Extended Life Extensions

[Antonin Duda]

I'm sorry WHAT

Code: Select all

x = 13, y = 13, rule = StateInvestigator
3.C5.C$C11.C$5.3A$5.A.A$5.3A4$5.3A$5.A.A$5.3A$C11.C$3.C5.C!

[hotcrystal0]

3-cell 180° reflector which can make oscillators of period 30+8n:

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x = 56, y = 11, rule = StateInvestigator
5.E19.E12.E12.E$2.Q19.Q12.Q12.Q$25.A.C$24.2A13.A.C$24.A.A11.2A13.A.C$
38.A.A11.2A$C19.C12.C12.C5.A.A$8.3A14.Q$8.A13.E16.Q$9.A26.E16.Q$50.E!

[b-engine]

Novelty(?):

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x = 17, y = 17, rule = B3/S23Investigator
14.A2B2$13.AB2$15.BA2$13.AB2$15.BA2$13.AB2$15.BA$2.A3.A3.A$A.B3.B3.B3.
B$B3.B3.B3.B$B3.A3.A3.A!

[get_Snacked]

Novelty(?):

Code: Select all

x = 17, y = 17, rule = B3/S23Investigator
14.A2B2$13.AB2$15.BA2$13.AB2$15.BA2$13.AB2$15.BA$2.A3.A3.A$A.B3.B3.B3.
B$B3.B3.B3.B$B3.A3.A3.A!

no, settles at a bit above 50K generations

[hotcrystal0]

“speed tunnel” with repeat time 51:

Code: Select all

x = 40, y = 22, rule = StateInvestigator
21.E$18.Q5$14.2B$24.3A$23.EA$23.E.A2$A11.2A10.E$3A9.2A$2.A$2.A2$20.A$
19.D.D$19.D.DE$19.C18.A$37.2A$37.A.A!

[Antonin Duda]

HWSS to LWSS+Glider Splitter (It acts like a heisenburp):

Code: Select all

x = 18, y = 10, rule = StateInvestigator
7.C3.DC$12.E$12.D.C$12.D2$2.2A9.C3.C$A4.A$6.A$A5.A$.6A!

It can be used with a Standard spaceship to HWSS Converter by hotcrystal0 (Ability to convert gliders as well realized by C_R_116) to create an extensible gun with periods 12n+192

Code: Select all

x = 30, y = 16, rule = StateInvestigator
8.C$C$12.2B3$19.C3.DC$24.E$.E4.E17.D.C$.E22.D$.R$2.2A10.2A9.C3.C$.E2.
A7.A4.A$.D3A13.A$.D10.A5.A$.E2DA8.6A$3.2EDE!

edit: pasted the wrong thing on accident
edit 2: it's not 8n+196, but 12n+192, sorry

[hotcrystal0]

3-cell G-to-H with a repeat time of 48:

Code: Select all

x = 21, y = 26, rule = B3/S23Investigator
Q2$E$Q8$6.3A$6.A$7.A10$18.3A$18.A$19.A!

It is used in this P229 glider gun:

Code: Select all

x = 30, y = 36, rule = B3/S23Investigator
25.B5$Q2$E$Q8$6.3A6.E$6.A$7.A6$29.E9$18.R2$22.E!

Edit: the Herschel can also function as a B if interacted with early enough, as seen in this connection to BFx59H:

Code: Select all

x = 24, y = 26, rule = B3/S23Investigator
4$15.2D4$9.Q2$9.E8.2A$9.Q8.2A8$15.3A$15.A$16.A!

P221 gun using this:

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x = 35, y = 25, rule = B3/S23Investigator
6.2D26.E4$Q33.E2$E8.2A$Q8.2A8$6.3A$6.A$7.A5$8.R2$12.E!

[Antonin Duda]

P122 Diehard sparker:

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x = 22, y = 39, rule = StateInvestigator
14.C3$5.A.A$4.A2.A$A4.A.A11.C$A$A5$16.C$16.C$21.C$10.C14$8.2A$7.A$6.A
$5.A$5.A3.H.A$11.A$9.2A$14.C2$12.C!

I used that same p122 engine that i used to make those extremely high period oscillators and guns.

[pifricted]

180 degree turner, rt 95:

Code: Select all

x = 34, y = 34, rule = B3/S23Investigator
A.A$.2A$.A14$22.E$30.E4$25.E2$25.A$26.A$24.3A3$31.A$30.A.A$29.A.D.A$30.
A.A$31.A$31.E!

