2o2bob2o7b2obo2b2o115b3o22b
2o107b3o22b2o$14bo3bo2bo3bo2bo3bo120bo5bo7b2o6bo111bo5bo7b2o6bo$14b2ob
o2b2o3b2o2bob2o119b2o4bo7bob2o17bo98b2o4bo7bob2o17bo$14b2o15b2o124bobo
6bo2bo17b3o101bobo6bo2bo17b3o$14b2o15b2o134b3o20bo110b3o20bo$8b2o2bo2b
o4b2o3b2o4bo2bo2b2o116b2o3bobo4b2o20bobo97b2o3bobo4b2o20bobo$8bo2bobob
obobo2bobo2bobobobobo2bo117b2ob4o26bobo98b2ob4o26bobo$10b2obobo6bobo6b
obob2o120b3o2bo27bo100b3o2bo27bo$12bobobo2b2obobob2o2bobobo124b2o132b
2o$12bobo7bobo7bobo125bo133bo$11b2obob3ob2obob2ob3obob2o$12bob2obo3bob
obo3bob2obo$12bobobo3bobobobo3bobobo157b3o10b2o119b3o10b2o$11b2obob2ob
3o3b3ob2obob2o113b2o40bo3bo9b2o76b2o40bo3bo9b2o$14bo2bobobobobobobo2bo
115bo2bo2b2o34bo5bo85bo2bo2b2o34bo5bo$14b2o2b3o5b3o2b2o116b2o2bobo13b
2o19bo5bo86b2o2bobo13b2o19bo5bo$19b9o123b2o16bobo18b3ob3o88b2o16bobo
18b3ob3o$8b2ob2o138bo19bo13b2o98bo19bo13b2o$9bobobo19b2o113b2obo2bo16b
2o11bobo95b2obo2bo16b2o11bobo$9bobobo18bobo113bob2obobo28bo97bob2obobo
28bo$7b2ob2o2b2o6bobo7bo119bobo28b2o101bobo28b2o$6bobobobob2o6b3o5b2ob
4o112b2o2bo129b2o2bo$5bo2bo4bobo6b3o6bobo2bo110b3ob2o128b3ob2o$5bobobo
19bo3bo112bo53b2obo76bo53b2obo$6bob3o3b3obobo5bo2b2ob2o113b3ob2o47b2ob
3o75b3ob2o47b2ob3o$8b3o5bobobo5bo3bobo7bo3b2o103bob2o53bo76bob2o53bo$
20bo17b2obo116bo41b2ob3o86bo41b2ob3o$38b3o118b2o38bo2b2o89b2o38bo2b2o$
22b3o12bo6bo114bo8b2o21bo6bobo92bo8b2o21bo6bobo$bob4o5b2o2b2o2bobo13bo
2bobobobo111bobo8bo11bo9bo6bobob2obo86bobo8bo11bo9bo6bobob2obo$3o3bo5b
3obo3b3o14b3obob2o121bobo11b3o6b3obo4bo2bob2o95bobo11b3o6b3obo4bo2bob
2o$2b2o2bob4o3b2o2b2obo4bo128b3o7b2o15bo5b2o2b2o6bo88b3o7b2o15bo5b2o2b
2o6bo$3bob2obo4bobo5b3obobo9b3obob2o137b2o5b2o2b2o5b2o114b2o5b2o2b2o5b
2o$bobo3bo2bo3b2o2bobobo3b2o8bo2bobobobo151bobo2b2o127bobo2b2o$b2ob4ob
o2bo6b3o15bo6bo144b2o6b2o2bo2bo118b2o6b2o2bo2bo$4bo2bo2b2o8bo17b3o105b
2o41bo4bo7b2o76b2o41bo4bo7b2o$4bobobobo21bo5b2obo104b2o41bo4bo85b2o41b
o4bo$5b2obobo19bobo7bo3b2o144bobo131bobo$7bobo21b2o133b3o34b2o95b3o34b
2o$7bo10b5o143bo36bo96bo36bo$6b2o9bo5bo143bo33bobo97bo33bobo$10b2o5bo
5bo5b2o131bo38b2o93bo38b2o$9bo2bo15bo2bo129bobo131bobo$10b2o2b2o3b3o3b
2o2b2o130bobo11b2o118bobo11b2o$11bob2ob3o3b3ob2obo132bo11bo121bo11bo$
9bobo5bobobobo5bobo131b3o9bobo5b2o112b3o9bobo5b2o$7b3obo6bo3bo6bob3o8b
o122bo10bo6b2o114bo10bo6b2o$6bo4bobo3b2obob2o3bobo4bo5bobo140bo133bo$
6b2o3bobob2o2bobo2b2obobo3b2o6b2o137b2o132b2o$7bo2b2o2b2o3bobo3b2o2b2o
2bo145bo2bo130bo2bo$7bobo2bo3b2obobob2o3bo2bobo145bobo131bobo$8bobob2o
5bobo5b2obobo14bo132bo25bo107bo25bo$10bob2o3b2o3b2o3b2obo9b2o3bobo139b
2o15bobo114b2o15bobo$10bo19bo9b3o3b2o139b2o16b2o114b2o16b2o$9b3o17b3o
2b2o2bo2bobo21bo158bo133bo$10b3obo2b2o3b2o2bob3o3b2o2b2o2b2o19b3o156b
3o131b3o$10b2obobo2bo3bo2bobob2o7b2o22bo158bo133bo$9bo3bob2o7b2obo3bo
30b2o157b2o132b2o$9bo2b2obo9bob2o2bo$13bobo9bobo$10bob2ob2o7b2ob2obo$
8b3obo2bo9bo2bob3o$7bo5bobo9bobo5bo$7b2o5bo11bo5b2o6$81b2o3bo153b2o3bo
$82bo2bobo153bo2bobo$80bo4bobo151bo4bobo$80b5obo152b5obo$73bo10bo147bo
10bo133bo$72bobo5b2o3bo145bobo5b2o3bo130b3o$72bobo5b2o4bo144bobo5b2o4b
o128bo$73bo11b2o145bo11b2o129bo2$68b2o7b2o148b2o7b2o$67bo2bo5bo2bo13b
2o131bo2bo5bo2bo13b2o$68b2o7b2o14bo133b2o7b2o14bo$91bobo156bobo$73bo
17b2o139bo17b2o$72bobo11bo144bobo11bo$72bobo10bobo143bobo10bobo$73bo
12bo145bo12bo$91b2o157b2o$91bobo156bobo$78b2o13bo143b2o13bo$77bo2bo12b
2o141bo2bo12b2o$78b2o157b2o2$396bo$394b3o$393bo$394bo12$412b2o3bo$413b
o2bobo$411bo4bobo$411b5obo$404bo10bo$403bobo5b2o3bo$403bobo5b2o4bo$
404bo11b2o2$399b2o7b2o$398bo2bo5bo2bo13b2o$399b2o7b2o14bo$422bobo$404b
o17b2o$403bobo11bo$403bobo10bobo$404bo12bo$422b2o$422bobo$409b2o13bo$
408bo2bo12b2o$409b2o!
#C [[ STEP 60 ]]

[MathAndCode]

Oh wow! This allows any even-period glider stream to form a crystallisation and decay oscillator:

Combining it with one of the reactions from the first post of this thread allows a more compact way of producing oscillators with very high periods.

Code: Select all

x = 148, y = 143, rule = B3/S23
8$23b2o$16b2o5b2o$16b2o3$18b2o17b2o8b2o$18b2o17bo9b2o$12b2o21bobo$12b
2o21b2o$53b2o$53b2o$49b2o$49b2o4$54b2o$12bo41b2o$12b3o$15bo$14b2o$20b
3o$22bo$21bo$16bo$15bo2bo$14bo4bo$14bo5bo$13b2ob2o$16b2obo30bo$15b2o2b
o28bobo$7b2o7b3o30b2o$7b2o8bo4$12b2o$12b2o$8b2o$8b2o$26b2o21b2o27bo$
25bobo21b2o25b3o$14b2o9bo17b2o30bo$14b2o8b2o17b2o30b2o3$45b2o$38b2o5b
2o$38b2o6$65b2o$65b2o13$73b2o$74bo$71b3o$71bo9$117b2o3bo$118bo2bobo$
58b2o56bo4bobo$58bobo55b5obo$60bo59bo$60b2o54b2o3bo$116b2o4bo$121b2o3$
94b2o33b2o$94bobo32bo$95b2o30bobo$127b2o$122bo$121bobo$122bo$127b2o$
127bobo$114b2o13bo$113bo2bo12b2o$114b2o15$7bo$6bobo$6bobo$7bo13b2ob2o$
21b2obo2bo$24bob2o$24bo$23b2o$12bo7bobo2b2o$11bobo6b2o2bo2bo$12bo12b2o
4$9b2o3b2o$10bo3bo$7b3o5b3o$7bo9bo!

[Kazyan]

Such long period-multipliers with a fixed minimum population may be useful for self-constructing circuitry. Does this method allow for a glider stream to be thinned by a factor of n for every sufficiently large n? Answering this will depend on whether there is a sufficient number of ways to get a glider out of a growing crystal and put it back into its decay state.

[dvgrn]

Does this method allow for a glider stream to be thinned by a factor of n for every sufficiently large n?

Seems like only a sparse scattering of sufficiently large n are available here. At least, I don't see offhand how to adjust this to make arbitrarily large prime period multipliers (for example).

[MathAndCode]

Seems like only a sparse scattering of sufficiently large n are available here. At least, I don't see offhand how to adjust this to make arbitrarily large prime period multipliers (for example).

I'm not sure whether or not this counts as a sparse scattering, but it seems to me that it would work for any integer of the form 11n+c, where c depends on the crystal seed, or any integer that can be expressed as a product of two or more numbers of the form 11n+c. That's one eleventh of arbitrarily high integers in the worst-case scenario, which is where c is a multiple of eleven or one more than a multiple of eleven. Also, I think that at least two of Sphenocorona's period-multiplying eaters work, and I don't think that their values of c would be the same or equivalent modulo eleven, so this should allow period multipliers for at least two-elevenths of arbitrarily large positive integers.

[Sphenocorona]

Oh wow! This allows any even-period glider stream to form a crystallisation and decay oscillator...

I must admit, I was so focused on trying to get something P1 out of this that I totally missed that! Those pesky blinkers made me stop paying attention

Anyway, on the subject of actually making use of this thing, it turns out we *can* get any sufficiently large pulse divisions with this technology, as Kazyan predicted. I started out trying to find ways to cap the crystal in order to get different offsets mod 13 (the number of gliders it normally takes to make and then remove one crystal segment), looking for examples with repeat times no more than 120. From that preliminary investigation I got the following results (by the way I'm going to refer to them as period multipliers because it's easier, even if it undersells them):

Code: Select all

#C Examples of multiple families of p2n glider stream pulse dividers / period multipliers
#C based on applying different glider-liberating "caps" to a high-period p2 glider crystal.
#C The smallest two members in each mod 13 family are shown; other members can be
#C obtained by allowing the crystals to grow more before being capped.
#C A spartan version of the 4 mod 13 family cap with a worse minimum multiplier is also shown.
#C The output glider streams on the 7 mod 13 family can be separated from the input
#C with a Snark, although only just barely in the non-stream-crossing, period agnostic orientation.
x = 312, y = 273, rule = LifeHistory
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$166.A86.3A$166.3A87.A$169.A85.2A$168.2A85.4B$76.A91.4B85.3B$8.A67.3A
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7B7.7B$2A5B2A7BA6B2A15.D2.D25.B.12BA7BAB20.D5.D44.7B7.7B18.D2.D2.D40.
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5.D44.21B2AB65.22B.B$4.8B6.10B12.D5.D27.7B7.7B18.D5.D46.22B.B63.16B2A
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71.4B.3B.B2.4B2.C9.C$6.21B2AB46.22B.B74.4B.3B.B2.4B72.4B13.3C5.3C$8.
22B.B44.16B2A5B2A74.4B84.4B15.C3.C$8.16B2A5B2A43.16B2A5B2A75.4B84.4B
13.2C.B.2C$8.16B2A5B2A44.18B.4B77.4B6.2A76.4B12.7B$9.18B.4B52.4B.3B.B
2.4B4.A24.A48.4B4.B2AB55.2A19.4B13.3B$16.4B.3B.B2.4B53.4B14.A.A21.3A
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9B$19.4B.3B61.4B7.A3.2A2.BA2B2A11.4B54.ABA8B2.2A52.3B18.A3B6.10B$11.
2A7.8B61.4B7.3A2.3AB.B2A10.3B57.2A8B.3B52.4B18.4B4.11B5.B$11.A.A7.7B
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3B2C4B.16B$15.28B41.2C5.29B54.B2A2B6.18B56.4B.9B4.16B$14.4B2.23B42.C
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10B7.15B$12.4B5.23B2.2B5.A32.2CB.28B57.B2AB7.9B.13B53.9B8.B.13B$11.4B
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11B5.B$6.4B23.16B37.C6.27B47.2A.2AB4.12B.2B.B6.A42.2B2E10.C7.4B.16B.B
2C$6.2A28.10B2D2B36.C.CB4.26B46.A2.A2.AB2.19B2.BA.A43.B2EB9.3C6.22B2C
$7.A28.10B2D3B36.2CB.28B46.A.A.A.ABA21B2.B2A45.4B11.C6.22B$4.3A30.14B
38.2B2C26B47.A.A.A.A26B47.4B9.2C5.20B$4.A34.12B38.BC.C2B.21B51.A.A.
26B49.4B8.27B$41.12B37.2C5.2B.13B.2B51.A.BAB.2B2.21B50.4B9.25B$41.12B
CB45.13B54.B2A2B6.18B53.4B7.2B2C21B$41.11BCBCB45.11B56.2B7.21B52.4B5.
2BC2BC18B$39.B.11BCBC49.14B51.2B7.22B51.4B4.3B2C4B.16B$35.2A.2A13BC2B
47.16B49.B2AB7.9B.13B50.4B.9B4.17B$33.A2.A.2A15B48.16B50.2A8.7B3.13B
51.12B6.16B$33.2A.A.17B49.16B58.9B2.14B51.10B7.17B$36.A2.2B3.9B50.17B
57.10B2.14B52.9B8.B.14B$36.2A.B5.7B52.18B56.8B3.10B2D2B53.9B9.10B2D2B
$34.2A2.A.A4.3BC3B54.18B53.8B4.10B2D3B9.2A3.A38.7B10.10B2D3B9.2A3.A$
33.A2.A2.2A3.3BCBC3B53.3B.15B51.9B5.14B10.A2.A.A38.6B11.14B10.A2.A.A$
34.2A8.4BC4B51.5B.14B51.8B6.15B8.A4.A.A40.2B12.15B8.A4.A.A$45.7B52.2C
B6.10B51.4B2.B8.17B6.5A.A55.17B6.5A.A$47.3B55.C9.B2D5B50.4B12.18B9.A
57.18B9.A$45.7B50.3C10.B2D6B48.4B13.18B5.2AB2.A56.18B5.2AB2.A$45.2A.B
.2A50.C13.9B46.4B14.19B3.B2A3B.A55.19B3.B2A3B.A$46.A3.A65.4B2.4B44.B
2EB16.18B4.4B.2A56.18B4.4B.2A$43.3A5.3A63.B5.4B5.B36.2B2E17.25B60.25B
$43.A9.A70.4B2.2D2B34.4B19.24B61.24B$124.5B.2D2B34.3B20.24B10.2A49.
24B10.2A$125.10B31.4B22.24B2.2B5.A51.24B2.2B5.A$126.9B31.2A25.5B3.20B
.BA.A52.5B3.20B.BA.A$127.10B30.A26.4B5.B2D15B.B2A54.4B5.B2D15B.B2A$
126.11BCB25.3A28.2B6.B2D12BC4B57.2B6.B2D12BC4B$125.11BCBCB24.A38.14BC
BC4B64.14BCBC4B$123.B.11BCBC65.14BC4B66.14BC4B$119.2A.2A13BC2B65.16B.
B2A65.16B.B2A$117.A2.A.2A15B69.13B.BA.A67.13B.BA.A$117.2A.A.17B69.2B
2C4B2.2B5.A67.2B2C4B2.2B5.A$120.A2.2B3.9B72.C2BC2B10.2A67.C2BC2B10.2A
$120.2A.B5.7B73.B2C3B79.B2C3B$118.2A2.A.A4.3BC3B74.B.B82.B.B$117.A2.A
2.2A3.3BCBC3B$118.2A8.4BC4B$129.7B$131.3B$129.7B$129.2A.B.2A17.B$130.
A3.A$127.3A5.3A$127.A9.A4$84.A$84.3A$87.A$86.2A$86.4B$88.3B$88.4B$77.
4B2.B.3B.4B$77.4B.12B2A2B2A$76.2A5B2A9B2A2B2AB15.4D2.4D6.D$76.2A5B2A
7BA6B2A18.D2.D2.D4.D.D.D$77.B.12BA7BAB18.D2.D2.D5.3D$79.B2A10B2AB2AB
2A3B13.4D2.D2.D3.3D.3D$80.2A7B2.3BA3B2A4B15.D2.D2.D5.3D$80.8B6.10B15.
D2.D2.D4.D.D.D$82.7B7.7B13.4D2.4D6.D$81.10B6.8B$81.13B2.7B2A$82.21B2A
B9.12D$84.22B.B$84.16B2A5B2A$84.16B2A5B2A$85.18B.4B$92.4B.3B.B2.4B21.
A$93.4B30.3A$94.4B28.A$95.5B26.2A$96.5B23.4B$95.10B18.3B$94.11B17.4B$
95.7BA3B15.2E2B$94.6BABA4B13.B2EB$94.7B2A4B12.4B$93.24B.4B$93.28B$93.
28B$91.2CB.27B$90.C.CB2.27B$90.C5.28B$89.2C6.28B$98.27B$98.26B$99.3B.
19B$97.5B2.5B2D11B$97.2C6.4B2D11B$98.C6.18B$95.3C9.16B$95.C12.18B$
109.B3.10B2D2B$113.10B2D3B$114.14B$116.12B$118.12B$118.12BCB$118.11BC
BCB$116.B.11BCBC$112.2A.2A13BC2B$110.A2.A.2A15B$110.2A.A.17B$113.A2.
2B3.9B$113.2A.B5.7B$111.2A2.A.A4.3BC3B$110.A2.A2.2A3.3BCBC3B$111.2A8.
4BC4B$122.7B$124.3B$122.7B$122.2A.B.2A$123.A3.A$120.3A5.3A$120.A9.A!

