Bespoke Oscillators/Periodic Catalysts

For discussion of specific patterns or specific families of patterns, both newly-discovered and well-known.
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Kazyan
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Bespoke Oscillators/Periodic Catalysts

Post by Kazyan » September 17th, 2021, 11:12 pm

Sparking oscillators have been used to modify reactions since time immemorial +/- a few generations, but recently, there has been growing interest in a new kind of oscillator that behaves more like a catalyst than a dot-dispenser. This thread is for those.

To start things off, in the p54 gun, a variant of this p3 catalyst is used. A p1 catalyst exists that does the same thing, but it doesn't fit due to clearance issues. These versions of the catalyst are by Scorbie:

Code: Select all

x = 74, y = 26, rule = B3/S23
5bo3bo25bo3bo25bo3bo$6b3o27b3o27b3o2$2b2o7b2o$2bo2b2ob2o2bo22b2ob2o25b
2ob2o$3b2obobob2o23b2ob2o25b2ob2o$6bobo$b5o3b5o21b2o28b2o$o2bo7bo2bo
18b3ob2o25bob2o2b2o$2o11b2o17bo4bo2bo29bobo$33b3ob4o21bo3b5obo$35bobo
24bob2o2bo2bo$37bob2o22bobo$36b2ob2o27bo$67bo2b2o$66b2o3bo$64b3ob3o2$
69b2o$68b2obo$67bobobo$67b2o2b2o$66bo2bobo$65bo3bo2bo$66bo3bobo$69b2ob
2o!
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Scorbie
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Re: Bespoke Oscillators/Periodic Catalysts

Post by Scorbie » September 17th, 2021, 11:17 pm

N.B. the p3 has a gazillion variants that vary in occupying space, so a tight weld should benefit from a bespoke oscillator search.
The p4 search is reluctant to give a small solution. Here's another one that's big:

Code: Select all

x = 12, y = 18, rule = B3/S23
4b2ob2o$4b2ob2o$6bo$4b3o$4b3o3bo$bo2bo2b4o$b3o$6b5o$b6ob2obo$o7bobo$6o
bobo$5bobob2o$4obo$o5b2ob2o$bo3bobo2bo$2bo2bobobo$3bobob2o$4bo!

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wwei47
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Re: Bespoke Oscillators/Periodic Catalysts

Post by wwei47 » September 17th, 2021, 11:26 pm

Scorbie wrote:
September 17th, 2021, 11:17 pm
The p4 search is reluctant to give a small solution. Here's another one that's big:

Code: Select all

x = 12, y = 18, rule = B3/S23
4b2ob2o$4b2ob2o$6bo$4b3o$4b3o3bo$bo2bo2b4o$b3o$6b5o$b6ob2obo$o7bobo$6o
bobo$5bobob2o$4obo$o5b2ob2o$bo3bobo2bo$2bo2bobobo$3bobob2o$4bo!
Smaller (by you!):

Code: Select all

x = 15, y = 13, rule = Life
5b2ob2o$b2o3bobo3b2o$obo9bobo$o13bo$b4o5b4o$5b5o$b3obo3bob3o$o2bobo3b
obo2bo$o6bo6bo$b13o2$3b4ob4o$3bo2bobo2bo!
https://www.conwaylife.com/forums/viewt ... sed#p72664
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Scorbie
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Re: Bespoke Oscillators/Periodic Catalysts

Post by Scorbie » September 18th, 2021, 1:22 am

Here's a p5 variant, thanks to wwei pointing out an alternative frontend that fits better towards odd-symmetric searching

Code: Select all

x = 19, y = 30, rule = B3/S23
7b2ob2o$4bo2b2ob2o2bo$2b5o5b5o$bo4b7o4bo$2b5ob3ob5o2$4obo2bobo2bob4o$o
3b2o3bo3b2o3bo$2bo5bobo5bo$b5o3bo3b5o$5bo7bo$b2ob2o3bo3b2ob2o$bo2b5ob
5o2bo$2b2o2bobobobo2b2o$4bob3ob3obo$2b2o3b2ob2o3b2o$3bobobo3bobobo$2bo
2b2o5b2o2bo$2b2o5bo5b2o$8b3o$7bobobo$5b3o3b3o$4bo9bo$3bobo7bobo$2bo2bo
bo3bobo2bo$2b2o2b2o3b2o2b2o$7bo3bo2$6b2o3b2o$6b2o3b2o!
Edit: Wider but shorter one:

Code: Select all

x = 21, y = 21, rule = B3/S23
8b2ob2o$5bo2b2ob2o2bo$3b5o5b5o$2bo4b7o4bo$o2b5ob3ob5o2bo$2obo13bob2o$
3bob2o2bobo2b2obo$2o2bobo3bo3bobo2b2o$ob2o3b2obob2o3b2obo$2bo5b5o5bo$
2bo2b11o2bo$b2obo11bob2o$o2bo13bo2bo$2obobo4bo4bobob2o$bob2o2b3ob3o2b
2obo$bobobo2bo3bo2bobobo$2obob3obobob3obob2o$2bobo3b2ob2o3bobo$2bo2b2o
7b2o2bo$3bobob3ob3obobo$4bo4bobo4bo!
Last edited by Scorbie on September 18th, 2021, 12:37 pm, edited 1 time in total.

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Re: Bespoke Oscillators/Periodic Catalysts

Post by GUYTU6J » September 18th, 2021, 5:19 am

Be aware that there are two kinds of periodic catalysts, depending on whether they are phase-shifted or not when catalysing a reaction.
As for what problems could be solved under two schemes respectively, think about p2 bumper or p3 bouncer for the no-phase-shifting case, and "p2" or "p3" supports for the long known p47 wick...

Code: Select all

x = 43, y = 21, rule = B3/S23
2o39b2o$2o16b3ob3o16b2o$2b2o14bobobobo14b2o$2b2o13bo2bobo2bo13b2o$19b
o3bo$4b4o7b2o2bo3bo2b2o7b4o$3b2o2bo6bo2bo7bo2bo6bo2b2o$2b2o2bo7bobo9b
obo7bo2b2o$3bo2bo8bo11bo8bo2bo$4b2o31b2o2$4b2o31b2o$3bo2bo8bo11bo8bo2b
o$2b2o2bo7bobo9bobo7bo2b2o$3b2o2bo6bo2bo7bo2bo6bo2b2o$4b4o7b2o2bo3bo2b
2o7b4o$19bo3bo$2b2o13bo2bobo2bo13b2o$2b2o14bobobobo14b2o$2o16b3ob3o16b
2o$2o39b2o!
...and the p41 wick (showing one of the many possibilities)...
wwei23 wrote:
October 9th, 2020, 4:12 pm
EDIT: P41 wick near-miss

Code: Select all

x = 17, y = 45, rule = Life
5bo5bo$4bobo3bobo$4bobo3bobo$3b2ob2ob2ob2o2$bo13bo$obo11bobo$bo13bo3$
4b3o3b3o$4bo2bobo2bo$2bo4bobo4bo$2bo11bo$6b2ob2o$6bo3bo$3b2o7b2o$2b3o
7b3o$4bo7bo$5b2o3b2o$b2o3bo3bo3b2o$b3obo5bob3o$o15bo$b3obo5bob3o$b2o3b
o3bo3b2o$5b2o3b2o$4bo7bo$2b3o7b3o$3b2o7b2o$6bo3bo$6b2ob2o$2bo11bo$2bo
4bobo4bo$4bo2bobo2bo$4b3o3b3o3$bo13bo$obo11bobo$bo13bo2$3b2ob2ob2ob2o$
4bobo3bobo$4bobo3bobo$5bo5bo!
...and the p43 glider gun...
goldenratio wrote:
April 15th, 2021, 11:09 am
Crossposting this absurdly close p43 gun partial:

Code: Select all

x = 29, y = 37, rule = B3/S23
4bo$3bobo$3bobo$b3ob2o$o$b3ob2o$3bob2o5$21b2o$2o19bo$2o11b3o3bobo$12b
o3bo2b2o$11bo5bo$11bo5bo$11bo5bo$12bo3bo$13b3o4$9b2o$9b2o$7b2o9b2o$7b
2o8bo2bo2b2o$17bobo4bo2bo$18bo5bobobo$21b2obo2bo$21bo2bo$18bo4bo$18b5o
2$20bo$19bobo$20bo!
Unfortunately it doesn't seem like any stable catalysts exist to replace the beacon, so we'll have to use something like a p3 block-faced catalyst which rephases when it's hit.
for the phase-shifting case.
Best wishes to our brave taikonauts on Shenzhou 13!