[b-engine]

P23 quasi-shuttle:

Code: Select all

x = 10, y = 5, rule = B3/S23Investigator
3.E2.E$B4.A$5.2A2.B$B4.A$3.E2.E!
 

[hotcrystal0]

180 degree turner, rt 95:

Code: Select all

x = 34, y = 34, rule = B3/S23Investigator
A.A$.2A$.A14$22.E$30.E4$25.E2$25.A$26.A$24.3A3$31.A$30.A.A$29.A.D.A$30.
A.A$31.A$31.E!

Glider-to-3 gliders splitter using the same starting catalyst:

Code: Select all

x = 27, y = 28, rule = StateInvestigator
.A$2.A$3A5$21.EBE7$15.A$16.A$14.3A.E6$24.A$23.A.A$22.A.D.A$23.A.A$24.
A$24.E!

[b-engine]

Glider-to-3 gliders splitter using the same starting catalyst:

Code: Select all

x = 27, y = 28, rule = StateInvestigator
.A$2.A$3A5$21.EBE7$15.A$16.A$14.3A.E6$24.A$23.A.A$22.A.D.A$23.A.A$24.
A$24.E!

90° reflector using same first and second stage catalyst:

Code: Select all

x = 27, y = 28, rule = B3/S23Investigator
.A$2.A$3A8$23.E4$15.A$16.A$14.3A.E6$24.A$23.A.A$22.A.D.A$23.A.A$24.A$
24.E!

[hotcrystal0]

3-cell reflector with a 180° variant and a 90° variant:

Code: Select all

x = 29, y = 20, rule = StateInvestigator
.A18.A$2.A18.A$3A16.3A5$9.E18.E3$9.D18.D9$12.R12.R!

Edit: this is annoying:

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#C [[ STOP 82 ]]
x = 8, y = 14, rule = StateInvestigator
4.D9$.A$2.A$3A2$7.R!

Edit 2: P84 R shuttle that cleans up its own blocks:

Code: Select all

x = 29, y = 13, rule = B3/S23Investigator
8.2A.C11.B$8.2A$D$24.A$22.A2.A$21.A$21.A4.A$21.2A2$23.3A$28.D2$5.B11.
C!

Edit 3: Another small G-to-H with a repeat time of 66:

Code: Select all

x = 25, y = 28, rule = StateInvestigator
2.A$A.A$.2A14$18.A$19.A$17.3A6$19.E2A$19.EHD$19.3E$24.C!

[hotcrystal0]

Sorry for the doublepost.
Two variations of an Lx122; one requires the FNG of the output Herschel in a staged recovery catalyst and the other does not:

Code: Select all

x = 53, y = 21, rule = StateInvestigator
36.EA$.2DE12.E18.EA.A3.E9.E$D.A32.A2.A$DA34.2A$.E5$A35.A$A.A33.A.A$3A
33.3A$2.A35.A8$10.B35.B!

[2 days later] Edit: Another seemingly unknown 2-cell reflector:

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x = 10, y = 8, rule = StateInvestigator
A$.2A$2A3$8.R2$9.C!

Edit 2: 5-cell glider-to-LWSS with a repeat time of 34:

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x = 22, y = 19, rule = StateInvestigator
A.A$.2A$.A6$9.A$10.2A$9.2A2$19.C3$17.Q2$21.B$16.E.B!

Edit 3 (3 days later): A different 3-cell G-to-H that unfortunately has a repeat time of 118:

Code: Select all

x = 41, y = 41, rule = StateInvestigator
A.A$.2A$.A27$30.A$31.2A$30.2A4$40.B4$38.Q$40.E!

[hotcrystal0]

Reposting these:

edit: they goin

Code: Select all

x = 49, y = 49, rule = StateInvestigator
31.2A$31.2A5.2A$38.2A3$7.2A27.2A$7.2A27.2A$42.2A$42.2A$.2A$.2A$5.2A$
5.2A15.A$22.A.A$22.3A$24.A$2A$2A$21.C3$30.C$34.3A$34.A$13.3A17.3A$14.
A$12.3A$18.C3$27.C$47.2A$47.2A$24.A$24.3A$24.A.A$26.A15.2A$42.2A$46.
2A$46.2A$5.2A$5.2A$11.2A27.2A$11.2A27.2A3$9.2A$9.2A5.2A$16.2A!