However, it turns out that we can use catalysts to produce a faster crystallization cycle of length 8+2 (contrasting with the natural 11+2):

Code: Select all

x = 142, y = 148, rule = LifeHistory
8.A$8.3A$11.A$10.2A$10.4B$12.3B$12.4B$.4B2.B.3B.4B$.4B.12B2AB2AB$2A5B
2A9BA4B2A$2A5B2A7B2A7B$.B.13B2ABA4BA$3.B2A10B2ABA2B2A3B$4.2A7B2.4BA2B
A5B$4.8B6.10B$6.7B7.7B$5.10B6.8B$5.13B2.7B2A$6.21B2AB$8.22B.B$8.16B2A
5B2A$8.16B2A5B2A$9.18B.4B$16.4B.3B.B2.4B$17.4B$18.4B$19.4B$20.4B$21.
4B$22.4B$23.BABA$24.B2AB$25.A3B$26.4B$27.4B$28.4B$29.4B$30.4B$31.4B$
32.4B$33.4B$34.4B$35.4B$36.4B$37.4B$38.4B$39.4B$40.4B$41.4B$42.4B$43.
4B$44.4B$45.4B$46.4B$47.4B$48.4B$49.4B$50.4B$51.4B$52.4B$53.BABA$54.B
2AB$55.A3B12.2C$56.4B10.B2CB$57.4B10.2B$58.4B8.2B$59.4B5.8B$60.4B3.
10B$61.4B2.11B$62.4B.11B$63.16B3.B$64.15B2.3B$64.14B.3B2C$63.2D13B.3B
C.CB$63.2D17B.2C2B$64.17B.4B$64.21B$65.20B$65.18B$67.15B$68.16B$71.2B
.12B$69.4B2.12B$69.2C4.12B$70.C4.12B$67.3C5.12B$67.C7.10B2D$75.10B2D
2B$81.10B$82.9B$79.13B5.2C$78.15B4.C$78.15B.BC.C$75.B.16B.B2C$74.2C
19B$74.2CB.17B$75.B2.15B$78.16B12.2C$78.22B5.B2CB$79.21B6.2B$80.20B5.
2B$82.2B2.14B3.8B$84.16B2.10B$84.16B2.11B$83.4B.13B.11B$82.2B2C.4B.
22B3.B$83.BC.C3B2.22B2.3B$85.2C3B3.20B.3B2C$85.3B5.5B2D13B.3BC.CB$86.
B7.4B2D17B.2C2B$99.17B.4B$99.21B$100.20B$100.18B$102.15B$103.16B$106.
2B.12B$104.4B2.12B$104.2C4.12B$105.C4.12B$102.3C5.12B$102.C7.10B2D$
110.10B2D2B$116.10B$117.9B$114.13B5.2C$113.15B4.C$113.15B.BC.C$110.B.
16B.B2C$109.2C19B$109.2CB.17B$110.B2.15B$113.16B$113.22B$114.22B$115.
21B$117.2B2.16B$119.18B$119.20B$118.4B.18B$117.2B2C.4B.15B$118.BC.C3B
2.14B$120.2C3B3.12B$120.3B5.5B2C4B$121.B7.4B2C3B$129.9B$131.6B$134.B!

Since 10 is (relatively) prime to 13, we can get to any other value mod 13 by adding at most 12 repetitions of the faster cycle. As adding multiples of 13 to the period multiplier just involves letting the crystal grow undisturbed for longer periods of time, this means we can get any output multiplier that is sufficiently large. Here's some example period multipliers to demonstrate, with multipliers in the range 267 to 271 (of which 269 and 271 are prime):

Code: Select all

#C Demonstration of universal p2n glider stream period multiplication for periods 267-271
#C The multipliers are achieved as following:
#C 267: 7 mod 13 cap, 19 normal crystal cycles
#C 268: 4 mod 13 cap, 3 fast crystal cycles, 17 normal crystal cycles
#C 269: 2 mod 13 cap, 2 fast crystal cycles, 18 normal crystal cycles
#C 270: 2 mod 13 cap, 6 fast crystal cycles, 15 normal crystal cycles
#C 271: 4 mod 13 cap, 2 fast crystal cycles, 18 normal crystal cycles
x = 1568, y = 308, rule = LifeHistory
8.A281.A329.A325.A353.A$8.3A279.3A327.3A323.3A351.3A$11.A281.A329.A
325.A353.A$10.2A280.2A328.2A324.2A352.2A$10.4B278.4B326.4B322.4B350.
4B$12.3B279.3B327.3B323.3B351.3B$12.4B278.4B326.4B322.4B350.4B$.4B2.B
.3B.4B266.4B2.B.3B.4B314.4B2.B.3B.4B310.4B2.B.3B.4B338.4B2.B.3B.4B$.
4B.4B2A12B259.4B.4B2A12B307.4B.4B2A12B303.4B.4B2A12B331.4B.4B2A12B$2A
2B2A4BABA12B12.4D2.4D2.4D229.2A2B2A4BABA12B12.4D2.4D2.4D277.2A2B2A4BA
BA12B12.4D2.4D2.4D273.2A2B2A4BABA12B12.4D2.4D3.4D300.2A2B2A4BABA12B
12.4D2.4D3.D$2A2BA7BA12B15.D2.D8.D229.2A2BA7BA12B15.D2.D5.D2.D277.2A
2BA7BA12B15.D2.D5.D2.D273.2A2BA7BA12B15.D5.D3.D2.D300.2A2BA7BA12B15.D
5.D3.D$.B.BABA3B3A12B15.D2.D8.D230.B.BABA3B3A12B15.D2.D5.D2.D278.B.BA
BA3B3A12B15.D2.D5.D2.D274.B.BABA3B3A12B15.D5.D3.D2.D301.B.BABA3B3A12B
15.D5.D3.D$3.2B2A20B10.4D2.4D5.D232.2B2A20B10.4D2.4D2.4D280.2B2A20B
10.4D2.4D2.4D276.2B2A20B10.4D5.D3.D2.D303.2B2A20B10.4D5.D3.D$4.9B2.
13B9.D5.D2.D5.D233.9B2.13B9.D5.D2.D2.D2.D281.9B2.13B9.D5.D2.D5.D277.
9B2.13B9.D8.D3.D2.D304.9B2.13B9.D8.D3.D$4.8B6.10B9.D5.D2.D5.D233.8B6.
10B9.D5.D2.D2.D2.D281.8B6.10B9.D5.D2.D5.D277.8B6.10B9.D8.D3.D2.D304.
8B6.10B9.D8.D3.D$6.7B7.7B10.4D2.4D5.D235.7B7.7B10.4D2.4D2.4D283.7B7.
7B10.4D2.4D2.4D279.7B7.7B10.4D5.D3.4D306.7B7.7B10.4D5.D3.D$5.10B6.8B
258.10B6.8B306.10B6.8B302.10B6.8B330.10B6.8B$5.13B2.7B2A258.13B2.7B2A
306.13B2.7B2A302.13B2.7B2A330.13B2.7B2A$6.21B2AB258.21B2AB306.21B2AB
302.21B2AB330.21B2AB$8.22B.B258.22B.B306.22B.B302.22B.B330.22B.B$8.
16B2A5B2A257.16B2A5B2A305.16B2A5B2A301.16B2A5B2A329.16B2A5B2A$8.16B2A
5B2A257.16B2A5B2A305.16B2A5B2A301.16B2A5B2A329.16B2A5B2A$9.9BA8B.4B
259.9BA8B.4B307.9BA8B.4B303.9BA8B.4B331.9BA8B.4B$16.3BA.3B.B2.4B2.C9.
C253.3BA.3B.B2.4B4.A309.3BA.3B.B2.4B310.3BA.3B.B2.4B338.3BA.3B.B2.4B
4.A$17.3AB13.3C5.3C254.3AB14.A.A309.3AB322.3AB350.3AB14.A.A$18.4B15.C
3.C258.4B12.A.A2.AB307.4B322.4B350.4B12.A.A2.AB$19.4B13.2C.B.2C258.4B
9.3A2.2A.AB.B305.4B.3B318.4B.3B346.4B9.3A2.2A.AB.B$20.4B12.7B259.4B7.
A3.2A2.BA2B2A296.2A7.8B309.2A7.8B346.4B7.A3.2A2.BA2B2A$21.4B13.3B262.
4B7.3A2.3AB.B2A296.A.A7.7B309.A.A7.7B347.4B7.3A2.3AB.B2A$22.4B11.5B
262.4B8.A.A2.2B2.B299.A8.7B310.A8.7B347.4B8.A.A2.2B2.B$23.4B9.8B261.
4B7.BABAB304.2A5.9B310.2A5.9B348.4B7.BABAB$24.4B8.9B261.4B7.BA3B305.A
B.12B10.2C299.AB.12B10.2C336.4B7.BA3B$25.4B6.10B262.4B7.4B11.4B288.3A
18B5.B2CB296.3A18B5.B2CB336.4B7.4B11.B$26.4B4.11B5.B257.4B6.3B11.4B
288.A2.B.18B5.2B296.A2.B.18B5.2B338.4B6.3B11.4B$19.C7.4B.16B.B2C257.
4B2.B.4B10.4B289.2A3.18B4.2B297.2A3.18B4.2B340.4B2.B.4B10.4B$9.B9.3C
6.22B2C258.12B.B4.B.4B295.19B.8B298.19B.8B337.12B.B4.B.4B$9.2B11.C6.
22B257.17B2.6B295.30B296.30B334.17B2.6B$9.3B9.2C5.20B258.27B294.32B
294.32B331.27B$9.4B8.27B250.2C5.29B292.4B2.27B293.4B2.27B323.2C5.29B$
10.4B9.25B251.C6.27B292.4B4.27B3.B287.4B4.27B3.B319.C6.27B$11.4B7.2B
2C21B252.C.CB4.26B291.4B5.27B2.3B285.4B5.27B2.3B318.C.CB4.26B$12.4B5.
2BC2BC18B255.2CB.28B291.4B6.4B4.18B.3B2C284.4B6.4B4.18B.3B2C319.2CB.
28B$13.4B4.3B2C4B.16B255.2B2C26B290.4B8.3B6.B2D13B.3BC.CB281.4B8.3B6.
B2D13B.3BC.CB319.2B2C26B$14.4B.9B4.16B254.BC.C2B.21B280.A10.4B10.B7.B
2D17B.2C2B279.4B10.B7.B2D17B.2C2B318.BC.C2B.21B$15.12B6.15B255.2C5.2B
.13B.2B281.3A7.4B19.19B.4B268.A10.4B19.19B.4B320.2C5.2B.13B.2B$16.10B
7.17B263.13B287.A5.4B21.22B269.3A7.4B21.22B331.13B$17.9B8.B.14B264.
11B12.2C273.2A4.4B23.21B264.B7.A5.4B23.21B332.11B12.2C$18.9B9.10B2D2B
267.14B5.B2CB267.B4.9B25.18B266.2B5.2A4.4B25.18B337.14B5.B2CB$19.7B
10.10B2D3B265.16B5.2B268.2B5.6B28.15B267.3B4.9B28.15B337.16B5.2B$20.
6B11.14B265.16B4.2B269.3B2.3BD4B29.16B265.4B5.6B30.16B335.16B4.2B$22.
2B12.15B266.16B.8B265.7BD7B30.2B.12B264.4B2.3BD4B33.2B.12B334.16B.8B$
36.17B.5B257.27B265.6B3D5B28.4B2.12B264.7BD7B29.4B2.12B332.27B$36.12B
A12B256.13BA13B265.13B28.2C4.4BA7B265.6B3D5B29.2C4.4BA7B333.13BA13B$
36.13BA13B256.12BA12B266.10B.B2A27.C4.5BA6B266.13B30.C4.5BA6B335.12BA
12B$36.11B3A14B255.3B.6B3A13B3.B263.3B2AB3.BA.A23.3C5.3B3A6B267.10B.B
2A25.3C5.3B3A6B335.3B.6B3A13B3.B$37.28B252.5B.22B2.3B262.3B2AB6.A23.C
7.10B2D2B267.3B2AB3.BA.A24.C7.10B2D2B331.5B.22B2.3B$37.29B251.2CB6.
18B.3B2C264.4B6.2A30.10B2D3B266.3B2AB6.A32.10B2D3B330.2CB6.18B.3B2C$
38.29B251.C9.B2D13B.3BC.CB262.3B40.15B267.4B6.2A32.15B330.C9.B2D13B.
3BC.CB$38.29B248.3C10.B2D17B.2C2B258.AB.2B43.16B264.3B43.16B324.3C10.
B2D17B.2C2B$39.27B249.C12.19B.4B258.A.AB2AB43.17B.2C256.AB.2B45.17B.
2C319.C12.19B.4B$40.5B.18B265.22B259.A.ABABAB41.18B.C256.A.AB2AB43.
18B.C334.22B$41.4B.5B2D13B264.21B256.2A.A.A.A.A2.A39.17BCBC256.A.ABAB
AB42.17BCBC335.21B$42.2B3.4B2D15B263.18B258.A2.A2.2A.4A36.B.18B2C254.
2A.A.A.A.A2.A37.B.18B2C337.18B$47.21B265.15B261.2A4.A39.2C21B254.A2.A
2.2A.4A36.2C21B339.15B$49.20B265.16B265.A.A37.2CB.20B255.2A4.A40.2CB.
20B339.16B$52.17B268.2B.12B264.2A38.B2.20B261.A.A39.B2.20B342.2B.12B$
55.10B2D2B266.4B2.12B306.20B262.2A42.20B8.2C330.4B2.12B$55.10B2D3B
265.2C4.12B306.22B.5B298.22B5.B2CB329.2C4.12B$56.14B266.C4.12B307.29B
297.22B5.2B331.C4.12B$55.15B263.3C5.12B308.30B296.21B4.2B329.3C5.12B$
55.17B.5B255.C7.10B2D2B308.29B297.20B.8B325.C7.10B2D2B$55.25B261.10B
2D3B309.28B298.28B332.10B2D3B$55.27B260.15B308.29B297.29B332.15B$55.
28B261.13B307.31B295.30B334.13B$56.28B261.13B5.2C298.2B2C28B294.2B2C
28B3.B330.13B5.2C$56.29B259.15B4.C300.BC.C26B296.BC.C27B2.3B328.15B4.
C$57.29B258.15B.BC.C302.2C5B.18B300.2C5B.20B.3B2C328.15B.BC.C$57.29B
255.B.16B.B2C303.7B.5B2D13B298.7B.5B2D13B.3BC.CB323.B.16B.B2C$58.27B
255.2C19B306.B2.2B3.4B2D15B297.B2.2B3.4B2D17B.2C2B321.2C19B$59.5B.18B
257.2CB.17B314.21B305.22B.4B322.2CB.17B$60.4B.5B2D13B256.B2.15B318.
20B306.24B324.B2.15B$61.2B3.4B2D15B257.16B12.2C306.17B309.21B327.16B$
66.12BA8B257.16BA5B5.B2CB308.7BA2B2D2B310.9BA8B329.16BA5B.5B$68.11BA
8B257.16BA5B5.2B309.8BAB2D3B311.8BA6B331.16BA12B$71.6B3A8B258.13B3A5B
4.2B311.5B3A6B312.5B3A8B330.13B3A14B$74.10B2D2B260.2B2.16B.8B306.15B
315.2B.12B330.2B2.25B$74.10B2D3B261.28B305.17B.5B305.4B2.12B331.28B$
75.14B261.29B304.25B303.2C4.12B331.29B$74.15B260.4B.25B304.27B302.C4.
12B330.4B.26B$74.17B.5B251.2B2C.4B.22B3.B299.28B298.3C5.12B329.2B2C.
4B.22B$74.25B250.BC.C3B2.22B2.3B299.28B297.C7.10B2D2B328.BC.C3B2.21B$
74.27B250.2C3B3.20B.3B2C299.29B304.10B2D3B329.2C3B3.18B$74.28B249.3B
5.5B2D13B.3BC.CB298.29B304.15B328.3B5.5B2D13B$75.28B249.B7.4B2D17B.2C
2B297.29B306.16B326.B7.4B2D15B$75.29B260.18B.4B299.27B308.17B.2C329.
21B$76.29B259.22B301.5B.18B309.18B.C332.20B$76.29B260.21B302.4B.5B2D
13B307.17BCBC335.17B$77.27B262.18B305.2B3.4B2D15B302.B.18B2C339.10B2D
2B$78.5B.18B266.15B311.21B301.2C21B339.10B2D3B$79.4B.5B2D13B265.16B
311.20B300.2CB.20B339.14B$80.2B3.4B2D15B266.2B.12B312.17B301.B2.20B
338.15B$85.21B264.4B2.13B313.10B2D2B304.20B8.2C328.17B.5B$87.20B263.
2C4.13B313.10B2D3B303.22B5.B2CB327.25B$90.17B264.C4.14B313.14B304.22B
5.2B328.27B$93.10B2D2B261.3C5.14B312.15B305.21B4.2B329.28B$93.10B2D3B
260.C7.10B2D2B312.17B.5B299.20B.8B326.28B$94.14B268.10B2D3B311.25B
299.28B325.29B$93.15B269.14B311.27B297.29B325.29B$93.17B.5B260.15B
311.28B295.30B325.29B$93.25B258.17B.5B304.28B293.2B2C28B3.B321.27B$
93.27B256.25B302.29B293.BC.C27B2.3B321.5B.18B$93.28B255.27B301.29B
294.2C5B.20B.3B2C322.4B.5B2D13B$94.14BA13B254.14BA13B300.16BA12B294.
7B.5B2D4BA8B.3BC.CB321.2B3.4B2D5BA9B$94.15BA13B254.14BA13B300.16BA10B
296.B2.2B3.4B2D5BA11B.2C2B325.12BA8B$95.12B3A14B253.12B3A14B300.5B.7B
3A8B306.9B3A10B.4B328.8B3A9B$95.29B254.29B300.4B.5B2D13B306.24B332.
17B$96.27B255.29B301.2B3.4B2D15B307.21B335.10B2D2B$97.5B.18B258.27B
307.21B308.18B337.10B2D3B$98.4B.5B2D13B257.5B.18B311.20B309.15B339.
14B$99.2B3.4B2D15B256.4B.5B2D13B312.17B310.16B336.15B$104.21B257.2B3.
4B2D15B313.10B2D2B313.2B.12B334.17B.5B$106.20B261.21B313.10B2D3B310.
4B2.12B333.25B$109.17B263.20B313.14B310.2C4.12B333.27B$112.10B2D2B
266.17B312.15B311.C4.12B333.28B$112.10B2D3B268.10B2D2B312.17B.5B300.
3C5.12B334.28B$113.14B268.10B2D3B311.25B298.C7.10B2D2B332.29B$112.15B
269.14B311.27B304.10B2D3B332.29B$112.17B.5B260.15B311.28B304.15B331.
29B$112.25B258.17B.5B304.28B305.16B329.27B$112.27B256.25B302.29B305.
17B.2C325.5B.18B$112.28B255.27B301.29B303.18B.C327.4B.5B2D13B$113.28B
254.28B300.29B303.17BCBC328.2B3.4B2D15B$113.29B254.28B300.27B301.B.
18B2C334.21B$114.29B253.29B300.5B.18B302.2C21B336.20B$114.29B254.29B
300.4B.5B2D13B300.2CB.20B338.17B$115.27B255.29B301.2B3.4B2D15B299.B2.
20B341.10B2D2B$116.5B.18B258.27B307.21B302.20B341.10B2D3B$117.4B.5B2D
13B257.5B.18B311.20B301.22B.5B334.14B$118.2B3.4B2D15B256.4B.5B2D13B
312.17B302.29B331.15B$123.21B257.2B3.4B2D15B313.10B2D2B303.30B329.17B
.5B$125.20B261.21B313.10B2D3B304.29B328.25B$128.17B263.20B313.14B306.
28B327.27B$131.7BA2B2D2B266.9BA7B312.10BA4B306.15BA13B326.14BA13B$
131.8BAB2D3B268.7BA2B2D2B312.11BA5B.5B297.17BA13B326.14BA13B$132.5B3A
6B268.5B3A2B2D3B311.9B3A13B294.2B2C12B3A13B326.12B3A14B$131.15B269.
14B311.27B293.BC.C26B328.29B$131.17B.5B260.15B311.28B294.2C5B.18B330.
29B$131.25B258.17B.5B304.28B293.7B.5B2D13B329.27B$131.27B256.25B302.
29B293.B2.2B3.4B2D15B328.5B.18B$131.28B255.27B301.29B300.21B329.4B.5B
2D13B$132.28B254.28B300.29B302.20B329.2B3.4B2D15B$132.29B254.28B300.
27B306.17B334.21B$133.29B253.29B300.5B.18B311.10B2D2B336.20B$133.29B
254.29B300.4B.5B2D13B309.10B2D3B338.17B$134.27B255.29B301.2B3.4B2D15B
308.14B341.10B2D2B$135.5B.18B258.27B307.21B307.15B341.10B2D3B$136.4B.
5B2D13B257.5B.18B311.20B306.17B.5B334.14B$137.2B3.4B2D15B256.4B.5B2D
13B312.17B306.25B331.15B$142.21B257.2B3.4B2D15B313.10B2D2B306.27B329.
17B.5B$144.20B261.21B313.10B2D3B305.28B328.25B$147.17B263.20B313.14B
306.28B327.27B$150.10B2D2B266.17B312.15B306.29B326.28B$150.10B2D3B
268.10B2D2B312.17B.5B299.29B326.28B$151.14B268.10B2D3B311.25B297.29B
326.29B$150.15B269.14B311.27B296.27B328.29B$150.17B.5B260.15B311.28B
296.5B.18B330.29B$150.25B258.17B.5B304.28B296.4B.5B2D13B329.27B$150.
27B256.25B302.29B296.2B3.4B2D15B328.5B.18B$150.28B255.27B301.29B300.
21B329.4B.5B2D13B$151.28B254.28B300.29B302.20B329.2B3.4B2D15B$151.29B
254.28B300.27B306.17B334.21B$152.29B253.29B300.5B.18B311.10B2D2B336.
20B$152.16BA12B254.15BA13B300.4B.5B2D4BA8B309.8BAB2D3B338.9BA7B$153.
16BA10B255.16BA12B301.2B3.4B2D5BA9B308.8BA5B341.7BA2B2D2B$154.5B.7B3A
8B258.13B3A11B307.9B3A9B307.7B3A5B341.5B3A2B2D3B$155.4B.5B2D13B257.5B
.18B311.20B306.17B.5B334.14B$156.2B3.4B2D15B256.4B.5B2D13B312.17B306.
25B331.15B$161.21B257.2B3.4B2D15B313.10B2D2B306.27B329.17B.5B$163.20B
261.21B313.10B2D3B305.28B328.25B$166.17B263.20B313.14B306.28B327.27B$
169.10B2D2B266.17B312.15B306.29B326.28B$169.10B2D3B268.10B2D2B312.17B
.5B299.29B326.28B$170.14B268.10B2D3B311.25B297.29B326.29B$169.15B269.
14B311.27B296.27B328.29B$169.17B.5B260.15B311.28B296.5B.18B330.29B$
169.25B258.17B.5B304.28B296.4B.5B2D13B329.27B$169.27B256.25B302.29B
296.2B3.4B2D15B328.5B.18B$169.28B255.27B301.29B300.21B329.4B.5B2D13B$
170.28B254.28B300.29B302.20B329.2B3.4B2D15B$170.29B254.28B300.27B306.
17B334.21B$171.29B253.29B300.5B.18B311.10B2D2B336.20B$171.29B254.29B
300.4B.5B2D13B309.10B2D3B338.17B$172.27B255.29B301.2B3.4B2D15B308.14B
341.10B2D2B$173.5B.18B258.27B307.21B307.15B341.10B2D3B$174.4B.5B2D13B
257.5B.18B311.20B306.17B.5B334.14B$175.2B3.4B2D15B256.4B.5B2D13B312.
17B306.25B331.15B$180.21B257.2B3.4B2D15B313.10B2D2B306.27B329.17B.5B$
182.20B261.21B313.10B2D3B305.28B328.25B$185.17B263.20B313.14B306.28B
327.27B$188.10B2D2B266.17B312.15B306.29B326.28B$188.10B2D3B268.10B2D
2B312.17B.5B299.29B326.28B$189.14B268.10B2D3B311.25B297.29B326.29B$
188.10BA4B269.8BA5B311.13BA13B296.16BA10B328.15BA13B$188.11BA5B.5B
260.10BA4B311.14BA13B296.5B.10BA7B330.16BA12B$188.9B3A13B258.8B3A6B.
5B304.11B3A14B296.4B.5B2DB3A9B329.13B3A11B$188.27B256.25B302.29B296.
2B3.4B2D15B328.5B.18B$188.28B255.27B301.29B300.21B329.4B.5B2D13B$189.
28B254.28B300.29B302.20B329.2B3.4B2D15B$189.29B254.28B300.27B306.17B
334.21B$190.29B253.29B300.5B.18B311.10B2D2B336.20B$190.29B254.29B300.
4B.5B2D13B309.10B2D3B338.17B$191.27B255.29B301.2B3.4B2D15B308.14B341.
10B2D2B$192.5B.18B258.27B307.21B307.15B341.10B2D3B$193.4B.5B2D13B257.
5B.18B311.20B306.17B.5B334.14B$194.2B3.4B2D15B256.4B.5B2D13B312.17B
306.25B331.15B$199.21B257.2B3.4B2D15B313.10B2D2B306.27B329.17B.5B$
201.20B261.21B313.10B2D3B305.28B328.25B$204.17B263.20B313.14B306.28B
327.27B$207.10B2D2B266.17B312.15B306.29B326.28B$207.10B2D3B9.2A3.A
253.10B2D2B312.17B.5B299.29B326.28B$208.14B10.A2.A.A252.10B2D3B311.
25B297.29B326.29B$207.15B8.A4.A.A253.14B311.27B296.27B328.29B$207.17B
6.5A.A253.15B311.28B296.5B.18B330.29B$207.18B9.A255.17B.5B304.28B296.
4B.5B2D13B329.27B$207.18B5.2AB2.A254.25B302.29B296.2B3.4B2D15B328.5B.
18B$207.19B3.B2A3B.A253.27B301.29B300.21B329.4B.5B2D13B$208.18B4.4B.
2A253.28B300.29B302.20B329.2B3.4B2D15B$208.25B258.28B300.27B306.17B
334.21B$209.24B258.29B300.5B.18B311.10B2D2B336.20B$209.24B10.2A247.
29B300.4B.5B2D13B309.10B2D3B338.17B$210.24B2.2B5.A248.29B301.2B3.4B2D
15B308.14B341.10B2D2B$211.5B3.20B.BA.A249.27B307.21B307.15B341.10B2D
3B$212.4B5.B2D4BA10B.B2A251.5B.10BA7B311.11BA8B306.11BA5B.5B334.8BA5B
$213.2B6.B2D5BA6BC4B254.4B.5B2D4BA8B312.9BA7B306.12BA12B331.10BA4B$
221.6B3A5BCBC4B254.2B3.4B2D2B3A10B313.4B3A3B2D2B306.10B3A14B329.8B3A
6B.5B$222.14BC4B260.21B313.10B2D3B9.2A3.A290.28B328.25B$223.16B.B2A
260.20B313.14B10.A2.A.A290.28B327.27B$226.13B.BA.A262.17B312.15B8.A4.
A.A290.29B326.28B$226.2B2C4B2.2B5.A265.10B2D2B312.17B6.5A.A292.29B
326.28B$227.C2BC2B10.2A264.10B2D3B311.18B9.A294.29B326.29B$227.B2C3B
277.14B311.18B5.2AB2.A294.27B328.29B$228.B.B278.15B311.19B3.B2A3B.A
294.5B.18B330.29B$509.17B.5B304.18B4.4B.2A295.4B.5B2D13B329.27B$509.
25B302.25B300.2B3.4B2D15B328.5B.18B$509.27B301.24B305.21B329.4B.5B2D
13B$509.28B300.24B10.2A295.20B329.2B3.4B2D15B$510.28B300.24B2.2B5.A
299.17B334.21B$510.29B300.5B3.20B.BA.A302.10B2D2B336.20B$511.29B300.
4B5.B2D15B.B2A303.10B2D3B338.17B$511.29B301.2B6.B2D12BC4B306.14B341.
10B2D2B$512.27B310.14BCBC4B304.15B341.10B2D3B9.2A3.A$513.5B.18B313.
14BC4B305.17B.5B334.14B10.A2.A.A$514.4B.5B2D13B312.16B.B2A303.25B331.
15B8.A4.A.A$515.2B3.4B2D15B313.13B.BA.A302.27B329.17B6.5A.A$520.21B
313.2B2C4B2.2B5.A302.28B328.18B9.A$522.20B313.C2BC2B10.2A302.28B327.
18B5.2AB2.A$525.17B313.B2C3B314.29B326.19B3.B2A3B.A$528.10B2D2B314.B.
B317.29B326.18B4.4B.2A$528.10B2D3B9.2A3.A618.29B326.25B$529.14B10.A2.
A.A618.27B328.24B$528.15B8.A4.A.A619.5B.18B330.24B10.2A$528.17B6.5A.A
621.4B.5B2D13B329.24B2.2B5.A$528.12BA5B9.A624.2B3.4B2D5BA9B328.5B3.8B
A11B.BA.A$528.13BA4B5.2AB2.A628.12BA8B329.4B5.B2D4BA10B.B2A$528.11B3A
5B3.B2A3B.A629.8B3A9B329.2B6.B2D2B3A7BC4B$529.18B4.4B.2A632.17B337.
14BCBC4B$529.25B639.10B2D2B338.14BC4B$530.24B639.10B2D3B338.16B.B2A$
530.24B10.2A628.14B341.13B.BA.A$531.24B2.2B5.A628.15B341.2B2C4B2.2B5.
A$532.5B3.20B.BA.A628.17B.5B334.C2BC2B10.2A$533.4B5.B2D15B.B2A629.25B
332.B2C3B$534.2B6.B2D12BC4B631.27B331.B.B$542.14BCBC4B630.28B$543.14B
C4B632.28B$544.16B.B2A630.29B$547.13B.BA.A630.29B$547.2B2C4B2.2B5.A
630.29B$548.C2BC2B10.2A630.27B$548.B2C3B643.5B.18B$549.B.B646.4B.5B2D
11B$1199.2B3.4B2D11B$1204.18B$1206.16B$1209.16B$1212.10B2D2B$1212.10B
2D3B$1213.14B$1215.12B$1217.12B$1217.12BCB$1217.11BCBCB$1215.B.11BCBC
$1211.2A.2A13BC2B$1209.A2.A.2A15B$1209.2A.A.17B$1212.A2.2B3.9B$1212.
2A.B5.7B$1210.2A2.A.A4.3BC3B$1209.A2.A2.2A3.3BCBC3B$1210.2A8.4BC4B$
1221.7B$1223.3B$1221.7B$1221.2A.B.2A$1222.A3.A$1219.3A5.3A$1219.A9.A!