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Scorbie
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Re: Bespoke Oscillators/Periodic Catalysts

Post by Scorbie » September 18th, 2021, 6:25 am

GUYTU6J wrote:
September 18th, 2021, 5:19 am
Be aware that there are two kinds of periodic catalysts, depending on whether they are phase-shifted or not when catalysing a reaction.
Good point; I think phase-shifting is interesting enough that there were (and IMHO should be) descriptions talking that the catalyst is phase-shifted.
Also with the description and the phase-shifting being uncommon means I haven't seen any confusion regarding this, which is a good thing.

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Kazyan
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Re: Bespoke Oscillators/Periodic Catalysts

Post by Kazyan » September 18th, 2021, 2:11 pm

Here's a p3 non-phase-shifting catalyst, demonstrated on this Herschel descendant:

Code: Select all

x = 45, y = 17, rule = B3/S23
4bo29bo$2b3o27b3o$bo4bo24bo4bo$o3b4o22bo3b4o$4b2ob2o25b2ob2o$bo5bo3b2o
bo2bo13bo5bo$2bo2b2o5bob4o14bo2b2o4b2o$3bo7bo21bo7bobo$11b9o23bo$12bo
7bo22b2o$11b2o3b2obobo$13b5o3bo$11b2obo4b2o$14b4o$13bo4b5o$14b3o2bo3bo
$16b2o4b2o!
Tanner Jacobi
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Scorbie
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Re: Bespoke Oscillators/Periodic Catalysts

Post by Scorbie » September 18th, 2021, 9:53 pm

Kazyan wrote:
September 18th, 2021, 2:11 pm
Here's a p3 non-phase-shifting catalyst, demonstrated on this Herschel descendant:

Code: Select all

x = 45, y = 17, rule = B3/S23
4bo29bo$2b3o27b3o$bo4bo24bo4bo$o3b4o22bo3b4o$4b2ob2o25b2ob2o$bo5bo3b2o
bo2bo13bo5bo$2bo2b2o5bob4o14bo2b2o4b2o$3bo7bo21bo7bobo$11b9o23bo$12bo
7bo22b2o$11b2o3b2obobo$13b5o3bo$11b2obo4b2o$14b4o$13bo4b5o$14b3o2bo3bo
$16b2o4b2o!
Reduction:

Code: Select all

x = 32, y = 13, rule = B3/S23
bo19bo$bo19bo$bob2ob2o13bob2ob2o$o3bobo13bo3bobobo$3bo2bobo14bo2bobo$
3bobob4o12bobob2ob2o$4bo6bo12bo4bobo$3b2ob2ob2o12b2ob2obo$5bobobo14bo
2bobo$3b2obo2bo14b3o2b2o$6bobo17bobo$5b2ob2o16bobo$27bo!
Failed to find a p4 version of that.

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Kazyan
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Re: Bespoke Oscillators/Periodic Catalysts

Post by Kazyan » September 19th, 2021, 10:45 am

p3 glider eater with a slightly different mechanism than the TWIT:

Code: Select all

x = 33, y = 20, rule = LifeHistory
6.A$5.A.A$3.3A.A$2.A4.2A$.A.AB2A$.A.A.B.4A$2A.ABA2B.A.A$.AB2.A2.A2.A$
BA3.2A3B.2A18.2A$BA.3A2B2A.A19.A$.AB2AB2.2A.A17.A.A$6.B2A.A17.A.A$7.A
BA14.2A3.A$8.D15.2A2.D4$6.2A18.2A$5.A.A17.A.A$7.A19.A!
This may be useful for hasslers.
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Re: Bespoke Oscillators/Periodic Catalysts

