Minimal versions of pattern types in non-totalistic rules

[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

[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?

[pipsqueek]

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

[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!

[pzq_alex]

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

[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!

[FWKnightship]

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!

[pipsqueek]

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

[confocaloid]

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 2167 times

Edit:

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

[breaker's glider gun]

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_

[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.

[breaker's glider gun]

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!

[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

• 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))

[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.