I don't know yet what the lower bounds are for 'sufficiently high multiplier' or 'universal minimum population' right now, but I think this is already a pretty good start towards answering those. I suspect that the 270x example showcases the current toolset's "worst case behavior", needing 6 adjustments with the faster crystallization. If I'm right about this, then I think that puts the upper bound on largest unsupported multiplier to 62 (which is a member of the same (and currently most inefficient) family as 270, 10 mod 13; the next smallest member, 75, should be attainable as 9 + 6 + 10*6)

[also, apologies if any of my terminology is confusing here, discussing this 'correctly' is confusing cause multiple/divide/factor all feel like synonyms and antonyms in this context and also feel like they have multiple meanings in this context - that's why i decided to just stick with "period multiplier" to make things simpler]

[GUYTU6J]

Could we get non-glider signals out of a growing crystal? With a rectifier I can extract two Herschels: (raw and possibly useless pattern)

Code: Select all

x = 98, y = 111, rule = B3/S23
52b2o$52b2o5b2o$59b2o3$28b2o8b2o17b2o$28b2o9bo17b2o$39bobo21b2o$40b2o
21b2o$22b2o$22b2o$26b2o$26b2o4$21b2o$21b2o41bo$62b3o$61bo$61b2o6$14b2o
$14bo$9b2o5bo$9bo5b2o$6b2obo80bob2o$6bo2bob2o2b2o32b3o16b2o20b2obo$8b
2obo3b2o34bo16b2o$11bo38bo37b5o$11b2o75bo4bo2b2o$4b2o11bo73bo2bo2bo$3b
obo10bobo15b3o26b2o26b2obobo$3bo13bo15bo2bo2bo23b2o23bo5bob2o$2obo2bo
26bo4bo28b2o18bobo4bo$bobobo3b2o22bobo2bobo26b2o18bo2bo2b2o$bobobo20b
2o6b2o3b2o8b2o37b2o$2obo7bo14b2o16b2o3bobo$o2b4ob4o9b2o9b2o10b2o5bo9b
2o$b2o3bo14bobo8b2o17b2o8b2o$3b2o18bo$3bo19b2o$5bo12bo11b2o$4b2o13bo
10b2o5b2o$17b3o17b2o$80b2o$80b2o6$28bo$29bo$27b3o36b2o22b2o$65bo2bo21b
o$66b2o23b3o$93bo3$36bo$37bo$35b3o$83b2o$83bo$84b3o$86bo13$80bo$78b3o$
57bo20bo$58bo19bo$56b3o4$74b2o$74bo$72bobo$36bo35b2o$36b3o$38bo29bo$
38bo30bo$67b3o8$61b2o$61bobo$62b2o$75b2o$75b2o!
#C [[ STOP 1810 ]]

Also, I really hope Kazyan's HF catalyst could play a part here...

Code: Select all

x = 139, y = 49, rule = LifeHistory
11$112.A$112.3A$115.A$114.2A$60.A53.4B$61.2A42.A10.2B$60.2A43.3A7.5BD
$108.A6.6BD$70.D36.2A5.7B2D$69.D.D35.13B2D$69.D.D37.2B2.7BD$23.3B3C8B
33.D34.BA2B5.6B$22.3BC3BC8B64.B2.2BA2.B3.7B$21.3BC5BC7B27.2D7.2C25.3B
.3A.3B2.7B$20.4BC5BC6B27.D2.D5.C2.C24.3B.3B.2AB2.6B$21.3BC5BC3B31.2D
7.2C26.B4.B2A2B2.3B$15.2E6.2BC3BC3B25.2E9.2C27.2E9.BA2.3B$16.E8.B3C4B
26.E9.2C28.E12.4B$16.E.EB4.9B26.E.E37.E.EB4.9B$17.2EB.4B.7B27.2E38.EC
B.4B.7B$19.4BE9B33.E35.4BC9B$14.2E3.3BEBE3B.B2.B24.2E6.E.E29.2E3.3BCB
C3B.B2DB$14.E2.B.3BEBE3B29.E7.E.E29.E2.B.3BCBC3B2.2D$15.3E5BE4B30.3E
5.E31.2EC5BC4B$17.EB.B2.5B32.E39.CB.B2.5B$15.2E7.2B32.2E38.2E7.2B$15.
E42.E39.E$13.E.E40.E.E37.E.E$13.2E41.2E38.2E!

EDIT: For future investigations, this 5n crystal grows with a p-odd glider stream and some assistance that spits a Herschel every period, though I don't see how to degrade it:

Code: Select all

x = 168, y = 143, rule = LifeHistory
45.2A$45.A.A$47.A4.2A$43.4A.2A2.A2.A$43.A2.A.A.A.A.2A$46.A.A.A.A$47.
2A.A.A$51.A2$37.2A$38.A7.2A$38.A.A5.2A11.A$39.2A18.3A$62.A$61.A.A$61.
A.A$62.A3$49.2A$49.A$50.3A24.2A$52.A24.2A4$57.2A$56.A.A$56.A$55.2A7.
2A$64.2A2$72.2A.A$72.2A.3A$78.A$72.2A.3A$71.A2.2A$70.A.A$69.A.A.2A.A$
52.2A16.A2.A.2A$11.2A40.A19.A$11.2A40.A.A16.2A$54.2A13.A.A2.2A$69.2A
2.A2.A$74.2A$2A$.A23.2A$.A.A21.A19.2A$2.2A19.A.A18.A.A3.2A$23.2A19.A
6.A$43.2A6.A.A$52.2A3$2.2A61.2A$.A.A53.2A6.A.A$.A38.2A25.A$2A38.2A12.
A.A10.2A$56.A$54.3A$61.A.A$62.2A$11.2A49.A$11.2A34.2A$30.2A16.A$30.A
14.3A6.A$31.3A11.A7.A.A$33.A20.A19$92.2D$92.2D6$155.2A$156.A$156.3A6$
149.2A$148.A.A$148.A$147.2A7$157.2A$157.2A$148.A$146.3A15.A.2A$145.A
18.2A.A$89.2A54.2A$88.A.A$78.A9.A26.2D$76.3A8.2A26.2D$75.A$75.2A$162.
A$161.A.A$162.2A2$67.A$67.3A$69.A15.2A$69.A15.2A3$97.A$96.A.A$97.2A$
88.2A$89.A$88.A$88.2A3$147.2A$147.2A!

EDIT2: this HF catalysis seems to be useless here

Code: Select all

x = 29, y = 15, rule = LifeHistory
7.3A$6.A3.A$5.A5.A5.A$5.A5.A4.A.A$2A3.A5.A3.A2.A$2A4.A3.A5.2A$7.3A15.
2A$25.A.A$27.A$27.2A2$5.2A$6.A$3.3A$3.A!

[Pavgran]

Such long period-multipliers with a fixed minimum population may be useful for self-constructing circuitry.

