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Minimal versions of pattern types in non-totalistic rules

Posted: October 10th, 2022, 9:12 pm

by pipsqueek

This topic is for sharing the smallest

• spaceship
• gun
• oscillator (preferably of high-period)
• methuselah (lasting at least 500 generations without growing infinitely)
• puffer
• rake
• sawtooth
• breeder
• metacell(?)

of all isotropic non-totalistic (or life-like) rule.
they should be small for all non-totalistic rules, not only for the rule it was made in.

to start off, here's the smallest puffer I could find:

Code: Select all

x = 2, y = 3, rule = B2cei3ei/S01e2ac
bo$o$bo!

this can probably be reduced in size or bounding box in one of its phases

so far we have found:

• P1 C/1 2x3 spaceship with 3 cells
• P5 gun with 1 cell
• 2x2 P4 diagonal rake with 3 cells
• quadratic sawtooth with 1 cell
* 3x1 1304731 generation methuselah with 2 cells

Re: Minimal versions of pattern types in non-totalistic rules

Posted: October 11th, 2022, 5:07 am

by rattlesnake

By metacell, do you mean a metacell like the 0E0P metacell that does not neat an infinite background grid of OFF metacells or a metacell like the OTCA metapixel thatb needs a background grid of OFF mtacells?

Re: Minimal versions of pattern types in non-totalistic rules

Posted: October 11th, 2022, 6:45 pm

by pipsqueek

rattlesnake wrote: October 11th, 2022, 5:07 am By metacell, do you mean a metacell like the 0E0P metacell that does not neat an infinite background grid of OFF metacells or a metacell like the OTCA metapixel thatb needs a background grid of OFF mtacells?

ether one would be fine, as long as it's small

Re: Minimal versions of pattern types in non-totalistic rules

Posted: October 11th, 2022, 9:32 pm

by rattlesnake

Spaceship:

Code: Select all

x = 3, y = 2, rule = B2a3r/S
2bo$obo!

Gun:

Code: Select all

x = 26, y = 2, rule = B2ae/S
o9bo4bo9bo$bo8bo4bo8bo!

Edit 1:

Code: Select all

x = 1, y = 1, rule = B1e2ci3ak4aeq5ei6e7c/S01e2ikn3ceiry4aceinq6c8
o!

Sawtooth:

Code: Select all

x = 1, y = 1, rule = B1357/S1357
o!

Rake:

Code: Select all

x = 6, y = 5, rule = B35nr/S23
b2o$o2bo$o2bo$2o$2b2obo!

Re: Minimal versions of pattern types in non-totalistic rules

Posted: October 12th, 2022, 9:22 am

by pzq_alex

rattlesnake wrote: October 11th, 2022, 9:32 pm Gun:
Code: Select all
x = 26, y = 2, rule = B2ae/S
o9bo4bo9bo$bo8bo4bo8bo!

That’s not minimal, see viewtopic.php?f=11&t=5791&p=150535&hili ... un#p150527

Re: Minimal versions of pattern types in non-totalistic rules

Posted: October 13th, 2022, 6:04 am

by bibunsekibun

Methuselah 2cell

Code: Select all

x = 3, y = 1, rule = B2-a3-ij4-ceity5-cqry6-cn78/S012-n3an4aenqtyz5aeij678
obo!

Rake 8cell

Code: Select all

x = 6, y = 3, rule = B2cek3-i8/S02ce3a4i5i8
ob3o$3bobo$bobo!

Re: Minimal versions of pattern types in non-totalistic rules

Posted: October 13th, 2022, 8:55 am

by FWKnightship

bibunsekibun wrote: October 13th, 2022, 6:04 am Rake 8cell
Code: Select all
x = 6, y = 3, rule = B2cek3-i8/S02ce3a4i5i8
ob3o$3bobo$bobo!

6 cells:

Code: Select all

x = 6, y = 3, rule = B2ac3ae4t5e/S1c2i3i
5bo$obob2o$5bo!

EDIT:3 cells:

Code: Select all

x = 2, y = 2, rule = B2ae3n6i/S1e2n3r
bo$2o!

Re: Minimal versions of pattern types in non-totalistic rules

Posted: October 13th, 2022, 5:00 pm

by pipsqueek

bibunsekibun wrote: October 13th, 2022, 6:04 am Methuselah 2cell
Code: Select all
x = 3, y = 1, rule = B2-a3-ij4-ceity5-cqry6-cn78/S012-n3an4aenqtyz5aeij678
obo!

cool, but it technically isn't a methuselah because it doesn't appear to ever stabilize

Re: Minimal versions of pattern types in non-totalistic rules

Posted: October 13th, 2022, 5:59 pm

by confocaloid

pipsqueek wrote: October 13th, 2022, 5:00 pm
bibunsekibun wrote: October 13th, 2022, 6:04 am Methuselah 2cell
Code: Select all
x = 3, y = 1, rule = B2-a3-ij4-ceity5-cqry6-cn78/S012-n3an4aenqtyz5aeij678
obo!
cool, but it technically isn't a methuselah because it doesn't appear to ever stabilize

The population does not appear to change after T = 1304731:

: gen1304731_pop601054426729.png (34.39 KiB) Viewed 2227 times

Edit:

breaker's glider gun wrote: October 14th, 2022, 1:52 pm
confocaloid wrote: October 13th, 2022, 5:59 pm The population does not appear to change after T = 1304731:
:star-eyes:
it's a square. its population is 775277^2