edit2: tried to do something cool here but made p6 pipsquirter

Code: Select all

x = 34, y = 16, rule = StateInvestigator
18.O.2O.O.4O2.O$18.O.O.3O.O.2O.O.O$18.O3.2O.O.4O.2O$18.2O.O.O2.7O$18.
3O.3O2.O4.2O$21.O4.O.5O$5.A13.O.O2.O.O3.2O.O$6.A12.O.4O.O.O3.O$A5.A
11.O.3O5.O2.3O$.6A13.2O3.O.O.2O.O$19.2O.O2.3O.O2.O$19.2O9.4O$19.O.O3.
O3.2O$18.O.O2.2O.3O.4O$18.2O.O.O.2O2.4O$18.2O.5O.3O2.O!

[b-engine]

Strange p12:

Code: Select all

x = 8, y = 12, rule = B3/S23Investigator
2.4A$.B4.B5$A6.A$2.4H$.A4.A2$3.2A$3.2A!

[d/dx]

reduced honey thieves (not by much but still)

Code: Select all

x = 11, y = 11, rule = StateInvestigator
2DE$DA7.E$9.2D$9.AD$3.2A$3.2A.2A$6.2A$DA$2D$.E7.AD$8.E2D!

[hotcrystal0]

reduced honey thieves (not by much but still)

Code: Select all

x = 11, y = 11, rule = StateInvestigator
2DE$DA7.E$9.2D$9.AD$3.2A$3.2A.2A$6.2A$DA$2D$.E7.AD$8.E2D!

More reduction:

Code: Select all

x = 11, y = 11, rule = StateInvestigator
ED$DA2$9.B$3.3A$3.2A.2A$5.3A$.B2$9.AD$9.DE!

[hotcrystal0]

Reposting this:

EDIT: Here is an even weirder StateInvestigator example (I can't think of a Life example like this). This is a (1 mod P5) reflector:

Code: Select all

x = 73, y = 67, rule = StateInvestigator
66.A.A$66.2A$67.A7$66.3R.3R$66.R3.R$66.3R.3R$54.A13.R.R.R$53.A12.3R.
3R$53.3A7$53.3R.2R$53.R4.R$53.3R2.R$42.A12.R2.R$42.A.A8.3R.3R$42.2A7$
42.R.R.3R$42.R.R.R$31.A10.3R.3R$30.A13.R.R.R$30.3A11.R.3R7$30.R.R.2R$
30.R.R2.R$20.A.A7.3R2.R$20.2A10.R2.R$21.A10.R.3R7$11.A.A6.3R.3R$11.2A
9.R.R$12.A7.3R.3R$22.R.R.R$20.3R.3R$.C$7.2A$EQA3.A2.A$ED.A3.A.A$Q2.E
4.A$DE.R9.E$12.2D!

[confocaloid]

Technically, in this particular example 1 mod p5 fails to capture the problem with trying to feed two gliders separated by 31 ticks. The notation would incorrectly suggest that that should work. Once you add the missing information, things become sufficiently complicated to deserve a human-readable explanation in natural language.

Code: Select all

x = 73, y = 67, rule = StateInvestigator
66.A.A$66.2A$67.A7$66.3R.3R$66.R3.R$66.3R.3R$54.A13.R.R.R$53.A12.3R.
3R$53.3A7$53.3R.2R$53.R4.R$53.3R2.R$42.A12.R2.R$42.A.A8.3R.3R$42.2A7$
42.R.R.3R$42.R.R.R$31.A10.3R.3R$30.A13.R.R.R$30.3A11.R.3R7$30.R.R.2R$
30.R.R2.R$20.A.A7.3R2.R$20.2A10.R2.R$21.A10.R.3R7$11.A.A6.3R.3R$11.2A
9.R.R$12.A7.3R.3R$22.R.R.R$20.3R.3R$.C$7.2A$EQA3.A2.A$ED.A3.A.A$Q2.E
4.A$DE.R9.E$12.2D!

[Entity Valkyrie 2]

Technically, in this particular example 1 mod p5 fails to capture the problem with trying to feed two gliders separated by 31 ticks. The notation would incorrectly suggest that that should work. Once you add the missing information, things become sufficiently complicated to deserve a human-readable explanation in natural language.