It is well-suited for timing, for example. It reminds me of the way OTCA metapixels is timed.
Is there a recipe for slow-salvo synthesis of the xs24 used in all the multipliers?

Code: Select all

x = 18, y = 21, rule = LifeHistory
4.2E3.E$5.E2.E.E$3.E4.E.E$3.5E.E$7.E$3.2E3.E$3.2E4.E$8.2E3$16.2A$16.A
$14.A.A$14.2A$9.A$8.A.A$9.A$14.2A$2A12.A.A$2A14.A$16.2A!

[dvgrn]

Is there a recipe for slow-salvo synthesis of the xs24 used in all the multipliers?

We have a multi-stage recipe for that xs24 that's pretty well-suited for making a slow-salvo synthesis, but we definitely don't have an optimized slow salvo yet that can build this in any orientation, let alone in all orientations with reasonable clearance.

The "easy" option of building a Spartan seed for this object, is probably relatively useless for building crystal oscillators with slow salvos. It would be much better to come up with optimized direct slow salvos for each orientation, with much better clearance than a 15-glider seed could possibly manage.

[confocaloid]

Do I understand correctly, that all known fast crystal-based pulse dividers have intermediate traffic lights (or other intermediate p2 states), and hence are not stable?

Here is a fully stable version of the crystal -- it does not have any intermediate p2 targets. By itself, it has repeat time 43 (due to the block -> honeyfarm step). I wonder if some variant of the extensible catalyst is glider-constructible for all sizes.

Code: Select all

x = 138, y = 150, rule = B3/S23
5bo$4bobo$4bobo$3b2ob3o$9bo$3b2ob3obo$3b2obo2bobo$9bobo$8b2ob3o$14bo$
8b2ob3obo$8b2obo2bobo$14bobo$13b2ob3o$19bo$13b2ob3obo$13b2obo2bobo$2o
17bobo$2o16b2ob3o$24bo$18b2ob3obo$18b2obo2bobo$24bobo$23b2ob3o$29bo$
23b2ob3o$23b2obo2$18bo$17b2o$17bobo9$28b2o$28bobo$28bo9$39b2o$38b2o$
40bo9$49b3o$49bo$50bo8$61bo$60b2o$60bobo9$71b2o$71bobo$71bo9$82b2o$81b
2o$83bo9$92b3o$92bo$93bo8$104bo$103b2o$103bobo9$114b2o$114bobo$114bo9$
125b2o$124b2o$126bo9$135b3o$135bo$136bo!

A single fishhook can stop the growth and initiate decay:

Code: Select all

x = 117, y = 129, rule = B3/S23
5bo$4bobo$4bobo$3b2ob3o$9bo$3b2ob3obo$3b2obo2bobo$9bobo$8b2ob3o$14bo$
8b2ob3obo$8b2obo2bobo$14bobo$13b2ob3o$19bo$13b2ob3obo$13b2obo2bobo$b2o
16bobo$o2bo14b2ob3o$b2o21bo$18b2ob3obo$18b2obo2bobo$5b2o17bobo$5b2o16b
2ob3o$29bo$23b2ob3obo$23b2obo2bobo$29bobo$17b2o9b2ob3o$16b2o16bo$18bo
9b2ob3o$28b2obo4$13b2o$14bo$11b3o$11bo2$29b2o$28b2o$30bo9$39b3o$39bo$
40bo8$51bo$50b2o$50bobo9$61b2o$61bobo$61bo9$72b2o$71b2o$73bo9$82b3o$
82bo$83bo8$94bo$93b2o$93bobo9$104b2o$104bobo$104bo9$115b2o$114b2o$116bo!

Although I did not find a simple clean way to get a glider out of the crystal, it is possible to extract a glider at the time when the crystal starts growing, by sacrificing a beehive:

Code: Select all

x = 34, y = 26, rule = B3/S23
19bo$18bobo$18bobo$17b2ob3o$23bo$bo15b2ob3obo$obo14b2obo2bobo$obo20bob
o$bo4b2o14b2ob3o$6b2o20bo$22b2ob3obo$22b2obo2bobo$28bobo$27b2ob3o$33bo
$27b2ob3o$27b2obo7$25b3o$25bo$26bo!

Stable pulse divider with repeat time 43 and coefficient 43

As a proof-of-concept, here is a period 1849 glider gun (capped to an oscillator by the yellow eater 1), made by attaching a period 43 glider gun to a stable pulse divider, with pulse division coefficient 43:

Code: Select all

x = 225, y = 137, rule = LifeHistory
28.2A54.2A7.A$27.A.A50.2A.A.A5.3A$21.2A4.A43.A7.A.A.A6.A$19.A2.A2.2A.
4A38.A.A5.A2.A2.A5.2A$19.2A.A.A.A.A2.A39.A7.2A2.2A$22.A.A.A.A$22.A.A.
2A$23.A70.2A$94.A$36.2A54.A.A$27.2A7.A34.3A12.2A4.2A$9.A17.2A5.A.A49.
2A$9.3A22.2A36.2A12.2A$12.A59.2A$11.2A13.3D37.2A4.2A12.3A$26.D38.A.A$
27.D37.A$3.2A59.2A$3.A$2A.A20.2A$A2.3A4.2A2.D10.A49.2A2.2A7.A$.2A3.A
3.2A2.D.D5.3A50.A2.A2.A5.A.A$3.4A7.2D6.A43.A9.A.A.A7.A$3.A15.2A.A.3A
2.A35.A8.A.A.2A$4.3A12.A.A.A2.4A35.3A6.2A$7.A13.A.A$2.5A14.2A3.4A$2.A
22.A3.A158.2A$4.A20.2A22.A138.A$3.2A44.3A124.A12.A$52.A41.2A80.3A7.4A
$51.2A41.A.A82.A6.A$96.A4.2A75.2A9.3A$92.4A.2A2.A2.A84.A2.A$54.D37.A
2.A.A.A.A.2A86.2A$53.D41.A.A.A.A68.2A2.A$53.3D40.2A.A.A68.A2.A.A$15.
2A83.A70.A.2A$14.A.A44.2A109.A$14.A39.2A5.A.A22.2A85.2A8.2A$13.2A39.
2A7.A23.A7.2A77.A4.2D2.A.A$63.2A22.A.A5.2A75.A5.D.D3.A$18.A.2A66.2A
82.2A6.D$16.3A.2A28.A90.A$15.A33.A.A.2A40.3D43.3A$16.3A.2A27.A.A.A.A
41.D46.A38.2A$18.A.A25.2A.A.A.A.A2.A37.D46.2A38.A$18.A.A2.A.2A19.A2.A
2.2A.4A97.A27.3A$19.A.3A.2A21.2A4.A99.3A29.A28.A$20.A33.A.A41.2A31.2A
20.A59.3A$21.3A.2A28.2A41.A32.A21.2A35.2A20.A$23.A.A73.3A27.A.A48.A9.
A.A.2A16.2A$23.A.A2.A.2A69.A27.2A36.2D11.3A9.A.A$24.A.3A.2A107.2A25.D
.D14.A7.2A.A$25.A113.2A27.D13.2A10.A.2A22.2A$26.3A.2A72.2A71.2A7.A4.
4A2.A23.A$28.A.A73.A2.A68.A.A6.A.A3.A3.2A24.A.2A$28.A.A2.A.2A68.3A66.
3A.A.A4.A2.A3.3A15.D2.2A4.3A2.A$29.A.3A.2A60.2A74.A5.2A5.2A6.A13.D.D
2.2A3.A3.2A$30.A66.A.A5.3A65.2A19.A.A12.2D7.4A$31.3A.2A55.A6.A4.A2.A
31.D55.2A7.2A15.A$33.A.A56.3A4.2A3.2A10.D21.D60.2A2.A.A12.3A$33.A.A2.
A.2A44.2A7.A20.3D18.2D44.D2.2D12.A2.A13.A$34.A.3A.2A44.A7.2A20.D.D15.
2A2.2D43.2D2.D10.A2.3A14.5A$35.A22.D28.A30.D15.2A3.D22.2A.D11.2A4.D2.
D11.3A21.A$36.3A.2A15.D.D6.A19.2A74.2A.3D9.2A5.3D14.A18.A$38.A.A16.D.
D5.A.A5.2D90.D.D32.2A18.2A$38.A.A2.A.2A11.D7.A5.D.D92.D$39.A.3A.2A27.
D$40.A20.2C122.A17.D$41.3A.2A14.2C74.2A45.A.A15.D$43.A.A21.D15.2A3.D
49.A39.2A4.A.A4.2A9.3D$43.A.A2.A.2A13.D.D15.2A2.2D48.A40.A2.A3.A3.A2.
A$44.A.3A.2A13.3D18.2D49.2A40.3A7.3A18.2A$45.A19.D21.D115.2A5.A.A$46.
3A.2A36.D88.7A3.7A9.2A7.A$48.A.A126.A6.A.A6.A18.2A$48.A.A127.A.A.2A3.
2A.A.A$49.A9.2C28.2A4.2A82.2A.A5.A.2A7.A$58.C2.C27.A5.2A8.2A77.A.A11.
A.A.2A$43.2A14.2C29.3A12.2A76.2A.2A10.A.A.A.A$25.2A17.A47.A102.2A.A.A
.A.A2.A$26.A17.A.A54.2A92.A2.A2.2A.4A$25.A19.2A55.A94.2A4.A$25.2A72.
3A101.A.A$99.A104.2A$12.2A$13.A72.2A$13.A.A47.2A21.A$14.2A47.2A23.A$
23.3D2.2A15.D22.2A14.5A$17.2A5.D3.2A15.D.D21.A13.A$17.A.A2.3D20.3D21.
A.A12.3A78.A$19.A27.D22.2A15.A75.3A$15.4A56.2D7.4A74.A$14.A59.D.D2.2A
3.A3.2A72.2A$14.2A.2A57.D2.2A4.3A2.A$15.A.A69.A.2A$15.A.A20.2A19.2A
26.A82.2A$16.A18.A3.A19.A26.2A83.A$35.4A21.3A108.A.2A$62.A97.D2.2A4.
3A2.A$35.2A41.2A78.D.D2.2A3.A3.2A$35.A7.2A33.A10.A69.2D7.4A$32.2A.A7.
2A34.3A7.3A62.2A15.A$32.2A.A.A43.A10.A60.A.A12.3A$36.2A53.2A60.A13.A$
152.2A14.5A$22.2A148.A$22.2A146.A$82.A49.A37.2A$13.2A.A63.3A47.3A$13.
A.2A5.D56.A49.A$22.3D29.D11.2A11.2A23.D11.2A11.2A11.A$22.D.D29.3D9.2A
36.3D9.2A24.3A$24.D29.D.D47.D.D38.A$56.D49.D37.2A$159.2A$24.2A133.A$
23.A2.A.A127.2A.A$23.2A.A.3A50.D49.D23.A2.A$26.A4.A47.D.D47.D.D13.D
10.2A$20.2A4.A.3A48.3D9.2A36.3D9.2A2.D.D$21.A5.2A50.D11.2A11.2A23.D
11.2A2.2D$18.3A83.A$18.A86.3A$107.A$45.2A$45.A83.2A3.A$46.3A80.A3.A.A
$48.A17.2A48.2A12.A3.A.A.2A$67.A49.A13.A4.A.2A$64.3A47.3A12.A.5A$64.A
28.2E19.A13.A.A4.A.2A.A.2A$93.E.E33.A2.2A.A2.A.2A.A$95.E34.2A.A.2A12.
2A$95.2E52.2A!

Plain two-state RLE of the same pattern:

Code: Select all

x = 225, y = 137, rule = B3/S23
28b2o54b2o7bo$27bobo50b2obobo5b3o$21b2o4bo43bo7bobobo6bo$19bo2bo2b2ob
4o38bobo5bo2bo2bo5b2o$19b2obobobobo2bo39bo7b2o2b2o$22bobobobo$22bobob
2o$23bo70b2o$94bo$36b2o54bobo$27b2o7bo34b3o12b2o4b2o$9bo17b2o5bobo49b
2o$9b3o22b2o36b2o12b2o$12bo59b2o$11b2o53b2o4b2o12b3o$65bobo$65bo$3b2o
59b2o$3bo$2obo20b2o$o2b3o4b2o13bo49b2o2b2o7bo$b2o3bo3b2o10b3o50bo2bo2b
o5bobo$3b4o15bo43bo9bobobo7bo$3bo15b2obob3o2bo35bo8bobob2o$4b3o12bobob
o2b4o35b3o6b2o$7bo13bobo$2b5o14b2o3b4o$2bo22bo3bo158b2o$4bo20b2o22bo
138bo$3b2o44b3o124bo12bo$52bo41b2o80b3o7b4o$51b2o41bobo82bo6bo$96bo4b
2o75b2o9b3o$92b4ob2o2bo2bo84bo2bo$92bo2bobobobob2o86b2o$95bobobobo68b
2o2bo$96b2obobo68bo2bobo$15b2o83bo70bob2o$14bobo44b2o109bo$14bo39b2o5b
obo22b2o85b2o8b2o$13b2o39b2o7bo23bo7b2o77bo8bobo$63b2o22bobo5b2o75bo
11bo$18bob2o66b2o82b2o$16b3ob2o28bo90bo$15bo33bobob2o86b3o$16b3ob2o27b
obobobo88bo38b2o$18bobo25b2obobobobo2bo84b2o38bo$18bobo2bob2o19bo2bo2b
2ob4o97bo27b3o$19bob3ob2o21b2o4bo99b3o29bo28bo$20bo33bobo41b2o31b2o20b
o59b3o$21b3ob2o28b2o41bo32bo21b2o35b2o20bo$23bobo73b3o27bobo48bo9bobob
2o16b2o$23bobo2bob2o69bo27b2o49b3o9bobo$24bob3ob2o107b2o42bo7b2obo$25b
o113b2o41b2o10bob2o22b2o$26b3ob2o72b2o71b2o7bo4b4o2bo23bo$28bobo73bo2b
o68bobo6bobo3bo3b2o24bob2o$28bobo2bob2o68b3o66b3obobo4bo2bo3b3o18b2o4b
3o2bo$29bob3ob2o60b2o74bo5b2o5b2o6bo18b2o3bo3b2o$30bo66bobo5b3o65b2o
19bobo21b4o$31b3ob2o55bo6bo4bo2bo87b2o7b2o15bo$33bobo56b3o4b2o3b2o93b
2o2bobo12b3o$33bobo2bob2o44b2o7bo104bo2bo13bo$34bob3ob2o44bo7b2o38b2o
62bo2b3o14b5o$35bo51bo46b2o26b2o13b2o19b3o21bo$36b3ob2o24bo19b2o74b2o
13b2o22bo18bo$38bobo24bobo132b2o18b2o$38bobo2bob2o19bo$39bob3ob2o$40bo
20b2o122bo$41b3ob2o14b2o74b2o45bobo$43bobo37b2o53bo39b2o4bobo4b2o$43bo
bo2bob2o31b2o52bo40bo2bo3bo3bo2bo$44bob3ob2o85b2o40b3o7b3o18b2o$45bo
157b2o5bobo$46b3ob2o125b7o3b7o9b2o7bo$48bobo126bo6bobo6bo18b2o$48bobo
127bobob2o3b2obobo$49bo9b2o28b2o4b2o82b2obo5bob2o7bo$58bo2bo27bo5b2o8b
2o77bobo11bobob2o$43b2o14b2o29b3o12b2o76b2ob2o10bobobobo$25b2o17bo47bo
102b2obobobobo2bo$26bo17bobo54b2o92bo2bo2b2ob4o$25bo19b2o55bo94b2o4bo$
25b2o72b3o101bobo$99bo104b2o$12b2o$13bo72b2o$13bobo47b2o21bo$14b2o47b
2o23bo$28b2o38b2o14b5o$17b2o9b2o39bo13bo$17bobo49bobo12b3o78bo$19bo50b
2o15bo75b3o$15b4o65b4o74bo$14bo64b2o3bo3b2o72b2o$14b2ob2o60b2o4b3o2bo$
15bobo69bob2o$15bobo20b2o19b2o26bo82b2o$16bo18bo3bo19bo26b2o83bo$35b4o
21b3o108bob2o$62bo100b2o4b3o2bo$35b2o41b2o83b2o3bo3b2o$35bo7b2o33bo10b
o78b4o$32b2obo7b2o34b3o7b3o62b2o15bo$32b2obobo43bo10bo60bobo12b3o$36b
2o53b2o60bo13bo$152b2o14b5o$22b2o148bo$22b2o146bo$82bo49bo37b2o$13b2ob
o63b3o47b3o$13bob2o62bo49bo$66b2o11b2o35b2o11b2o11bo$66b2o48b2o24b3o$
145bo$144b2o$159b2o$24b2o133bo$23bo2bobo127b2obo$23b2obob3o124bo2bo$
26bo4bo124b2o$20b2o4bob3o60b2o48b2o$21bo5b2o62b2o11b2o35b2o$18b3o83bo$
18bo86b3o$107bo$45b2o$45bo83b2o3bo$46b3o80bo3bobo$48bo17b2o48b2o12bo3b
obob2o$67bo49bo13bo4bob2o$64b3o47b3o12bob5o$64bo28b2o19bo13bobo4bob2ob
ob2o$93bobo33bo2b2obo2bob2obo$95bo34b2obob2o12b2o$95b2o52b2o!

Fast pulse dividers for almost all coefficients

I believe this technique provides sufficiently fast (for all practical purposes) stable pulse dividers for all sufficiently large pulse-division coefficients:

• Increasing length of the crystal by one unit of repetition (5 cells diagonal) has the effect of increasing the pulse-division coefficient by 6. (There are 5 extra steps when growing and 1 extra step when decaying.)
• Considering how the crystal decays, for all sufficiently long crystals you can delete between 0 and 5 beehives using gliders duplicated from the output, to decrease the number of decay steps. This covers all sufficiently large pulse-division coefficients.
• All sufficiently long pulse dividers should have repeat time 43. The recovery circuitry does not have to be fast, since it is invoked only once per complete cycle of the pattern.

I'm not sure just how far this can be pushed, in terms of covering medium pulse-division coefficients (starting from 5 and up to somewhere around 50). It should be possible to significantly speed up the above proof-of-concept recovery.

edit (2024-11): fixed some terminology.

[confocaloid]

• Considering how the crystal decays, for all sufficiently long crystals you can delete between 0 and 5 beehives using gliders duplicated from the output, to decrease the number of decay steps. This covers all sufficiently large pulse-division coefficients.