Post by Sokwe » September 19th, 2021, 3:05 pm

What p2 catalysts do we have? I can only think of these two:

Code: Select all

x = 34, y = 16, rule = B3/S23
24b3o$22bo$22bo3bo5bo$22bobo5b2o$24bo2b2o3b2o$26bo4bo2$3bo$bobo4b3o17b
3o$o4bo2bo19bo$5obo$5bo$2b2o$2bo$obo$2o!
The p2 on the left is essentially the catalyst used in Noam Elkies' original p22 oscillator. The catalysis shown here was noted by A for awesome. Candlefrobra can perform the same catalysis at p3:

Code: Select all

x = 14, y = 5, rule = B3/S23
4b2o5b3o$2obob4o2bo$2obo2b2obo$3bo4bo$3b2o!
The p2 on the right is from the failed p2 bumper by Goldtiger997.
-Matthias Merzenich

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Re: Bespoke Oscillators/Periodic Catalysts

Post by hotdogPi » September 19th, 2021, 3:13 pm

Killer toads is p2.
User:HotdogPi/My discoveries

Periods discovered: 6,8,10-16,18,20,21G,22,24,25,27-31,32SG,35,36,40,42,45,48,50,54G,55G,57G,60,63-66,70,74S,75,76S,84,96S,100,117G,120,126,128S,138,147,156,196S,217,486,576

S: SKOP
G: gun

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Re: Bespoke Oscillators/Periodic Catalysts

Post by wwei47 » September 19th, 2021, 7:48 pm

Sometimes you can have a singular killer toad.

Code: Select all

x = 23, y = 13, rule = B3/S23
2o$obo$b2o2$7b3o$7bo2bo$8bobo$9bo2$20bo$19bo2bo$19bo2bo$21bo!
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Re: Bespoke Oscillators/Periodic Catalysts

Post by GUYTU6J » September 19th, 2021, 10:06 pm

Sokwe wrote:
September 19th, 2021, 3:05 pm
What p2 catalysts do we have? ...
How about the supports for p26 queen bee shuttle or the LWSS eater variant? Are they too specific to apply elsewhere?
Sokwe wrote:
February 8th, 2021, 7:32 am
... If anyone wants to try, they could use this variant with better clearance around the queen bee:

Code: Select all

x = 41, y = 18, rule = B3/S23
13bo13bo$12bobo11bobo$9bo2bo2bo9bob2o2bo$9b3o4bo7bobo2b3o$12b3obo7bob
2o$7b5obobo9bo3b5o$6bo6bo13bobo4bo$5bobo2bo2b5obobob8o2bobo$5bob4obo3b
ob2ob2obo5bo2bobo$3bobobo2bo3bo11bo3bo2bobobo$3b2o2bo2bo2b3o9b4ob4o2b
2o$7bo2b3o4b2o11bo2bo$b6o4bobo5bo7bo6b6o$bo2bo4bo2bo7bo5bobobo5bo2bo$
2bo6bo3b2obo3bo6bo3b2o$8bo11bo16bobo$obobobo10bobo13bobo4bo$2o4bo11bo
16bo3b2o!
Sokwe wrote:
December 21st, 2019, 9:04 pm
Little-known fact about this LWSS eater: one of the blocks can be replaced with a spark coil.

Code: Select all

x = 15, y = 12, rule = B3/S23
10b2ob2o$10bo3bo$11b3o3$b4o6b3o$o3bo5bo3bo$4bo5b2ob2o$o2bo2$9b2o$9b2o!
This was found in a Bellman search several years ago. As I recall, the search gave a result that couldn't be completed as a still life, but I noticed that it could be stabilized at p2, and miraculously it still worked as an eater.
---

Also, is there any way to search for possible phase-shifting p2 and p3 catalysts, for the sake of prime periods?
Best wishes to our brave taikonauts on Shenzhou 13!