Code: Select all

x = 73, y = 67, rule = StateInvestigator
66.A.A$66.2A$67.A7$66.3R.3R$66.R3.R$66.3R.3R$54.A13.R.R.R$53.A12.3R.
3R$53.3A7$53.3R.2R$53.R4.R$53.3R2.R$42.A12.R2.R$42.A.A8.3R.3R$42.2A7$
42.R.R.3R$42.R.R.R$31.A10.3R.3R$30.A13.R.R.R$30.3A11.R.3R7$30.R.R.2R$
30.R.R2.R$20.A.A7.3R2.R$20.2A10.R2.R$21.A10.R.3R7$11.A.A6.3R.3R$11.2A
9.R.R$12.A7.3R.3R$22.R.R.R$20.3R.3R$.C$7.2A$EQA3.A2.A$ED.A3.A.A$Q2.E
4.A$DE.R9.E$12.2D!

Is there any reason why something like "1 mod 5; RT 36+" doesn't work for this particular reflector?
Syringe would be "stable; RT 74, 75, 78+"?

edit: In general, it's more complicated than just modular arithmetic. One could engineer a glider reflector able to reflect gliders separated by any number of ticks above (and including) 314, except the gap of precisely 666 ticks is disallowed and will damage the contraption, while the gap of precisely 1000 ticks will toggle an internal boat-bit without causing any other consequences apart from that.

and the hypothetical reflector you gave would be "stable; RT 314+ (≠666)"?

[confocaloid]

I think that's too abbreviated. By itself that wouldn't explain enough to help readers understand what "1 mod 5" is supposed to mean, and would rely on the readers knowing that "RT" means "repeat time". An explicit explanation of the interesting properties of a device is better.

Is there any reason why something like "1 mod 5; RT 36+" doesn't work for this particular reflector?

[hotcrystal0]

Here’s a rephasing bouncer that works at periods 3 mod 7:

Code: Select all

x = 43, y = 35, rule = StateInvestigator
37.A$35.2A$36.2A7$36.3R.3R$26.A.A9.R.R.R$26.2A8.3R.3R$27.A10.R.R.R$36.
3R.3R4$19.A8.3R.2R$18.A11.R2.R$18.3A7.3R2.R$30.R2.R$28.3R.3R2$13.A$12.
A$12.3A5.3R.R.R$22.R.R.R$20.3R.3R$20.R5.R$14.2A4.3R3.R$B2.EDE.E2.2A2.
2A$3.A5.A.A$3.A2.A3.A$3.A9.E$3.EDE5.E2D!

[confocaloid]

Out of the numbers 24, 31, 38 visible inside the pattern, only 31 is "7 mod 3".
That is (edit: Wikipedia link), [ 31 ≡ 7 (mod 3) ] is true; however, both [ 24 ≡ 7 (mod 3) ] and [ 38 ≡ 7 (mod 3) ] are false.

Further, apparently the posted device cannot safely consume uniform glider streams with periods lower than 24, but the notation does not seem to tell that.

Here’s a rephasing bouncer that works at periods 7 mod 3:

Code: Select all

x = 43, y = 35, rule = StateInvestigator
37.A$35.2A$36.2A7$36.3R.3R$26.A.A9.R.R.R$26.2A8.3R.3R$27.A10.R.R.R$36.
3R.3R4$19.A8.3R.2R$18.A11.R2.R$18.3A7.3R2.R$30.R2.R$28.3R.3R2$13.A$12.
A$12.3A5.3R.R.R$22.R.R.R$20.3R.3R$20.R5.R$14.2A4.3R3.R$B2.EDE.E2.2A2.
2A$3.A5.A.A$3.A2.A3.A$3.A9.E$3.EDE5.E2D!

[Sokwe]

Here’s a rephasing bouncer that works at periods 7 mod 3:

Code: Select all

x = 43, y = 35, rule = StateInvestigator
37.A$35.2A$36.2A7$36.3R.3R$26.A.A9.R.R.R$26.2A8.3R.3R$27.A10.R.R.R$36.
3R.3R4$19.A8.3R.2R$18.A11.R2.R$18.3A7.3R2.R$30.R2.R$28.3R.3R2$13.A$12.
A$12.3A5.3R.R.R$22.R.R.R$20.3R.3R$20.R5.R$14.2A4.3R3.R$B2.EDE.E2.2A2.
2A$3.A5.A.A$3.A2.A3.A$3.A9.E$3.EDE5.E2D!

I think you mean 3 mod 7. The reflection reaction causes a phase shift that makes the p7 sparker take 3 extra generations to return to its initial state. If a glider gets reflected, then the next glider must have a relative spacing of 24+7n generations, where n is a nonnegative integer.