I forgot to say that deletion of beehives before they decay in the normal way would require extracting gliders from later steps, to avoid interference between the crystal growth and the recovery. Here is one way to get gliders from the middle of the growing crystal without stopping the growth:

Code: Select all

x = 203, y = 214, rule = B3/S23
5bo$4bobo$4bobo$3b2ob3o$9bo$3b2ob3obo$3b2obo2bobo$9bobo$8b2ob3o$14bo$
8b2ob3obo$8b2obo2bobo$14bobo$13b2ob3o$19bo$13b2ob3obo$13b2obo2bobo$2o
17bobo$2o16b2ob3o$24bo$18b2ob3obo$18b2obo2bobo$24bobo$23b2ob3o$29bo$
23b2ob3obo$23b2obo2bobo$29bobo$18bo9b2ob3o$17b2o15bo$17bobo8b2ob3obo$b
2o25b2obo2bobo$o2bo5b2o23bobo$bobo5b2o22b2ob3o$2bo36bo$9b2o22b2ob3o$9b
2o22b2obo3$28b2o$28bobo$11b2o15bo$10bo2bo5b2o$11bobo5b2o$12bo$19b2o$
19b2o4$39b2o$38b2o$40bo9$49b3o$49bo$50bo8$61bo$60b2o$60bobo9$71b2o$71b
obo$71bo9$82b2o$81b2o$83bo9$92b3o$92bo$93bo8$104bo$103b2o$103bobo9$
114b2o$114bobo$114bo9$125b2o$124b2o$126bo9$135b3o$135bo$136bo8$147bo$
146b2o$146bobo9$157b2o$157bobo$157bo9$168b2o$167b2o$169bo9$178b3o$178b
o$179bo8$190bo$189b2o$189bobo9$200b2o$200bobo$200bo!

[dvgrn]

This is some very nice new technology -- I like it!

The reset system seemed a little convoluted, so I tried to simplify it ... and then discovered exactly why it was designed that way: the block can't be replaced until after a glider has deleted the extra beehive.

However, I did just by blind luck happen to stumble over a workable simplification, as long as you don't mind finding another trick to get odd multipliers. This version allows for 32x, 38x, 44x, etc. -- move the white eater NW to the red positions, and/or add more eater2s in the chain to extend further than 44x:

Code: Select all

x = 158, y = 130, rule = LifeHistory
7.A$7.3A$2A8.A$.A7.2A$.A.AB4.5B$2.2AB6.6B$4.B2A2.8B3.BA$4.BABA7B2A3BA
.A$5.A9B2A4BA$6.13B.B$2A2.B2.3BA7B$A2.2A4B2A5B$.2ABA3B2A2BA3B97.2A$4.
6B3A3B97.A.A$.3A.9BA2B4.A93.A4.2A$.A2.A2.2BA5BAB3.A.A88.4A.2A2.A2.A$
2.A.A3.BA5BA2B2.A2.A87.A2.A.A.A.A.2A$3.A4.2BA9B.3A89.BABABA.A$9.3B3A
6B93.B2ABA.A$9.3BA2B2A3BAB2A91.2B.BA$9.5B2A4B2A2.A89.3B$7.7BA3B2.B2.
2A80.2A6.4B$4.B.13B13.D73.A6.B2A3B$3.A4B2A9BA10.3D73.A.AB3.B2A3B$2.A.
A3B2A7BABAB8.D77.2AB.10B$3.AB3.8B2.2A2B7.2D78.13B$8.6B5.4B3.5B78.5B3D
6B$11.5B4.4B2.3B8.D71.7BD7B$14.2A5.9B5.3D73.4BD3B2.4B$14.A7.8B4.D76.
6B5.4B$15.3A5.8B3.2D74.9B4.4B$17.A3.15B73.4B4.2A5.4B$21.14B7.C65.4B5.
A7.4B$21.14B5.3C64.4B7.3A5.4B$17.A.2AB.5BABA4B4.C66.4B10.A6.4B7.A$15.
3AB2AB3.4B2A7B.2C64.4B19.4B6.3A$14.A4.B5.4BA11B63.4B21.4B8.A$15.3A.2A
5.14B63.4B23.4B6.A.A$17.A.A7.13B62.4B25.4B5.A.AB$17.A.A2.A.2A2.12B61.
4B27.4B5.A3B$18.A.3AB2A4.13B57.4B29.4B6.4B$19.A4.B5.14B55.4B31.4B5.6B
$20.3A.2A5.14B53.4B33.4B4.7B$22.A.A4.16B52.4B35.4B2.8B.4B.B$22.A.A2.A
.2AB.7BA4B51.4B37.17B.B2A$23.A.3AB2AB3.6BA6B47.4B39.18B2A$24.A4.B5.4B
3A7B45.4B40.16B.2B$25.3A.2A5.14B43.4B41.5BD10B$27.A.A4.16B42.4B42.6BD
8B$27.A.A2.A.2AB.12B41.4B41.2AB.2B3D7B$28.A.3AB2AB3.13B37.4B41.A.AB2.
11B$29.A4.B5.14B35.4B42.A5.10B3.2A$30.3A.2A5.14B33.4B42.2A5.2B2A6B3.A
$32.A.A4.16B32.4B49.3B2A6B4.A$32.A.A2.A.2AB.12B31.4B51.10B3.2A$33.A.
3AB2AB3.5BA7B27.4B52.8B.B2A$34.A4.B5.6B2A6B25.4B52.7B3.B2AB2A$35.3A.
2A5.4B2A8B23.4B53.6B6.B.A$37.A.A4.16B22.4B55.6B4.2A3.A$37.A.A2.A.2AB.
12B21.4B5.2A49.8B.A2.4A$38.A.3AB2AB3.13B17.4B6.A49.9BA.A.A$39.A4.B5.
14B15.4B8.A11.A27.A8.7B.2BAB.A.2A$40.3A.2A5.14B5.A7.4B8.2A9.3A27.3A6.
6B3.2B2.A.A$42.A.A4.16B4.A.A5.2D2B9.B9.A33.A4.2B3D2B4.B.2A2.A$42.A.A
2.A.2AB.12B5.A5.DBDB8.3B9.2A10.2A19.2A4.4BD2B3.A.A2.A.A$43.A.3AB2AB3.
12B8.3BD7.6B5.5B10.A15.A4.4B.4B3DB3.2A2.A.A$44.A4.B5.7BA2B2C2B5.4B5.
10B3.4B9.BA.A15.3A4.11B8.A$45.3A.2A5.4BABA2B2C3B3.6B3.11B2.6B4.3B.B2A
19.A2.12B$47.A.A4.7B2A6B2.D15B2A3BD9B.7B20.2A2.12B$47.A.A2.A.2AB.11BD
BD15B2A2B2D17B20.B3.11B$48.A.3AB2AB3.9B3D18B2D17B19.3B4.7B$49.A4.B5.
7B2.D21BD18B16.6B3.8B$50.3A.2A5.31BD19B11.10B2.9B$52.A.A6.10B2.4B.13B
3.B.19B2.2B3.23B$52.A.A7.8B4.4B4.B.7B5.15BD15B2A3BD12B.B$53.A6.3B2C4B
6.4B18.7B.4BDBD15B2A2B2D13B2A$59.3BC2BC3B7.4B16.7B2.4B3D18B2D14B2A$
47.2A10.4B2CB11.4B16.2A2B4.4BD21BD15B$29.2A17.A9.8B12.4B15.2A4B3.26BD
9B2.5B$30.A17.A.AB5.10B10.6B18.2A10.4B.13B5.5B6.2A$29.A19.2AB.3B.11B
10.6B10.2A5.A12.4B4.B.7B3.3B.2B7.A$29.2A20.17B11.6B9.A7.3A10.4B15.2A
12.3A$30.B20.16B15.4B10.A7.A11.4B15.A14.A$16.2A12.3B19.13B11.2A5.4B5.
5A20.4B11.3A$17.A11.6B16.14B.2B9.A5.4B4.A26.4B10.A$17.A.AB7.10B11.18B
2A8.A.AB.7B2.B3A24.4B$18.2AB7.11B3.2B2.19B.B2A9.2AB.7B3.2B.A24.4B$20.
3B4.3D2B2A15BD15B2.B12.3B2D7B4A25.4B$20.B2AB3.BD3B2A15BDBD4B.7B16.2BD
BD2B2A3BAB2.2A24.4B13.A$21.ABA2B3D20B3D4B.7B16.4BD2B2A2B.B3A2.A24.4B
10.3A$22.BA27BD4B2.7B15.10B3.B.A.2A25.4B8.A$19.4A32B4.6B14.8B8.A29.4B
7.2A$18.A4.20B.4B10.7B13.9B7.2A30.4B3.5B$18.2A.2A3.11B.B5.3B12.4B14.
4B2.3B41.4B2.3B$19.A.A4.6B10.4B14.5B11.4B3.5B40.9B7.2A$19.A.A3.6B11.
2A19.2A10.4B7.2A41.8B8.A$20.A4.7B7.A3.A19.A10.4B8.A43.10B3.B.A.2A$26.
6B7.4A21.3A6.4B10.3A40.4BD2B2A2B.B3A2.A$26.6B34.A5.4B13.A40.2BDBD2B2A
3BAB2.2A$26.6B7.2A30.4B55.3B2D7B4A$25.8B6.A7.2A21.4B54.2AB.7B3.2B.A$
24.8B4.2A.A5.2B2AB19.4B54.A.AB.7B2.B3A$24.9B3.2A.A.AB2.4B19.4B12.2A
41.A5.4B4.A$24.9B7.2AB.7B16.4B13.A24.2A15.2A5.4B5.5A$23.10B8.11B14.4B
15.3A6.2A13.A22.4B10.A$23.3B2A5B9.9B14.4B18.A4.2B2AB9.BA.A21.4B9.A$
22.4B2A5B6.12B13.4B20.3B.4B6.3B.B2A10.A10.4B10.2A$22.12B.16B12.4B4.B.
7B7.11B2.7B12.3A7.4B$17.2A.A31B10.4B.13B3.B.22B15.A5.4B$17.A.2A2.3BD
24B4.26BD24B15.2A4.4B$24.2B3D23B2.4BD21BD26B14.9B6.2A$26.DBD23B2.4B3D
18B2D28B14.6B7.A$28.D24B.4BDBD15B2A2B2D30B2.2B2.B3.6B5.2A.A$28.4B2.2B
3.21BD15B2A3BD26BD19B4.A2.A$28.4B10.22B2.2B3.30B.4BDBD13BD6B3.B2A$27.
B2A2B12.17B11.10B2.16B2.4B3D9B2A2BDBD9B$26.BA2BA.A11.15B16.6B7.4B.7B
2.4BD11B2A2B2D9B$26.B2A.A.3A8.17B17.3B9.2B2.6B4.29B$24.4B2.A4.A5.19B
19.B13.6B11.4B.17B$24.2A4.A.3A5.19B20.2A14.3B13.2B3.15B$25.A5.2A8.10B
.6B22.A12.7B10.3B3.15B$22.3A17.9B.6B19.3A13.2A.B.2A6.2A.2BA5.13B$22.A
19.7B4.4B20.A16.A3.A7.A.2BA.A2.13B$43.8B3.B36.3A5.3A5.A2.BA.A.2A4.8B$
43.2B4.2A40.A9.A6.A4.AB2A6.6B$49.A56.A.5A2.B8.5B$50.3A52.A.A4.A.2A.A.
2A5.B.B$52.A53.A2.2A.A2.A.2A.A4.3B$107.2A.A.2A11.B2AB$126.2A!

[confocaloid]

The reset system seemed a little convoluted, so I tried to simplify it ... and then discovered exactly why it was designed that way: the block can't be replaced until after a glider has deleted the extra beehive.

However, I did just by blind luck happen to stumble over a workable simplification, as long as you don't mind finding another trick to get odd multipliers. This version allows for 32x, 38x, 44x, etc. -- move the white eater NW to the red positions, and/or add more eater2s in the chain to extend further than 44x:

That simpler restoration is cool -- an unexpected use of the H-to-block factory compensates for the added block pull.

It is possible to get back to the 1 (mod 6) series by using a block instead of eater 1 to stop the growth without leaving the last beehive. If the same tweak is combined with the previous design for the 1 (mod 6) series, it will give the 0 (mod 6) series.

Example 31x pulse division (1 mod 6), although without an output signal:

Code: Select all

x = 158, y = 130, rule = LifeHistory
7.A$7.3A$2A8.A$.A7.2A$.A.AB4.5B$2.2AB6.6B$4.B2A2.8B3.BA$4.BABA7B2A3BA
.A$5.A9B2A4BA$6.13B.B$2A2.B2.3BA7B$A2.2A4B2A5B$.2ABA3B2A2BA3B97.2A$4.
6B3A3B97.A.A$.3A.9BA2B4.A93.A4.2A$.A2.A2.2BA5BAB3.A.A88.4A.2A2.A2.A$
2.A.A3.BA5BA2B2.A2.A87.A2.A.A.A.A.2A$3.A4.2BA9B.3A89.BABABA.A$9.3B3A
6B93.B2ABA.A$9.3BA2B2A3BAB2A91.2B.BA$9.5B2A4B2A2.A89.3B$7.7BA3B2.B2.
2A80.2A6.4B$4.B.13B87.A6.B2A3B$3.A4B2A9BA86.A.AB3.B2A3B$2.A.A3B2A7BAB
AB86.2AB.10B$3.AB3.8B2.2A2B87.13B$8.6B5.4B4.2D80.5B3D6B$11.5B4.4B3.2D
80.7BD7B$14.2A5.4B86.4BD3B2.4B$14.A7.4B85.6B5.4B$15.3A5.4B83.9B4.4B$
17.A6.4B4.2D75.4B4.2A5.4B$25.4B3.2D8.D65.4B5.A7.4B$26.4B10.3D64.4B7.
3A5.4B$17.A.2A6.BABA8.D66.4B10.A6.4B7.A$15.3A.2A7.B2AB7.2D64.4B19.4B
6.3A$14.A14.A3B4.2C65.4B21.4B8.A$15.3A.2A9.4B2.B2CB63.4B23.4B6.A.A$
17.A.A11.4B.3B63.4B25.4B5.A.AB$17.A.A2.A.2A6.4B.B63.4B27.4B5.A3B$18.A
.3A.2A7.8B.B57.4B29.4B6.4B$19.A13.11B55.4B31.4B5.6B$20.3A.2A5.13B54.
4B33.4B4.7B$22.A.A6.14B52.4B35.4B2.8B.4B.B$22.A.A2.A.2AB.7BA4B51.4B
37.17B.B2A$23.A.3AB2AB2.7BA6B47.4B39.18B2A$24.A4.B5.4B3A7B45.4B40.16B
.2B$25.3A.2A5.14B43.4B41.5BD10B$27.A.A4.16B42.4B42.6BD8B$27.A.A2.A.2A
B.12B41.4B41.2AB.2B3D7B$28.A.3AB2AB3.13B37.4B41.A.AB2.11B$29.A4.B5.
14B35.4B42.A5.10B3.2A$30.3A.2A5.14B33.4B42.2A5.2B2A6B3.A$32.A.A4.16B
32.4B49.3B2A6B4.A$32.A.A2.A.2AB.12B31.4B51.10B3.2A$33.A.3AB2AB3.5BA7B
27.4B52.8B.B2A$34.A4.B5.6B2A6B25.4B52.7B3.B2AB2A$35.3A.2A5.4B2A8B23.
4B53.6B6.B.A$37.A.A4.16B22.4B55.6B4.2A3.A$37.A.A2.A.2AB.12B21.4B5.2A
49.8B.A2.4A$38.A.3AB2AB3.13B17.4B6.A49.9BA.A.A$39.A4.B5.14B15.4B8.A
11.A27.A8.7B.2BAB.A.2A$40.3A.2A5.14B5.A7.4B8.2A9.3A27.3A6.6B3.2B2.A.A
$42.A.A4.16B4.A.A5.2D2B9.B9.A33.A4.2B3D2B4.B.2A2.A$42.A.A2.A.2AB.12B
5.A5.DBDB8.3B9.2A10.2A19.2A4.4BD2B3.A.A2.A.A$43.A.3AB2AB3.12B8.3BD7.
6B5.5B10.A15.A4.4B.4B3DB3.2A2.A.A$44.A4.B5.7BA2B2C2B5.4B5.10B3.4B9.BA
.A15.3A4.11B8.A$45.3A.2A5.4BABA2B2C3B3.6B3.11B2.6B4.3B.B2A19.A2.12B$
47.A.A4.7B2A6B2.D15B2A3BD9B.7B20.2A2.12B$47.A.A2.A.2AB.11BDBD15B2A2B
2D17B20.B3.11B$48.A.3AB2AB3.7B.B3D18B2D17B19.3B4.7B$49.A4.B5.7B2.D21B
D18B16.6B3.8B$50.3A.2A5.4B3.24BD19B11.10B2.9B$52.A.A6.4B2.4B2.4B.13B
3.B.19B2.2B3.23B$52.A.A7.8B4.4B4.B.7B5.15BD15B2A3BD12B.B$53.A6.3B2C4B
6.4B18.7B.4BDBD15B2A2B2D13B2A$59.3BC2BC2B8.4B16.7B2.4B3D18B2D14B2A$
47.2A10.4B2CB11.4B16.2A2B4.4BD21BD15B$29.2A17.A9.8B12.4B15.2A4B3.26BD
9B2.5B$30.A17.A.AB5.10B12.4B18.2A10.4B.13B5.5B6.2A$29.A19.2AB.3B.11B
12.4B10.2A5.A12.4B4.B.7B3.3B.2B7.A$29.2A20.17B13.4B9.A7.3A10.4B15.2A
12.3A$30.B20.16B15.4B10.A7.A11.4B15.A14.A$16.2A12.3B19.13B11.2A5.4B5.
5A20.4B11.3A$17.A11.6B16.14B.2B9.A5.4B4.A26.4B10.A$17.A.AB7.10B11.18B
2A8.A.AB.7B2.B3A24.4B$18.2AB7.11B3.2B2.19B.B2A9.2AB.7B3.2B.A24.4B$20.
3B4.3D2B2A15BD15B2.B12.3B2D7B4A25.4B$20.B2AB3.BD3B2A15BDBD4B.7B16.2BD
BD2B2A3BAB2.2A24.4B13.A$21.ABA2B3D20B3D4B.7B16.4BD2B2A2B.B3A2.A24.4B
10.3A$22.BA27BD4B2.7B15.10B3.B.A.2A25.4B8.A$19.4A32B4.6B14.8B8.A29.4B
7.2A$18.A4.20B.4B10.7B13.9B7.2A30.4B3.5B$18.2A.2A3.11B.B5.3B12.4B14.
4B2.3B41.4B2.3B$19.A.A4.6B10.4B14.5B11.4B3.5B40.9B7.2A$19.A.A3.6B11.
2A19.2A10.4B7.2A41.8B8.A$20.A4.7B7.A3.A19.A10.4B8.A43.10B3.B.A.2A$26.
6B7.4A21.3A6.4B10.3A40.4BD2B2A2B.B3A2.A$26.6B34.A5.4B13.A40.2BDBD2B2A
3BAB2.2A$26.6B7.2A30.4B55.3B2D7B4A$25.8B6.A7.2A21.4B54.2AB.7B3.2B.A$
24.8B4.2A.A5.2B2AB19.4B54.A.AB.7B2.B3A$24.9B3.2A.A.AB2.4B19.4B12.2A
41.A5.4B4.A$24.9B7.2AB.7B16.4B13.A24.2A15.2A5.4B5.5A$23.10B8.11B14.4B
15.3A6.2A13.A22.4B10.A$23.3B2A5B9.9B14.4B18.A4.2B2AB9.BA.A21.4B9.A$
22.4B2A5B6.12B13.4B20.3B.4B6.3B.B2A10.A10.4B10.2A$22.12B.16B12.4B4.B.
7B7.11B2.7B12.3A7.4B$17.2A.A31B10.4B.13B3.B.22B15.A5.4B$17.A.2A2.3BD
24B4.26BD24B15.2A4.4B$24.2B3D23B2.4BD21BD26B14.9B6.2A$26.DBD23B2.4B3D
18B2D28B14.6B7.A$28.D24B.4BDBD15B2A2B2D30B2.2B2.B3.6B5.2A.A$28.4B2.2B
3.21BD15B2A3BD26BD19B4.A2.A$28.4B10.22B2.2B3.30B.4BDBD13BD6B3.B2A$27.
B2A2B12.17B11.10B2.16B2.4B3D9B2A2BDBD9B$26.BA2BA.A11.15B16.6B7.4B.7B
2.4BD11B2A2B2D9B$26.B2A.A.3A8.17B17.3B9.2B2.6B4.29B$24.4B2.A4.A5.19B
19.B13.6B11.4B.17B$24.2A4.A.3A5.19B20.2A14.3B13.2B3.15B$25.A5.2A8.10B
.6B22.A12.7B10.3B3.15B$22.3A17.9B.6B19.3A13.2A.B.2A6.2A.2BA5.13B$22.A
19.7B4.4B20.A16.A3.A7.A.2BA.A2.13B$43.8B3.B36.3A5.3A5.A2.BA.A.2A4.8B$
43.2B4.2A40.A9.A6.A4.AB2A6.6B$49.A56.A.5A2.B8.5B$50.3A52.A.A4.A.2A.A.
2A5.B.B$52.A53.A2.2A.A2.A.2A.A4.3B$107.2A.A.2A11.B2AB$126.2A!