熠熠种花 - Glimmering Garden

China - The Atomic Era

●━━━━━━━━────── 03:19
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Bullet51
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Re: Bespoke Oscillators/Periodic Catalysts

Post by Bullet51 » September 19th, 2021, 11:51 pm

GUYTU6J wrote:
September 19th, 2021, 10:06 pm
Also, is there any way to search for possible phase-shifting p2 and p3 catalysts, for the sake of prime periods?
There is the example of a period-(2n+1) blinker rephaser:
Bullet51 wrote:
November 13th, 2019, 12:14 am
I would like to propose the blinker+eater phase-changing reaction featured in 50P35, Pre-pulsar shuttle 47, and the recently discovered P13 oscillator, with an example catalysis:

Code: Select all

x = 19, y = 7, rule = B3/S23
11b3o3b2o$5b3o3bobo2b2o$11b3o2b3o$2b2o$bobo$bo$2o!
It may be beneficial to gather more data about it, and work out the general form of the catalyzing reaction.
Not sure if there are more period-(2n+1) catalyses featuring blinker rephrasing. A possible way may be running a Scorbie-like search on catalyst + blinker constellations and find out which has the highest catalyzing power.

No period-(3n+1) or (3n+2) catalysts that rephase a period-3 oscillator are known.
Still drifting.

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Re: Bespoke Oscillators/Periodic Catalysts

Post by Scorbie » September 20th, 2021, 6:36 am

The bottom two p4 t-noses can act as a block catalyst:
https://www.conwaylife.com/forums/viewt ... wer#p85342

Code: Select all

x = 22, y = 15, rule = B3/S23
15b2ob2o$11b2obobobo2bo$11bob2o3bob2o$15b2obo$12b3o2b2o$11bobobo$6bo4b
o3b4o$5b3o2b2o6bo$5b5o6bobob2o$5bo4b3o3bobob2o$o2b2ob2o2b2o3bobo$3b2ob
2o5b2o$2o$bo$o!
Edit: A dump of related p4s

Code: Select all

x = 43, y = 16, rule = B3/S23
8b2o2b2o19b2o$5bo2b2o2b2o2bo16b2o$3b5o6b5o18bo$2bo4b8o4bo13b2o2b3o$bo
2b4ob4ob4o2bo12b2o2bo$b3o14b3o14b2o$4b3obo4bob3o17b3o$3bo2bobo4bobo2bo
12b2o4bo$3bob3o6b3obo13bo3b2o$2obobo4b2o4bobob2o10bobobo2b2o$bo2b2o3bo
2bo3b2o2bo9b2obob2o2bobo$bo5bo2b2o2bo5bo8bobo9bo$2b8o2b8o9bobo9b2o$4bo
5b2o5bo10b2ob2o$6bo2bo2bo2bo$5b2o3b2o3b2o!

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Kazyan
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Re: Bespoke Oscillators/Periodic Catalysts

Post by Kazyan » September 21st, 2021, 12:34 am

Sokwe wrote:
September 19th, 2021, 3:05 pm
What p2 catalysts do we have? I can only think of these two:
GUYTU6J wrote:
September 19th, 2021, 10:06 pm
Also, is there any way to search for possible phase-shifting p2 and p3 catalysts, for the sake of prime periods?
Some observations that are relevant to these questions:

- p2 catalysts are apparently harder to look for, according to LLS. I suspect that this is because p3 oscillators can use rotors with overpopulation deaths at the forefront of the reaction site, but p2 basically cannot. p2 should still be viable for supporting the backends of Bellman-like catalysts with p1 frontends, though.

- For phase-shifting catalysts, they can't use their full period for backend support. Shifted p2 and p3 only work if the entire rotor shifts, after all. If p4 is shifted by 2 generations, it still gets to have p2 backend support.

- LLS is can find p3 catalysts with a narrow scope, but we don't actually have a tool that is specialized for periodic catalysts. More-clever use of LLS can probably find better catalysts than I've cooked up so far, though.
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Re: Bespoke Oscillators/Periodic Catalysts

Post by ihatecorderships » September 22nd, 2021, 3:32 pm

There's the blinker-rephasing catalyst from 50P35:

Code: Select all

x = 16, y = 12, rule = B3/S23
$14b2o$14bo$3bo8bobo$2b3o7b2o$bobobo$3ob3ob3o$bobobo$2b3o7b2o$3bo8bob
o$bo12bo$bo12b2o!


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