Larger than Life

[TheWayOfTheCon]

Some more discoveries in the rule I've talked about before (HighPottery):
Period-27 from D8_1.

Code: Select all

x = 41, y = 41, rule = R2,C2,S4,6-9,20,B7-9,18
19bobo2$19b3o8$16bo7bo$16b2o5b2o$14b2o9b2o$14b2o9b2o$12b2o13b2o$12b2o
13b2o$10b2o17b2o$11bo17bo2$obo35bobo$2bo35bo$obo35bobo2$11bo17bo$10b2o
17b2o$12b2o13b2o$12b2o13b2o$14b2o9b2o$14b2o9b2o$16b2o5b2o$16bo7bo8$19b
3o2$19bobo!

And a very sparky, very expansive period-100 from C2_1.

Code: Select all

x = 13, y = 5, rule = R2,C2,S4,6-9,20,B7-9,18
b2o4b3o$4o6b2o$2ob2o3b2ob2o$b2o6b4o$3b3o4b2o!

I've been trying to gun this for some time. I did find a reaction between two of them that makes a small methuselah/common evolutionary sequence (which itself releases a spaceship, but there isn't enough time and it wouldn't go the right way anyways) which moves away from the oscillators, so maybe I can have another copy turn that into a spaceship.

Code: Select all

x = 20, y = 37, rule = R2,C2,S4,6-9,20,B7-9,18
16b4o$16bob2o$15b2o2bo$15b2obo$16b2o$16b3o$16b3o$16b3o$17b2o$16bob2o$
15bo2b2o$15b2obo$15b4o20$b2o4b3o$4o6b2o$2ob2o3b2ob2o$b2o6b4o$3b3o4b2o
!
#C [[ STOP 47 ]]

Speaking of guns, a few days ago (August 9, 2026) yyh_baboon made guns for a c/6 and c/2, the former based off a c/3d-to-c/6o converter, and the latter based off of a synthesis. Both are based off of the original four p160s gun I posted to this thread. It would be neat to find a "simple" gun for the c/6 since its much more common than the c/2.

C/6 gun:

Code: Select all

 x = 114, y = 98, rule = R2,C2,S4,6-9,20,B7-9,18
90b3o$88b2o3bo$94bo$87bo7bo$87bo$87bo3b2o3bo$79b3o6bo2bo4bo$78b2o2bo6b
o5bo$77bo5bo5bo5bo$84bo$76bo6b2o6b4o$76bo4bob2o$76bo6b2o$77bo4b3o$78b
2o2bo$80bobo$80bo2$42b3o$41b4o3b4o$40b2ob2o3b5o13bo$40b2o2bob4o2b2o$39b
2o2bo4bo5bo19bo$39b4o5b2o4bo19b4o$39b4o7bo3bo19b2o3bo$54bo17b2o6bo$41b
o7bo14bo6b2o8bo$49bo3bo10b7o10bo$49bo3bo10b3o$49b4o12b2o11b3o$65b2o9b
2o$73b2o$66bo5bo$66bo4bo$66b2o2bo$68bo10$101b3o$100b4o3b4o$73bo25b2ob
2o3b5o$71bobo25b2o2bob4o2b2o$71bo2b2o22b2o2bo4bo5bo$69b3o4bo21b4o5b2o
4bo$69b2o6bo20b4o7bo3bo$69b2obo4bo35bo$59b4o6b2o6bo22bo7bo$69bo38bo3b
o$58bo5bo5bo5bo31bo3bo$58bo5bo6bo2b2o32b4o$57bo4bo2bo6b3o$57bo3b2o3bo
$66bo$58bo7bo$59bo$60bo3b2o$61b3o9$17bo$15b2obo$14b2o3bo$15b2obo$16b3o
$17bo4$28b2o$27bob2o$27bo2bo$27bob2o$28b2o4$4b2o$4b2obo$4b4o$5b4o$2ob
5o$o3b3obo$2ob4o$b5o$b3o!

c/2 gun!