Example 42x pulse divider (0 mod 6):

Code: Select all

x = 225, y = 137, rule = LifeHistory
28.2A54.2A7.A$27.A.A50.2A.A.A5.3A$21.2A4.A43.A7.A.A.A6.A$19.A2.A2.2A.
4A38.A.A5.A2.A2.A5.2A$19.2A.A.A.A.A2.A39.A7.2A2.2A$22.A.A.A.A$22.A.A.
2A$23.A70.2A$94.A$36.2A54.A.A$27.2A7.A34.3A12.2A4.2A$9.A17.2A5.A.A49.
2A$9.3A22.2A36.2A12.2A$12.A59.2A$11.2A13.3D37.2A4.2A12.3A$26.D38.A.A$
27.D37.A$3.2A59.2A$3.A$2A.A20.2A$A2.3A4.2A2.D10.A49.2A2.2A7.A$.2A3.A
3.2A2.D.D5.3A50.A2.A2.A5.A.A$3.4A7.2D6.A43.A9.A.A.A7.A$3.A15.2A.A42.A
8.A.A.2A$4.3A12.A.A.2A40.3A6.2A$7.A13.A2.A$2.5A14.2A$2.A185.2A$4.A44.
A138.A$3.2A18.2C24.3A124.A12.A$23.2C27.A41.2A80.3A7.4A$51.2A41.A.A82.
A6.A$96.A4.2A75.2A9.3A$92.4A.2A2.A2.A84.A2.A$54.D37.A2.A.A.A.A.2A86.
2A$53.D41.A.A.A.A68.2A2.A$53.3D40.2A.A.A68.A2.A.A$100.A70.A.2A$61.2A
109.A$54.2A5.A.A22.2A85.2A8.2A$54.2A7.A23.A7.2A77.A4.2D2.A.A$63.2A22.
A.A5.2A75.A5.D.D3.A$18.A.2A66.2A82.2A6.D$16.3A.2A28.A90.A$15.A33.A.A.
2A40.3D43.3A$16.3A.2A27.A.A.A.A41.D46.A38.2A$18.A.A25.2A.A.A.A.A2.A
37.D46.2A38.A$18.A.A2.A.2A19.A2.A2.2A.4A97.A27.3A$19.A.3A.2A21.2A4.A
99.3A29.A28.A$20.A33.A.A41.2A31.2A20.A59.3A$21.3A.2A28.2A41.A32.A21.
2A35.2A20.A$23.A.A73.3A27.A.A48.A9.A.A.2A16.2A$23.A.A2.A.2A69.A27.2A
36.2D11.3A9.A.A$24.A.3A.2A107.2A25.D.D14.A7.2A.A$25.A113.2A27.D13.2A
10.A.2A22.2A$26.3A.2A72.2A71.2A7.A4.4A2.A23.A$28.A.A73.A2.A68.A.A6.A.
A3.A3.2A24.A.2A$28.A.A2.A.2A68.3A66.3A.A.A4.A2.A3.3A15.D2.2A4.3A2.A$
29.A.3A.2A60.2A74.A5.2A5.2A6.A13.D.D2.2A3.A3.2A$30.A66.A.A5.3A65.2A
19.A.A12.2D7.4A$31.3A.2A55.A6.A4.A2.A31.D55.2A7.2A15.A$33.A.A56.3A4.
2A3.2A10.D21.D60.2A2.A.A12.3A$33.A.A2.A.2A44.2A7.A20.3D18.2D44.D2.2D
12.A2.A13.A$34.A.3A.2A44.A7.2A20.D.D15.2A2.2D43.2D2.D10.A2.3A14.5A$
35.A22.D28.A30.D15.2A3.D22.2A.D11.2A4.D2.D11.3A21.A$36.3A.2A15.D.D6.A
19.2A74.2A.3D9.2A5.3D14.A18.A$38.A.A16.D.D5.A.A5.2D90.D.D32.2A18.2A$
38.A.A2.A.2A11.D7.A5.D.D92.D$39.A.3A.2A27.D$40.A20.2C122.A17.D$41.3A.
2A14.2C74.2A45.A.A15.D$43.A.A21.D15.2A3.D49.A39.2A4.A.A4.2A9.3D$43.A.
A2.A.2A13.D.D15.2A2.2D48.A40.A2.A3.A3.A2.A$44.A.3A.2A13.3D18.2D49.2A
40.3A7.3A18.2A$45.A19.D21.D115.2A5.A.A$46.3A.2A36.D88.7A3.7A9.2A7.A$
48.A.A126.A6.A.A6.A18.2A$48.A.A127.A.A.2A3.2A.A.A$49.A9.2C28.2A4.2A
82.2A.A5.A.2A7.A$58.C2.C27.A5.2A8.2A77.A.A11.A.A.2A$43.2A14.2C29.3A
12.2A76.2A.2A10.A.A.A.A$25.2A17.A47.A102.2A.A.A.A.A2.A$26.A17.A.A54.
2A92.A2.A2.2A.4A$25.A19.2A55.A94.2A4.A$25.2A72.3A101.A.A$99.A104.2A$
12.2A$13.A72.2A$13.A.A47.2A21.A$14.2A47.2A23.A$23.3D2.2A15.D22.2A14.
5A$17.2A5.D3.2A15.D.D21.A13.A$17.A.A2.3D20.3D21.A.A12.3A78.A$19.A27.D
22.2A15.A75.3A$15.4A56.2D7.4A74.A$14.A59.D.D2.2A3.A3.2A72.2A$14.2A.2A
57.D2.2A4.3A2.A$15.A.A69.A.2A$15.A.A20.2A19.2A26.A82.2A$16.A18.A3.A
19.A26.2A83.A$35.4A21.3A108.A.2A$62.A97.D2.2A4.3A2.A$35.2A41.2A78.D.D
2.2A3.A3.2A$35.A7.2A33.A10.A69.2D7.4A$32.2A.A7.2A34.3A7.3A62.2A15.A$
32.2A.A.A43.A10.A60.A.A12.3A$36.2A53.2A60.A13.A$152.2A14.5A$22.2A148.
A$22.2A146.A$82.A49.A37.2A$13.2A.A63.3A47.3A$13.A.2A5.D56.A49.A$22.3D
29.D11.2A11.2A23.D11.2A11.2A11.A$22.D.D29.3D9.2A36.3D9.2A24.3A$24.D
29.D.D47.D.D38.A$56.D49.D37.2A$159.2A$24.2A133.A$23.A2.A.A127.2A.A$
23.2A.A.3A50.D49.D23.A2.A$26.A4.A47.D.D47.D.D13.D10.2A$20.2A4.A.3A48.
3D9.2A36.3D9.2A2.D.D$21.A5.2A50.D11.2A11.2A23.D11.2A2.2D$18.3A83.A$
18.A86.3A$107.A$45.2A$45.A83.2A3.A$46.3A80.A3.A.A$48.A17.2A48.2A12.A
3.A.A.2A$67.A49.A13.A4.A.2A$64.3A47.3A12.A.5A$64.A28.2E19.A13.A.A4.A.
2A.A.2A$93.E.E33.A2.2A.A2.A.2A.A$95.E34.2A.A.2A12.2A$95.2E52.2A!

The next one is incomplete -- if the yellow boat (or anything else that stops the growth at a block pull attempt) can be restored without interfering with the glider stream, that will give the 5 (mod 6) series.

Code: Select all

#C This would be a 41x pulse divider if the yellow boat was restored
#C [[ STOP 1763 HARDRESET ]]
x = 230, y = 135, rule = LifeHistory
7.A$7.3A$2A8.A$.A7.2A$.A.AB4.5B$2.2AB6.6B$4.3B2.8B3.BA$4.10BA5BA.A$5.
5B3ABA6BA$6.4B3ABA4B.B$2A2.B2.11B$A2.2A11B$.2ABA11B$4.12B$.3A.12B4.A$
.A2.A2.10B3.A.A$2.A.A3.10B2.A2.A$3.A4.12B.3A$9.12B$9.11BAB2A$9.11B2A
2.A$7.11B2.B2.2A$4.B.4BAB3A4B$3.A6BAB3A5B$2.A.A5BA10B$3.AB3.8B2.4B
171.2A$8.6B5.4B170.A$11.5B4.4B157.A12.A$14.2A5.3BA4.2E68.2A80.3A7.4A$
14.A7.ABAB3.E.E67.A.A82.A6.A$15.3A5.2A2B3.E70.A4.2A75.2A9.3A$17.A6.4B
69.4A.2A2.A2.A84.A2.A$25.4B68.A2.A.A.A.A.2A86.2A$26.4B70.A.A.A.A68.2A
2.A$27.4B70.2A.A.A68.A2.A.A$28.4B73.A70.A.2A$29.4B144.A$30.4B57.2A85.
2A8.2A$31.4B57.A7.2A77.A4.2D2.A.A$32.BABA56.A.A5.2A75.A5.D.D3.A$23.A.
2A6.B2AB56.2A82.2A6.D$21.3A.2A7.A3B108.A$20.A14.4B61.3D43.3A$21.3A.2A
9.4B62.D46.A38.2A$23.A.A11.4B60.D46.2A38.A$23.A.A2.A.2A6.4B119.A27.3A
$24.A.3A.2A7.4B116.3A29.A28.A$25.A14.4B59.2A31.2A20.A59.3A$26.3A.2A9.
4B58.A32.A21.2A35.2A20.A$28.A.A11.3BA58.3A27.A.A48.A9.A.A.2A16.2A$28.
A.A2.A.2A6.3BA59.A27.2A36.2D11.3A9.A.A$29.A.3A.2A7.3AB96.2A25.D.D14.A
7.2A.A$30.A14.4B95.2A27.D13.2A10.A.2A22.2A$31.3A.2A9.4B59.2A71.2A7.A
4.4A2.A23.A$33.A.A11.4B58.A2.A68.A.A6.A.A3.A3.2A24.A.2A$33.A.A2.A.2A
6.4B58.3A66.3A.A.A4.A2.A3.3A15.D2.2A4.3A2.A$34.A.3A.2A7.4B49.2A74.A5.
2A5.2A6.A13.D.D2.2A3.A3.2A$35.A14.4B48.A.A5.3A65.2A19.A.A12.2D7.4A$
36.3A.2A9.4B42.A6.A4.A2.A31.D55.2A7.2A15.A$38.A.A11.4B41.3A4.2A3.2A
10.D21.D60.2A2.A.A12.3A$38.A.A2.A.2A6.2BCB34.2A7.A20.3D18.2D44.D2.2D
12.A2.A13.A$39.A.3A.2A7.2B2C33.A7.2A20.D.D15.2A2.2D43.2D2.D10.A2.3A
14.5A$40.A14.2C6.D28.A30.D15.2A3.D22.2A.D11.2A4.D2.D11.3A21.A$41.3A.
2A15.D.D6.A19.2A74.2A.3D9.2A5.3D14.A18.A$43.A.A16.D.D5.A.A5.2D90.D.D
32.2A18.2A$43.A.A2.A.2A11.D7.A5.D.D92.D$44.A.3A.2A27.D$45.A20.2C122.A
17.D$46.3A.2A14.2C74.2A45.A.A15.D$48.A.A21.D15.2A3.D49.A39.2A4.A.A4.
2A9.3D$48.A.A2.A.2A13.D.D15.2A2.2D48.A40.A2.A3.A3.A2.A$49.A.3A.2A13.
3D18.2D49.2A40.3A7.3A18.2A$50.A19.D21.D115.2A5.A.A$51.3A.2A36.D88.7A
3.7A9.2A7.A$53.A.A126.A6.A.A6.A18.2A$53.A.A127.A.A.2A3.2A.A.A$54.A9.
2C28.2A4.2A82.2A.A5.A.2A7.A$63.C2.C27.A5.2A8.2A77.A.A11.A.A.2A$48.2A
14.2C29.3A12.2A76.2A.2A10.A.A.A.A$30.2A17.A47.A102.2A.A.A.A.A2.A$31.A
17.A.A54.2A92.A2.A2.2A.4A$30.A19.2A55.A94.2A4.A$30.2A72.3A101.A.A$
104.A104.2A$17.2A$18.A72.2A$18.A.A47.2A21.A$19.2A47.2A23.A$28.3D2.2A
15.D22.2A14.5A$22.2A5.D3.2A15.D.D21.A13.A$22.A.A2.3D20.3D21.A.A12.3A
78.A$24.A27.D22.2A15.A75.3A$20.4A56.2D7.4A74.A$19.A59.D.D2.2A3.A3.2A
72.2A$19.2A.2A57.D2.2A4.3A2.A$20.A.A69.A.2A$20.A.A20.2A19.2A26.A82.2A
$21.A18.A3.A19.A26.2A83.A$40.4A21.3A108.A.2A$67.A97.D2.2A4.3A2.A$40.
2A41.2A78.D.D2.2A3.A3.2A$40.A7.2A33.A10.A69.2D7.4A$37.2A.A7.2A34.3A7.
3A62.2A15.A$37.2A.A.A43.A10.A60.A.A12.3A$41.2A53.2A60.A13.A$157.2A14.
5A$27.2A148.A$27.2A146.A$87.A49.A37.2A$18.2A.A63.3A47.3A$18.A.2A5.D
56.A49.A$27.3D29.D11.2A11.2A23.D11.2A11.2A11.A$27.D.D29.3D9.2A36.3D9.
2A24.3A$29.D29.D.D47.D.D38.A$61.D49.D37.2A$164.2A$29.2A133.A$28.A2.A.
A127.2A.A$28.2A.A.3A50.D49.D23.A2.A$31.A4.A47.D.D47.D.D13.D10.2A$25.
2A4.A.3A48.3D9.2A36.3D9.2A2.D.D$26.A5.2A50.D11.2A11.2A23.D11.2A2.2D$
23.3A83.A$23.A86.3A$112.A$50.2A$50.A83.2A3.A$51.3A80.A3.A.A$53.A17.2A
48.2A12.A3.A.A.2A$72.A49.A13.A4.A.2A$69.3A47.3A12.A.5A$69.A28.2E19.A
13.A.A4.A.2A.A.2A$98.E.E33.A2.2A.A2.A.2A.A$100.E34.2A.A.2A12.2A$100.
2E52.2A!

[dvgrn]

Example 31x pulse division (1 mod 6), although without an output signal...