For some reason "Select All" selected 775279 x 775279 instead

Re: Minimal versions of pattern types in non-totalistic rules

Posted: October 14th, 2022, 1:52 pm

by breaker's glider gun

confocaloid wrote: October 13th, 2022, 5:59 pm The population does not appear to change after T = 1304731:

:star-eyes:
it's a square. its population is 775277^2

hmm, IG it's not a square but somethung with the same population. it could be something like:
O_
_O
O_

Re: Minimal versions of pattern types in non-totalistic rules

Posted: October 14th, 2022, 3:24 pm

by toroidalet

I tried deleting the smaller square to see if anything popped out, and even though I could only delete a few rows in a reasonable amount of time, that turned out to be enough to see them while scrolling across. Anyway, there are 8 "knobs" on the side that look like this:

Code: Select all

x = 15, y = 9, rule = B2-a3-ij4-ceity5-cqry6-cn78/S012-n3an4aenqtyz5aeij678
7bo$7ob7o$15o$15o$15o$15o$15o$15o$15o!

Because the protruding cell is balanced out by a missing cell, the population is equal to that of the square.
They are located at (61,293, 387,639), (-61,291, 387,639), (-387,638, -61,292), (-387,638, 61,292), (61,293, -387,639), (-61,291, -387,639), (387,640, -61,292) and (387,640, 61,292). A little signal travels up the wavefront and lands at these spots at generation 978,388 (its signal form does include a phase as this protrusion). I have not determined where the signals came from and I don't care to.
EDIT: I apologize for getting off-topic. Technically the smallest metacell is from B1357/S1357 or B1357/S2468, which simulates itself at a speed of 1/2:

Code: Select all

x = 21, y = 24, rule = B1357/S1357
2o16bobo19$2o16bobo$bo$bo18bo2$20bo!

The metacell is a 2*2 square with a single cell in the corner, and it simulates itself.

EDIT 2:
Sawtooth with minimum population 3:

Code: Select all

x = 10, y = 1, rule = B2cik3-cikq4eijtyz5eijk6cn7c/S02ikn3-aiy4iqrtwy5-ckn6-an7c
obo6bo!

This is the minimum minimum population for a sawtooth, since there are only finitely many 2-cell patterns that are active {a}. The B1c/S and B2a/S replicators have minimum population 4.

{a}: With a B1 transition, infinitely many such patterns exist, but they consist of isolated dots, and those dots will expand in all directions and never stop, meaning that the population will always be at least 4.

Re: Minimal versions of pattern types in non-totalistic rules

Posted: October 26th, 2022, 10:15 pm

by breaker's glider gun

toroidalet wrote: October 14th, 2022, 3:24 pm EDIT 2:
Sawtooth with minimum population 3:
Code: Select all
x = 10, y = 1, rule = B2cik3-cikq4eijtyz5eijk6cn7c/S02ikn3-aiy4iqrtwy5-ckn6-an7c
obo6bo!

that's only a three-cell predecessor to a three-cell sawtooth; this is the real thing:

Code: Select all

x = 9, y = 3, rule = B2cik3-cikq4eijtyz5eijk6cn7c/S02ikn3-aiy4iqrtwy5-ckn6-an7c
o$8bo$o!

Re: Minimal versions of pattern types in non-totalistic rules

Posted: November 19th, 2023, 4:33 pm

by confocaloid

Actually each of these is a family of pattern types.
• Spaceships: LifeWiki:Smallest Spaceships Supporting Specific Speeds
• Guns: Highest Period Guns of Specific Population (HPGSP)
• Oscillators: Smallest Oscillators Supporting Specific Periods, Project OmniOsci
• Rakes: INT rule siderake competition

pipsqueek wrote: October 10th, 2022, 9:12 pm • rake

For rakes, there are more subtypes, even with just one barrel there can be up to 8 possibilities for each combination of speeds. (even more possibilities taking into account asymmetric non-oblique output spaceships)

orthogonal rake, orthogonal output:
• same simplified speed: 2 subtypes (90°; 180°)
• different simplified speeds: 3 subtypes (90°; 180°; 0°)
diagonal rake, diagonal output: analogous to the previous case
orthogonal rake, diagonal output: 2 subtypes (45°; 135°)
diagonal rake, orthogonal output: analogous to the previous case
orthogonal rake, oblique output: 4 subtypes by the angle
diagonal rake, oblique output: 4 subtypes by the angle
oblique rake, orthogonal output: 4 subtypes by the angle
oblique rake, diagonal output: 4 subtypes by the angle
oblique rake, oblique output:
• same simplified speed: 7 subtypes by the angle
• different simplified speed: 8 subtypes by the angle

Time for SSBRSSS? (= Smallest Single Barrelled Rakes Supporting Specific Signatures, where a signature is (rake speed, output speed, angle))

Re: Minimal versions of pattern types in non-totalistic rules

Posted: November 19th, 2023, 5:24 pm

by toroidalet

538-generation 1-cell methuselah:

Code: Select all

x = 1, y = 1, rule = B1e2in3ck4-iknty5q7c8/S12-e3-ai4-ejkqy5ry6ce8
o!

It looks like it stabilizes in generation 537, but check the p3 oscillators in the corners.