Code: Select all

 x = 403, y = 229, rule = R2,C2,S4,6-9,20,B7-9,18
183b4o$181bob2ob3ob2o$180bo6bo3b2o$180bo5b2o5bo$150b3o27bo5b2o5bo$151b
o28bo5bob3o2bo$28b3o118bobobo27bo4bo3bo2bo$23bo3bo3bo150bob3o3b3o$21b
3o3bo3b2o150b4o2b3o$20bo3b3o5bo29bobo84bob2o32bo3b2o$20bo3bo7bo30b2o85b
2ob2o16b2o14b2o$20bo4b3o3b2o29b2o86b4o17b2o$20bo3b4o3bo29b3o86b3o17b4o
$21bo2b5obo29b3o3bo84b2o17b4o$22b7o31b3o$25b2o33bobobo$42b2obo14b5o$41b
2o3bo12bob3o103bo$47bo118b3o$41bo124b4o$40b3o5bo117b3o2$43bo5bo$49bo$
44bo3bo$44b2o2bo$45b3o5$209b3o$210bo$175b2o31bobobo$173b2o3bo$172b3o2b
4o$3bobo165b3o3b3obo26bob2o$4b2o164bo2bo3bo4bo26b2ob2o$3b2o165bo2b3ob
o5bo25b4o$2b3o165bo5b2o5bo25b3o$b3o3bo29b2o131bo5b2o5bo26b2o$b3o31b7o
129b2o3bo6bo$bobobo27bob5o2bo129b2ob3ob2obo$b5o26bo3b4o3bo133b4o$ob3o
26b2o3b3o4bo$31bo7bo3bo$31bo5b3o3bo$31b2o3bo3b3o$32bo3bo3bo$33b3o21$113b
3o$112b2o2bo$112b2o2bo$113b4o$114b2o$97b3o$96bo2b2o$96bo3bo$96b2ob2o$
97b3o12$399b2o$398b3o$398b4o$398b2ob2o$397bob2o2$139bo25b2o25b2o25bo25b
2o25b2o25bo25b2o25b2o25bo$137b2obo23b2obo22b2o2bo22b2obo23b2obo22b2o2b
o22b2obo23b2obo22b2o2bo22b2obo16bobobo$137b2o2bo22bo2bo22b2o2bo22b2o2b
o22bo2bo22b2o2bo22b2o2bo22bo2bo22b2o2bo22b2o2bo17bo$137b2obo23b2obo22b
2o2bo22b2obo23b2obo22b2o2bo22b2obo23b2obo22b2o2bo22b2obo17b3o$139bo25b
2o25b2o25bo25b2o25b2o25bo25b2o25b2o25bo26$143b2o150bob4o$142b4o151b5o
$141b2o2bo148b5o2b3o$141b2o2bo152bo2b3o49b2o$142b3o156bob2o47b4o$299b
o2b2o48bo2b2o$303b4o45bo2b2o$303b2o48b3o$302b2ob3o23b2obo$302bo2b3o22b
o4bo$302bo2b2o23bo4bo$302bo2b2o22b2o4bo$302bo2b2o23b7o$301bo3b2o21b4o
$302bobo$301b3o24b2o$303bo2$315b2o$314b3o$314bob2o$313bo3bo$313b4o$315b
o$322bo$321b4o$320bo3bo$320b2obo30bob4o$321b3o32b5o$321b2o30b5o2b3o$357b
o2b3o$360bob2o$308b2o48bo2b2o$362b4o$306b4o52b2o$301b7o53b2ob3o$302bo
4b2o52bo2b3o$206bo2bo92bo4bo53bo2b2o$203b3o5bo90bo4bo53bo2b2o$202b5o2b
3o91bob2o54bo2b2o$202b3obo4bo148bo3b2o$204b2o3bo151bobo$205bo154b3o$362b
o11$195b3o$195b4o$195b3o$196bo$175b4o23b2o$174bo4bo22b4o$173b2o4b2o21b
4o$173bo3b5o20b2o$177bo2b2o$173bo3bo4bo$173b4o5bo$172b2ob6o$172bo6b3o
$172b2o5b2o$172b2o6bo29b4o$179bo29bo4bo$173bo4bo29bo$174b4o29bo6b2o$207b
2o5b2o$206b3o6bo$207b6ob2o$205bo5b4o$205bo4bo3bo$206b2o2bo$206b5o3bo$
207b2o4b2o$208bo4bo$209b4o15$179bo2bo$176b3o5bo$175b5o2b3o$175b3obo4b
o$177b2o3bo$178bo!

Here's an eater for the methuselah I talk about above:

Code: Select all

x = 13, y = 16, rule = R2,C2,S4,6-9,20,B7-9,18
10b3o$10bobo$10bobo$10b3o8$3o$3o$3o$3o$o!

Because the first pattern it releases is a spaceship, we could also potentially hassle the methuselah to make a c/3d gun, almost like a Quetzal.

All catalysis reactions I've found so far:

Code: Select all

x = 44, y = 17, rule = R2,C2,S4,6-9,20,B7-9,18
o8b2o5bo2bo$34bo6b2o$4o4b4o4b4o4b4o4b4o4b4o$o2bo4bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo$4o4b4o4b4o4b5o3b4o4b4o8$b2o2$3o4bobobo$3o6bobo$3o4bobobo!

Like I say, that hollow rectangle is just a superb eater.

Could this rule be threadworthy, or is there not enough to justify that yet?

[yyh_baboon]

I think it’s worthy for a thread
This rule seems like the first LtL with stable catalysts.
LtL rules are often underlooked (except some exceptions like Bosco) , so maybe it’s time to research in some LtL rule

[TheWayOfTheCon]

I think it’s worthy for a thread
This rule seems like the first LtL with stable catalysts.
LtL rules are often underlooked (except some exceptions like Bosco) , so maybe it’s time to research in some LtL rule

Alright, I'll get to work on making the thread.

[g0t0]

How is the convolution step implemented? If the neighbourhood is a n-by-n square, you can first perform a convolution by a 1-by-n rectangle, followed by a convolution by a n-by-1 rectangle. So you only have to do ~ 2n additions instead of ~ n^2 additions per cell.

Also, if n is composite, you can get a further speedup. For example, if n = 15, you can replace the convolution by:

Code: Select all

***************

with two successive convolutions by each of:

Code: Select all

*****

Code: Select all

*....*....*

For large neighbourhoods which don't easily 'factorise' in this manner, such as a circular neighbourhood, then an FFT (over F_p for large p) is probably the way to go.

What about 2D prefix sum?
https://en.oi-wiki.org/basic/prefix-sum ... prefix-sum