It's not too painful to get an output signal, at least for anything above 31x. Here's 37x:

Code: Select all

x = 166, y = 130, rule = LifeHistory
7.A$7.3A105.2A$2A8.A104.A.A$.A7.2A106.A4.2A$.A.A109.4A.2A2.A2.A$2.2A
109.A2.A.A.A.A.2A$5.2A14.A94.A.A.A.A$5.A.A7.2A3.A.A94.2A.A.A$5.A9.2A
4.A99.A2$2A8.A96.2A$A2.2A4.2A97.A7.2A$.2A.A3.2A2.A95.A.A5.2A$10.3A96.
2A$.3A10.A6.A$.A2.A4.A5.A4.A.A93.3D$2.A.A4.A5.A4.A2.A94.D$3.A6.A10.3A
93.D$12.3A$12.A2.2A3.A.2A$14.2A4.2A2.A74.2A18.2A$14.A8.2A75.A18.A$32.
D65.A21.3A$3.A4.2A9.A10.3D65.5A14.3A2.A$2.A.A3.2A7.A.A9.D73.A13.A2.A$
3.A14.2A9.2D69.3A12.A.A2.2A$27.2D70.A15.2A$27.2D8.D61.4A7.2D$14.2A19.
3D59.2A3.A3.2A2.D.D$14.A19.D61.A2.3A4.2A2.D35.A$15.3A16.2D60.2A.A46.
3A$17.A14.2C65.A49.A$32.2C8.D56.2A47.A.A$40.3D105.A.A$17.A.2A7.A.A8.D
109.A$15.3A.2A8.2A8.2D66.2A$14.A14.A7.2D48.2A11.A7.A$15.3A.2A16.2D48.
2A10.A.A3.3A$17.A.A79.A.A3.A27.2A$17.A.A2.A.2A72.2A.2A3.2A25.A30.2A$
18.A.3A.2A81.A23.A.A30.2A$19.A78.2A.2A4.A.A21.2A$20.3A.2A72.2A.A2.A3.
2A41.D$22.A.A78.2A47.D$22.A.A2.A.2A9.A103.2A4.3D$23.A.3A.2A10.A101.A.
A$24.A14.3A101.A18.2A$25.3A.2A111.2A7.2A9.A$27.A.A121.2A10.A$27.A.A2.
A.2A59.2A13.2A50.2A$28.A.3A.2A59.2A13.2A47.2A$29.A50.2A77.2A.2A$30.3A
.2A43.A2.A79.A$32.A.A43.A.2A77.2A3.A$32.A.A2.A.2A37.A79.A2.4A$33.A.3A
.2A9.A26.2A78.A.A.A$34.A16.2A39.2A64.A2.A.2A$35.3A.2A9.2A40.A46.2A20.
A.A$37.A.A53.3A23.2A19.A8.3D8.2A2.A$37.A.A2.A.2A42.A6.A24.A19.A.A8.D
5.A.A2.A.A$38.A.3A.2A42.3A26.3A4.2A15.2A7.3D4.2A2.A.A$39.A51.A11.A13.
A6.2A36.A$40.3A.2A24.A19.2A9.3A$42.A.A24.A.A5.2D21.A$42.A.A2.A.2A19.A
5.D.D21.2A10.2A$43.A.3A.2A27.D33.A15.A$44.A17.A2.2C43.A.A15.3A6.2A$
45.3A.2A9.A.A2.2C43.2A19.A6.A$47.A.A11.2A8.D15.2A3.D37.2A6.A.A$47.A.A
2.A.2A13.D.D15.2A2.2D46.2A$48.A.3A.2A13.3D18.2D$49.A19.D21.D$50.3A.2A
36.D59.2A$52.A.A97.A.A$52.A.A56.D15.2A3.D21.A$53.A9.2C44.D.D15.2A2.2D
21.2A$62.C2.C43.3D18.2D11.2D$47.2A14.2C32.2A10.D21.D10.2D$29.2A17.A
48.2A33.D10.D$30.A17.A.A50.2A$29.A19.2A43.2A5.A$29.2A63.A7.3A29.2A$
96.A7.A30.A$16.2A58.2A14.5A35.3A6.A$17.A59.A13.A40.A7.A.A$17.A.A47.2A
8.A.A12.3A46.A$18.2A47.2A9.2A15.A$27.3D2.2A15.D33.2D7.4A$21.2A5.D3.2A
15.D.D30.D.D2.2A3.A3.2A41.A$21.A.A2.3D20.3D32.D2.2A4.3A2.A38.3A$23.A
27.D43.A.2A37.A$19.4A72.A40.2A$18.A75.2A$18.2A.2A$19.A.A122.2A$19.A.A
20.2A19.2A21.2A57.A$20.A18.A3.A19.A22.A58.A.2A$39.4A21.3A20.3A44.D2.
2A4.3A2.A$66.A22.A42.D.D2.2A3.A3.2A$39.2A92.2D7.4A$39.A7.2A79.2A15.A$
36.2A.A7.2A78.A.A12.3A$36.2A.A.A42.2A41.A13.A$40.2A42.A24.2A15.2A14.
5A$85.3A6.2A13.A36.A$26.2A59.A6.2A11.A.A34.A$26.2A79.2A10.A24.2A$119.
3A$17.2A.A101.A$17.A.2A5.D54.D39.2A$26.3D29.D21.D55.2A$26.D.D29.3D18.
2D55.A$28.D29.D.D15.2A2.2D51.2A.A$60.D15.2A3.D26.D23.A2.A$106.D.D13.D
10.2A$28.2A76.3D9.2A2.D.D$27.A2.A.A73.D11.2A2.2D$27.2A.A.3A$30.A4.A$
24.2A4.A.3A44.2A$25.A5.2A47.A$22.3A52.3A13.2A3.2A6.2A3.A$22.A54.A16.A
3.A7.A3.A.A$91.3A5.3A5.A3.A.A.2A$49.2A40.A9.A6.A4.A.2A$49.A56.A.5A$
50.3A52.A.A4.A.2A.A.2A$52.A53.A2.2A.A2.A.2A.A$107.2A.A.2A12.2A$126.2A!

The odds are actually pretty good that there's a way to get a signal out at the end of each cycle, that needs only one or two input signals to restore it, rather than the current three. Just haven't thought of it yet... one idea that came to mind would be to let a whole pile of signals out at the end of the cycle, and bounce them around with quadri-Snarks and tremi-Snarks and so on so that just one signal gets back to place a new block.

This means doing a lot of custom adjustments for each period of gun that you want to use, and the base period can't be too low or there's no way to adjust the reset signal to fit in between the gliders. But any given adjusted solution will look relatively simple. Here's period 3397 = base period 79, multiplier 43:

Code: Select all

x = 242, y = 173, rule = LifeHistory
30.2A$30.A.A$32.A4.2A$28.4A.2A2.A2.A$28.A2.A.A.A.A.2A$31.A.A.A.A$32.
2A.A.A$36.A2$22.2A$23.A$23.A.A$24.2A5.3A11.A$30.A3.A10.3A$29.A5.A12.A
$30.A3.A12.A.A$31.3A13.A.A$48.A2$34.2A$34.A$35.3A$37.A12.3A10.2A$49.A
3.A9.2A$48.A5.A$48.A5.A$48.3A.3A$43.2A$42.A.A$42.A$3.2A10.A25.2A$4.A
10.2A$2.A11.A.A$2.5A14.2A35.2A.A$7.A13.A36.2A.3A$4.3A12.A.A42.A$3.A
15.2A37.2A.3A$3.4A50.A2.2A$.2A3.A3.2A44.A.A$A2.3A4.2A26.A10.A5.A.A.2A
.A$2A.A34.3A7.3A5.A2.A.2A$3.A37.A9.A7.A$3.2A35.2A6.2A.2A5.2A$47.2A.2A
3.A.A2.2A$47.2A.2A3.2A2.A2.A$11.2A35.A2.A8.2A$12.A36.3A$9.3A37.2A$9.A
51.2A$26.2A33.A$26.A.A30.A.A$26.A8.3A21.2A$37.A9.2A$33.3A.A8.A.A$32.A
2.A10.A2.A$31.A2.2A4.2A2.2A2.A23.D$36.A2.2A6.2A21.3D$36.A.A3.A3.A22.D
$33.A2.A.2A2.4A23.2D$33.2A27.A4.2D$63.A3.2D8.D$61.3A11.3D$45.2A27.D$
45.2A27.2D$72.2D$72.2D8.D$80.3D$57.A.2A18.D$55.3A.2A18.2D$54.A22.2C$
55.3A.2A16.2C$57.A.A$57.A.A2.A.2A$58.A.3A.2A$59.A$60.3A.2A$62.A.A$62.
A.A2.A.2A$63.A.3A.2A$64.A16.A$65.3A.2A11.2A$67.A.A11.2A$67.A.A2.A.2A
104.2A2.A$68.A.3A.2A103.A.4A$69.A109.A$70.3A.2A101.2A.7A$72.A.A100.A
2.A.A6.A$72.A.A2.A.2A94.2A3.A.2A2.2A$73.A.3A.2A98.2A.2A$74.A$75.3A.2A
$77.A.A$77.A.A2.A.2A42.A$78.A.3A.2A42.3A60.2A$79.A51.A11.A38.2A7.A$
80.3A.2A24.A19.2A9.3A38.2A5.A.A$82.A.A24.A.A28.A48.2A$82.A.A2.A.2A19.
A29.2A10.2A$83.A.3A.2A61.A$84.A17.A2.2C43.A.A$85.3A.2A9.A.A2.2C43.2A
10.A$87.A.A11.2A8.D15.2A3.D29.3A$87.A.A2.A.2A13.D.D15.2A2.2D32.A$88.A
.3A.2A13.3D18.2D32.2A13.2A$89.A19.D21.D48.A$90.3A.2A36.D44.3A$92.A.A
81.A$92.A.A4.2A50.D23.A2.2A$93.A6.A48.D.D13.D10.2A2.A$97.3A49.3D9.2A
2.D.D11.2A$97.A39.2A10.D11.2A2.2D$137.2A93.A2.2A$141.2A89.4A.A$141.A
95.A$142.3A85.7A.2A$144.A4.2A3.A74.A6.A.A2.A$149.A3.A.A73.2A2.2A.A3.
2A$150.A3.A.A.2A73.2A.2A$151.A4.A.2A$149.A.5A$148.A.A4.A.2A.A.2A$149.
A2.2A.A2.A.2A.A$150.2A.A.2A12.2A53.2A$169.2A54.A7.2A$176.2A11.A35.A.A
5.2A$176.2A10.A.A35.2A$188.A.A31.2A$187.2A.3A2.2A25.A$193.A2.A23.A.A$
187.2A.3A3.A.A21.2A$187.2A.A6.2A2$236.2A$236.A$237.3A$239.A2$184.2A
13.2A$184.2A13.2A$169.2A$168.A2.A$167.A.2A$167.A$166.2A$181.2A$181.A$
182.3A23.2A$184.A24.A$162.A43.3A$160.3A43.A7.2A$159.A55.A$159.2A51.3A
$212.A4$145.2A.2A$143.A2.A.2A$143.2A$156.2A$148.A2.A4.2A$148.4A$145.A
$145.5A$149.A$147.A$147.2A7.2A.2A$152.2A2.2A.A3.2A$152.A6.A.A2.A$153.
7A.2A$160.A$155.4A.A$155.A2.2A!

Replace the tremi-Snarks at the right with quadri-Snarks, and in this case you'll get p3713 = base period 79, multiplier 47. But you'll get different multipliers, or sometimes explosions until you re-adjust the trombone slide, as soon as you swap out the base period 79 gun for another period.

Code: Select all

x = 245, y = 173, rule = LifeHistory
30.2A$30.A.A$32.A4.2A$28.4A.2A2.A2.A$28.A2.A.A.A.A.2A$31.A.A.A.A$32.
2A.A.A$36.A2$22.2A$23.A$23.A.A$24.2A5.3A11.A$30.A3.A10.3A$29.A5.A12.A
$30.A3.A12.A.A$31.3A13.A.A$48.A2$34.2A$34.A$35.3A$37.A12.3A10.2A$49.A
3.A9.2A$48.A5.A$48.A5.A$48.3A.3A$43.2A$42.A.A$42.A$3.2A10.A25.2A$4.A
10.2A$2.A11.A.A$2.5A14.2A35.2A.A$7.A13.A36.2A.3A$4.3A12.A.A42.A$3.A
15.2A37.2A.3A$3.4A50.A2.2A$.2A3.A3.2A44.A.A$A2.3A4.2A26.A10.A5.A.A.2A
.A$2A.A34.3A7.3A5.A2.A.2A$3.A37.A9.A7.A$3.2A35.2A6.2A.2A5.2A$47.2A.2A
3.A.A2.2A$47.2A.2A3.2A2.A2.A$11.2A35.A2.A8.2A$12.A36.3A$9.3A37.2A$9.A
51.2A$26.2A33.A$26.A.A30.A.A$26.A8.3A21.2A$37.A9.2A$33.3A.A8.A.A$32.A
2.A10.A2.A$31.A2.2A4.2A2.2A2.A23.D$36.A2.2A6.2A21.3D$36.A.A3.A3.A22.D
$33.A2.A.2A2.4A23.2D$33.2A27.A4.2D$63.A3.2D8.D$61.3A11.3D$45.2A27.D$
45.2A27.2D$72.2D$72.2D8.D$80.3D$57.A.2A18.D$55.3A.2A18.2D$54.A22.2C$
55.3A.2A16.2C$57.A.A$57.A.A2.A.2A$58.A.3A.2A$59.A$60.3A.2A$62.A.A$62.
A.A2.A.2A$63.A.3A.2A$64.A16.A$65.3A.2A11.2A$67.A.A11.2A$67.A.A2.A.2A
104.2A2.A$68.A.3A.2A103.A.4A$69.A109.A$70.3A.2A101.2A.7A$72.A.A100.A
2.A.A6.A$72.A.A2.A.2A94.2A3.A.2A2.2A$73.A.3A.2A98.2A.2A7.2A$74.A117.A
$75.3A.2A109.A$77.A.A110.5A$77.A.A2.A.2A42.A51.A13.A$78.A.3A.2A42.3A
48.A.A6.4A$79.A51.A11.A35.A.A6.A2.A$80.3A.2A24.A19.2A9.3A36.A$82.A.A
24.A.A28.A54.2A$82.A.A2.A.2A19.A29.2A10.2A36.2A.A2.A$83.A.3A.2A61.A
37.2A.2A$84.A17.A2.2C43.A.A$85.3A.2A9.A.A2.2C43.2A10.A$87.A.A11.2A8.D
15.2A3.D29.3A$87.A.A2.A.2A13.D.D15.2A2.2D32.A$88.A.3A.2A13.3D18.2D32.
2A13.2A$89.A19.D21.D48.A$90.3A.2A36.D44.3A$92.A.A81.A$92.A.A4.2A50.D
23.A2.2A$93.A6.A48.D.D13.D10.2A2.A54.A2.2A$97.3A49.3D9.2A2.D.D11.2A
54.4A.A$97.A39.2A10.D11.2A2.2D73.A$137.2A94.7A.2A$141.2A89.A6.A.A2.A$
141.A90.2A2.2A.A3.2A$142.3A82.2A7.2A.2A$144.A4.2A3.A72.A$149.A3.A.A
73.A$150.A3.A.A.2A65.5A$151.A4.A.2A65.A13.A$120.A.A26.A.5A72.4A6.A.A$
121.2A25.A.A4.A.2A.A.2A64.A2.A6.A.A$121.A27.A2.2A.A2.A.2A.A75.A$150.
2A.A.2A12.2A52.2A$169.2A52.A2.A.2A$176.2A11.A35.2A.2A$176.2A10.A.A$
188.A.A31.2A$187.2A.3A2.2A25.A$193.A2.A23.A.A$187.2A.3A3.A.A21.2A17.
2A$187.2A.A6.2A40.A$240.3A$242.A5$180.2D2.2A11.D.2A$141.A37.CAD2.2A9.
3D.2A$142.A26.2A7.A.AD13.D.D$140.3A25.A2.A8.A14.D$167.A.2A$167.A$166.
2A$181.2A$181.A$182.3A23.2A$184.A24.A$162.A43.3A$160.3A43.A7.2A$159.A
55.A$159.2A51.3A$212.A4$145.2A.2A$143.A2.A.2A$143.2A$159.A$148.A2.A6.
A.A$148.4A6.A.A$145.A13.A$145.5A$149.A$147.A$147.2A7.2A.2A$152.2A2.2A
.A3.2A$152.A6.A.A2.A$153.7A.2A$160.A$155.4A.A$155.A2.2A!

[confocaloid]

No big improvements yet, but a Bandersnatch rescues the 31x pulse divider:

Code: Select all

x = 176, y = 140, rule = LifeHistory
7.A$7.3A$2A8.A$.A7.2A$.A.A$2.2A$5.2A14.A$5.A.A7.2A3.A.A$5.A9.2A4.A2$
2A8.A$A2.2A4.2A$.2A.A3.2A2.A$10.3A$.3A10.A6.A$.A2.A4.A5.A4.A.A$2.A.A
4.A5.A4.A2.A$3.A6.A10.3A$12.3A$12.A2.2A3.A.2A$14.2A4.2A2.A$14.A8.2A2$
3.A4.2A9.A$2.A.A3.2A7.A.A118.2A$3.A14.2A118.A.A$140.A4.2A$136.4A.2A2.
A2.A$14.2A120.A2.A.A.A.A.2A$14.A124.A.A.A.A$15.3A122.2A.A.A$17.A126.A
$42.D$40.3D87.2A$39.D60.A30.A7.2A$39.2D58.A.A29.A.A5.2A$37.2D60.A.A7.
2A21.2A$37.2D8.D49.3A.2A6.2A$45.3D48.A19.2A$44.D52.3A.2A13.2A38.A$44.
2D53.A.2A53.3A$42.2D115.A$21.2A.2A16.2D8.D105.A.A$22.A.A25.3D89.2A14.
A.A$22.A.A2.A.2A18.D62.A29.A16.A$21.2A.4A.2A18.2D60.A.A29.3A$47.2C61.
A2.A31.A$21.2A.4A.2A16.2C62.2A9.2A$21.2A.A2.A.A92.2A$27.A.A2.A.2A138.
2A$26.2A.4A.2A138.2A$100.2A$26.2A.4A.2A64.2A59.D$26.2A.A2.A.A127.D$
32.A.A2.A.2A113.2A4.3D$31.2A.4A.2A112.A.A$153.A18.2A$31.2A.4A.2A111.
2A7.2A9.A$31.2A.A2.A.A121.2A10.A$37.A.A2.A.2A126.2A$36.2A.4A.2A123.2A
$169.2A.2A$36.2A.4A.2A68.2A56.A$36.2A.A2.A.A69.A54.2A3.A$42.A.A2.A.2A
64.3A50.A2.4A$41.2A.4A.2A66.A49.A.A.A$168.A2.A.2A$41.2A.4A.2A98.2A20.
A.A$41.2A.A2.A.A100.A8.3D8.2A2.A$47.A.A2.A.2A42.A51.A.A8.D5.A.A2.A.A$
46.2A.4A.2A42.3A50.2A7.3D4.2A2.A.A$101.A11.A58.A$46.2A.4A.2A44.2A9.3A
$46.2A.A2.A.A32.2D21.A$52.A.A2.A.2A25.D.D21.2A10.2A$51.2A.4A.2A27.D
33.A15.A$120.A.A15.3A6.2A$51.2A.4A.2A16.2C41.2A19.A6.A$51.2A.A2.A.A
17.2C2.D15.2A3.D37.2A6.A.A$57.A.A2.A.2A13.D.D15.2A2.2D46.2A$56.2A.4A.
2A13.3D18.2D$79.D21.D$56.2A.4A.2A36.D59.2A$56.2A.A2.A.A97.A.A$62.A.A
56.D15.2A3.D21.A$61.2A.2A7.2C44.D.D15.2A2.2D21.2A$72.C2.C43.3D18.2D
11.2D$57.2A14.2C32.2A10.D21.D10.2D$39.2A17.A48.2A33.D10.D$40.A17.A.A
50.2A$39.A19.2A43.2A5.A$39.2A63.A7.3A29.2A$106.A7.A30.A$26.2A58.2A14.
5A35.3A6.A$27.A59.A13.A40.A7.A.A$27.A.A47.2A8.A.A12.3A46.A$28.2A47.2A
9.2A15.A$37.3D2.2A15.D33.2D7.4A$31.2A5.D3.2A15.D.D30.D.D2.2A3.A3.2A
41.A$31.A.A2.3D20.3D32.D2.2A4.3A2.A38.3A$33.A27.D43.A.2A37.A$29.4A72.
A40.2A$28.A75.2A66.2E$28.2A.2A139.E$29.A.A122.2A17.3E$29.A.A20.2A19.
2A21.2A57.A19.E$30.A18.A3.A19.A22.A58.A.2A$49.4A21.3A20.3A44.D2.2A4.
3A2.A$76.A22.A42.D.D2.2A3.A3.2A$49.2A92.2D7.4A$49.A7.2A79.2A15.A$46.
2A.A7.2A78.A.A12.3A$46.2A.A.A42.2A41.A13.A$50.2A42.A24.2A15.2A14.5A$
95.3A6.2A13.A36.A$36.2A59.A6.2A11.A.A34.A$36.2A79.2A10.A24.2A$129.3A$
27.2A.A101.A$27.A.2A5.D54.D39.2A$36.3D29.D21.D55.2A$36.D.D29.3D18.2D
55.A$38.D29.D.D15.2A2.2D51.2A.A$70.D15.2A3.D26.D23.A2.A$116.D.D13.D
10.2A$38.2A76.3D9.2A2.D.D$37.A2.A.A73.D11.2A2.2D$37.2A.A.3A$40.A4.A$
34.2A4.A.3A44.2A$35.A5.2A47.A$32.3A52.3A13.2A3.2A6.2A3.A$32.A54.A16.A
3.A7.A3.A.A$101.3A5.3A5.A3.A.A.2A$59.2A40.A9.A6.A4.A.2A$59.A56.A.5A$
60.3A52.A.A4.A.2A.A.2A$62.A53.A2.2A.A2.A.2A.A$117.2A.A.2A12.2A$136.2A!

Even though for gun-building purposes there might be better approaches, and for any given period there will be period-specific improvements, I guess it just seems attractive to have a universal reusable pulse-dividing component that always works no matter what, for regular and irregular streams, as long as there are at least 43 ticks between successive inputs.

Example 31x pulse division (1 mod 6), although without an output signal...

It's not too painful to get an output signal, at least for anything above 31x. Here's 37x:

Code: Select all

rle

Edit 3:

The odds are actually pretty good that there's a way to get a signal out at the end of each cycle, that needs only one or two input signals to restore it, rather than the current three. Just haven't thought of it yet...

This block keeper can convert the beehive into the block in the "before block pull" location:

Code: Select all

x = 48, y = 53, rule = LifeHistory
19.2C$20.C$20.C.CB$21.2CB$23.3B$23.4B$24.4B$25.4B$26.4B$27.4B$26.8B$
25.10B$24.11B$25.10B12.C$25.13B7.3C$22.17B5.C$21.2A15B6.2C$21.2A14B5.
4B$8.4B2DB3.B3.2B.10B6.3B$7.4BDBD2B.3B4.9B.10B$6.7BD7B3.8B.4BE5B$.2A
29B.4B3E2B$ABDC28B.4BEBE3B$.ACD35BE2B$3.39B$3.37B$3.35B$4.33B$7.31B$
8.30B$9.27B.B2A$10.23B4.BA.A$11.23B6.A$12.3B.18B6.2A$17.17B$17.17B$
16.AB2.13B$15.A.A3.11B$15.2A4.12B$22.7B.4B$22.7B2.4B$22.7B3.4B$22.8B
3.4B$22.B.B2.4B3.4B$23.3B2.4B3.4B$22.B2AB3.4B3.4B$23.2A5.4B3.4B$31.4B
3.4B$32.3B4.3B$34.B2C4.B2C$34.BC.C3.BC.C$37.C6.C$37.2C5.2C!

Two ways to convert the leftover beehive into the block in the "after block pull" location:

Code: Select all

x = 80, y = 26, rule = LifeHistory
10.D39.D$9.2BD37.2BD$9.3DB5.B30.3DB5.B$10.4B3.BAB30.4B3.BAB$11.4B2.AB
A31.4B2.ABA$12.5BABAB31.5BABAB$3.A.2A6.5BA2B22.A.2A6.5BA2B$.3A.2A7.9B
18.3A.2A7.9B$A11.9BDCAB15.A11.9BDCAB$.3A.2A5.9BCDBA16.3A.2A5.9BCDBA$
3.A.A6.10B2AB18.A.A6.10B2AB$3.A.A2.A.2AB.9B20.A.A2.A.2AB.9B$4.A.3AB2A
B3.5B23.A.3AB2AB3.5B$5.A4.B5.5B24.A4.B5.5B$6.3A.2A5.4B3.B21.3A.2A5.4B
3.B$8.A.A6.4B2.2B23.A.A6.4B2.2B$8.A.A7.7B23.A.A7.7B$9.A8.B2D4B24.A8.B
2D4B$18.D2BD2B34.D2BD2B14.2C$19.2DB37.2DB15.2C$78.2C$79.C2$28.C$27.3C
$27.C.2C!

Another way:

Code: Select all

x = 7, y = 5, rule = LifeHistory
DCA$CD.A2.A$.2A3.A$5.A$6.A!

It works, but I could not make it into an actual improvement. Still three gliders to restore:

Code: Select all

x = 222, y = 152, rule = LifeHistory
7.A$7.3A$2A8.A$.A7.2A$.A.A6.3A$2.2A7.3A$10.5A6.A$9.2A3.2A4.A.A$8.3A3.
3A4.A$9.2A3.2A$2A8.5A$A2.2A6.3A$.2A.A7.A2$.3A17.A$.A2.A15.A.A$2.A.A
15.A2.A$3.A17.3A2$12.A7.A.2A$11.3A6.2A2.A$10.5A8.2A$9.2A3.2A105.2A$3.
A4.3A3.3A104.2A12.2A.A.2A21.A$2.A.A4.2A3.2A112.A.2A.A2.A.2A2.A18.3A$
3.A6.5A113.2A.A.2A.A4.A.A16.A9.2A$11.3A122.5A.A17.2A8.A$12.3A117.2A.A
4.A27.A.A$14.2A116.2A.A.A3.A10.2A14.2A$14.A121.A.A3.A9.2A$15.3A8.A
110.A3.2A$17.A6.A.A$25.2A15.D$40.3D$39.D$39.2D84.2D2.2A11.D$37.2C85.D
.D2.2A9.3D$37.2C8.C66.2A10.D13.D.D$45.3C65.A2.A23.D$44.C67.A.2A$44.2C
66.A$35.A.A4.2D67.2A$21.2A.2A10.2A4.2D8.D73.2A$22.A.A11.A13.3D73.A$
22.A.A2.A.2A18.D77.3A28.2A$21.2A.4A.2A18.2D78.A10.2A16.A.A$47.2D90.A.
A18.A$26.2A.2A16.2D90.A20.2A$26.2A.A108.2A$29.A2.A.2A$29.4A.2A$47.A$
31.2A.2A12.A$31.2A.A11.3A97.A2.A.2A$34.A2.A.2A105.4A.A$34.4A.2A110.A.
A$148.2A2.2A$36.2A.2A107.A29.A$36.2A.A109.A26.3A$39.A2.A.2A102.2A25.A
$39.4A.2A129.2A2$41.2A.2A11.A154.A$41.2A.A13.2A75.C47.2A25.3A$44.A2.A
.2A6.2A74.3C48.A24.A$44.4A.2A52.2A27.C51.A.2A21.2A$103.A2.2A24.2C39.D
2.2A4.3A2.A$46.2A.2A53.2A.A63.D.D2.2A3.A3.2A$46.2A.A55.A.A.A62.2D7.4A
32.2A$49.A2.A.2A49.A2.2A2.2A37.A15.2A15.A33.A$49.4A.2A47.3A6.2A35.3A
10.2A2.A.A12.3A34.A.2A$102.A45.A14.A2.A13.A26.D2.2A4.3A2.A$51.2A.2A
46.2A19.D11.2A11.2A11.A2.3A14.5A19.D.D2.2A3.A3.2A$51.2A.A14.A17.2D34.
3D9.2A24.3A21.A20.2D7.4A$54.A2.A.2A6.A.A16.D.D34.D.D38.A18.A17.2A15.A
$54.4A.2A7.2A18.D36.D37.2A18.2A15.A.A12.3A$75.2C101.2A20.A13.A$56.2A.
2A14.2C101.A20.2A14.5A$56.2A.A21.D93.2A.A40.A$59.A2.A.2A13.D.D18.3D
47.D23.A2.A39.A$59.4A.2A13.3D18.D47.D.D13.D10.2A40.2A$79.D20.3D45.3D
9.2A2.D.D$61.2A.2A58.2A22.D11.2A2.2D$62.A.A59.A.A$62.A.A61.A$63.A9.2C
51.2A$72.C2.C$57.2A14.2C73.2A3.A$58.A89.A3.A.A$58.A.A60.2C12.2A12.A3.
A.A.2A$59.2A51.2A7.C.C12.A13.A4.A.2A$112.2A9.C9.3A12.A.5A$40.A82.2C8.
A13.A.A4.A.2A.A.2A$40.3A5.2A98.A2.2A.A2.A.2A.A$43.A4.2A44.2A18.A34.2A
.A.2A12.2A$42.2A33.2A15.2A17.A.A52.2A$77.2A35.A$59.D55.3A$43.2A14.D.D
55.A$43.2A3.2A9.3D35.2A$48.2A11.D35.2A7.D14.2A$107.D13.A$123.A$103.2A
14.5A$104.A13.A$73.2A29.A.A12.3A$41.2A30.A31.2A15.A$42.A23.2A6.3A33.
2D7.4A$42.A.A21.A9.A32.D.D2.2A3.A3.2A$43.2A19.A.A44.D2.2A4.3A2.A$64.
2A56.A.2A$122.A$84.A36.2A$42.2A31.2A5.3A$42.2A31.2A4.A$81.2A30.2A$
113.A$65.D27.2C19.3A$63.D.D14.2A11.C22.A$63.3D9.2A3.2A9.C.C$63.D11.2A
14.2C4$109.2A$109.A24.2A$110.3A6.2A13.A$112.A6.2A11.A.A$55.2A75.2A10.
A$55.A88.3A$56.3A88.A$58.A47.D39.2A$83.D21.D55.2A$83.3D18.2D55.A$83.D
.D15.2A2.2D51.2A.A$85.D15.2A3.D26.D23.A2.A$131.D.D13.D10.2A$131.3D9.
2A2.D.D$131.D11.2A2.2D3$104.2A$105.A$102.3A13.2A3.2A6.2A3.A$102.A16.A
3.A7.A3.A.A$116.3A5.3A5.A3.A.A.2A$116.A9.A6.A4.A.2A$131.A.5A$130.A.A
4.A.2A.A.2A$131.A2.2A.A2.A.2A.A$132.2A.A.2A12.2A$151.2A!

Edit 4 (2023-02-01): this might possibly be easier to restore:

Code: Select all

x = 41, y = 81, rule = LifeHistory
2.A$A.A$.2A14$5.A.2A$3.3A.2A$2.A$3.3A.2A$5.A.A$5.A.A2.A.2A$6.A.3A.2A$
7.A20.2C$8.3A.2A11.E2.2C$10.A.A16.2D$10.A.A2.A.2A9.D2.D$11.A.3A.2A10.
2D$12.A$13.3A.2A$15.A.A$15.A.A$16.A.2A7.2C$18.C7.C2.C9.2C$16.A.C8.C.C
9.C$14.3A.C.C7.C8.C.C$13.A5.2C16.2C$13.2A18.2D$33.2D4$14.2A$15.A$15.A
.A$16.2A6.D.D$24.D.D$24.3D5.2C$32.2C$12.A$11.A.A$12.A5$36.2A$36.2A4$
11.2A$10.A.A$10.A21.2A$9.2A21.A$33.3A$35.A9$23.3D$23.D$22.3D2$22.2A$
22.2A!

[GUYTU6J]

I'm not sure where to post this, but I just found this stable x5 pulse divider (shown attached to a simkin glider gun)

Code: Select all

x = 75, y = 81, rule = B3/S23
9bo$9b3o$12bo$11b2o5$2o5b2o$2o5b2o2$4b2o$4b2o4$20b2o5b2o$18bo8b2o$16b
2o4b2o$16bo6b2o6b2o$16bo2b2o2b3o5b2o$17bob2o17$35bo$36bo$34b3o11$61bo$
59b3o$58bo$58b2o$41bo$41b3o$44bo25b2o$43b2o25bo$67bo3b3o$67b4o3bo$46b
2o24bobo$45bo2bo20b2ob2o$46b2o21b2o$72b2o$73bo$72bo$53b2o17b2o$54bo$
51b3o$51bo11b2o5b2o$62bo2bo4bobo$58b2o3bobo6bo$54b2obobo4bo7b2o$55bobo
9b2o$54bo2b2o8bo$55b2o11b3o$57b2o11bo$57bo$58bo$57b2o!

Congratulations! This is a derivative of Jubjub reflector (itself a derivarive of speed tunnel). Compared with the block factory in Sphenocorona's multipliers, your block factory adds 7 (or minus 6) mod 13 in the multiplying factor. For instance, the original 2 mod 13 family (minimum 15) becomes 9 mod 13 (minimum 9) here:

Code: Select all

x = 64, y = 177, rule = LifeHistory
6.4D18.D4.D2.4D$6.D2.D18.D4.D5.D$6.D2.D18.D4.D5.D$6.4D4.4D3.2D3.3D4.D
2.4D$9.D4.D.D.D.D2.D.D2.D4.D5.D$9.D4.D.D.D.D2.D.D2.D4.D5.D$6.4D4.D.D.
D2.2D3.3D4.D2.4D5$39.4D$8.D6.D23.D2.D$39.D2.D$2.4D2.D.3D2.D.4D2.D2.D.
4D7.4D$2.D.D.D.D.D2.D.D.D.D.D.D2.D.D.D.D9.D$2.D.D.D.D.D2.D.D.D.D.D.D
2.D.D.D.D9.D$2.D.D.D.D.D2.D.D.D.D.D2.3D.D.D.D6.4D23$11.A$11.3A$14.A$
13.2A$13.4B$15.3B$3.B2AB2.B.B2A.4B$3.4A.3B5A10B$2.ABABA4BA4BA10B$2.2A
B3A3B3A2BA10B$3.B.2ABA3BA2B2A10B$5.2ABA4B2A14B$6.BA7B2.13B$6.8B6.10B$
8.7B7.7B$7.10B6.8B$7.13B2.7B2A$8.21B2AB$10.22B.B$10.16B2A5B2A$10.16B
2A5B2A23.4D$11.18B.4B18.A5.D2.D$18.3BA.3B.B2.4B16.3A5.D2.D$19.3BA26.A
8.4D$20.3AB25.2A10.D$21.4B8.2A12.4B10.D$22.4B7.A5.2A5.4B8.4D$23.4B7.
3A.A.A4.4B$24.4B8.A.A5.4B$25.4B8.2AB3.4B$26.4B7.2B3.4B$27.4B7.7B$28.
4B5.7B$29.4B4.7B$30.4B2.9B$31.4B.12B$32.17B$33.17B$32.17B$32.15B$32.
15B$33.16B$35.15B$37.13B$38.12B9.2A$38.12B9.A$38.10B2D2B4.A3.3A$38.
10B2D3B3.4A3.A$39.17B3.B.A.A$41.17B2AB2A$43.15B2A$43.15B3.2A$44.14B4.
A$44.3B2.9B3.A$45.B4.9B2.2A$50.9B$50.9B$50.2B2A3B.B2A$48.3BA2BA2B.BA.
A$47.2A3BABAB5.A$43.2A.A.AB.2BA4B3.2A$44.A.A.2B6.2A$43.A2.2AB7.A$44.
2A2.B8.3A$46.2A11.A$46.A$47.A$46.2A3$9.A$9.3A$12.A$11.2A$11.4B$13.3B$
.4B2.B.3B.4B$.4B.4B2A12B$2A2B2A4BABA12B$2A2BA7BA12B$.B.BABA3B3A12B$3.
2B2A20B$4.9B2.13B$4.8B6.10B$6.7B7.7B$5.10B6.8B$5.13B2.7B2A$6.21B2AB$
8.22B.B$8.16B2A5B2A$8.16B2A5B2A$9.9BA8B.4B$16.3BA.3B.B2.4B$17.3AB$18.
4B.3B$10.2A7.8B$10.A.A7.7B$12.A8.7B$12.2A5.9B$14.AB.12B$12.3A18B.5B
13.4D2.4D$11.A2.B.25B14.D5.D$11.2A3.27B12.D5.D$16.28B8.4D2.4D$15.30B
7.D5.D$14.32B6.D5.D$13.4B2.28B5.4D2.4D$12.4B4.27B$11.4B5.26B$10.4B6.
4B2.18B$10.3B8.3B2.5B2D11B$8.2A2B10.B4.4B2D11B$7.A.AB16.18B$7.A21.16B
11.2A$6.2A24.15B9.A$35.10B2D2B4.A3.3A$35.10B2D3B3.4A3.A$36.17B3.B.A.A
$38.17B2AB2A$40.15B2A$40.15B3.2A$41.14B4.A$41.3B2.9B3.A$42.B4.9B2.2A$
47.9B$47.9B$47.2B2A3B.B2A$45.3BA2BA2B.BA.A$44.2A3BABAB5.A$40.2A.A.AB.
2BA4B3.2A$41.A.A.2B6.2A$40.A2.2AB7.A$41.2A2.B8.3A$43.2A11.A$43.A$44.A
$43.2A!

[Entity Valkyrie 2]

Just trying to make a thing with the P1 crystal: (Herschel output)

Code: Select all

x = 77, y = 95, rule = B3/S23
19bo$17b3o$16bo$16b2o$28bo$26b2o$28b2o$27bo$33b2o$33bo$31bobo$31b2o$
20b2o$19bobo$19bo$19b2obo$2b2o17b2o$bobo$bo$2o7$5bo$5bobo$4bobo$6bo12$
34b2o$34b2o2$7b2o5bo$7bo6b3o$4b2obo9bo$4b2obob4o3b2o$8bo$11bo$11bobo2$
9bobo$2b2ob2o4bo$2b2obo$5bo3b2o4bo$5bob2o4b3o$6bo5bo$12b2o$28b2o$28bob
o$31bobob2o$21b2o9b2ob2o$21b2o$32b2ob2o$32b2obo$35bo2bob2o$35b4ob2o2$
37b2ob2o$37b2obo$40bo2bob2o25b2o$40b4ob2o25bo$69bo3b3o$42b2ob2o22b4o3b
o$42b2obo28bobo$45bo2bob2o19b2ob2o$45b4ob2o19b2o$74b2o$20b3o24b2ob2o
23bo$20bo26b2obo23bo$19b2o29bo2bob2o17b2o$50b4ob2o2$52b2ob2o8b2o5b2o$
53bobo8bo2bo4bobo$52bo2bo4b2o3bobo6bo$52b2o2b2obobo4bo7b2o$57bobo9b2o$
24b2o30bo2b2o8bo$23bo2bo30b2o11b3o$24b2o33b2o11bo$59bo$60bo$59b2o!

Note: the p3 oscillator is only used to delete a blinker and works at any timing.