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B2-a3i5/S2-a3

Posted: January 8th, 2021, 5:42 pm

by hotdogPi

This rule is non-explosive and somewhat similar to Life in complexity despite having B2-a as its primary condition instead of B3, although things do settle more quickly. In addition, it's one of the simpler non-totalistic rules.

The objects I have found:

Code: Select all

x = 34, y = 104, rule = B2-a3i5/S2-a3
5b2o$5b2o5$25bobo$6bo4bo5bo6bo3bo$5bo5bo4bo$11bo6bo5bo3bo$25bobo9$5bo$
3bo3bo14bo$21b3o$2bo5bo13bo2$3bo3bo$5bo8$20bo$5bo$4bobo11bo3bo$3bobo$
4bo11bo3bo2$18bo6$7bo7b2ob2o10bo$5bo26bo$4bobo8b2ob2o9bo$5bo23bo3bo$
15b2ob2o10b2o5$25bobo$15bo11b2o$b2o13bo12bo$3bo8b2o3bo10bo$b2o13bo9b2o
$15bo10bo13$4bo$3bobo$4bo$bobo$2bo25$o2b2o$o4bo$o2b2o!

Row 1: Your typical block. Not nearly as common as it is in Life, as a pre-block dies out.
Row 2: The duoplet, blinker, shiplet, and unnamed, all P2. The first two are extremely common, and the shiplet is medium-common. The last one is not natural, at least yet.
Row 3: Mini-star (P10) and star (P31). Despite being larger, the P31 star is extremely common, and while the mini-star does appear, it's rare. (Note that the 5-cell version of the star in the RLE above is a predecessor, not actually one of its phases.)
Row 4: Barge (P42, mod 21) and large barge (P6).
Row 5: 1st: P16, mod 8. 2nd: P10, one of two non-natural objects above. 3rd: P4, mod 2.
Row 6: Three c/2 spaceships; the first is more common than the second, and the third has been seen only once. The third can have zero, one, or two disconnected dots.
Row 7: A natural c/3 spaceship; has appeared only once.
Row 8: A puffer based on the first of the c/2 spaceships above.

(The patterns in this next paragraph have already been found and are included in the viewer above.)
I've found two other patterns that I can't seem to replicate. The first (I think) is a P4 flipper that reminds me of Life's pond, found when goofing off but not in an actual soup. The other is a c/3 spaceship, period 12, glide symmetric, that was from an actual soup. Can anyone find the patterns for me?

This rule has absolutely nothing in Catagolue right now, and I'm not sure how to do it.

Re: B2-a3i5/S2-a3

Posted: January 8th, 2021, 6:34 pm

by ENORMOUS_NAME

i found the c/3

Code: Select all

x = 5, y = 5, rule = B2-a3i5/S2-a3
bo$obo$bobo$4bo$3bo!

Re: B2-a3i5/S2-a3

Posted: January 8th, 2021, 6:50 pm

by creeperman7002

Found the p4

Code: Select all

x = 5, y = 5, rule = B2-a3i5/S2-a3
2b2o$o3bo$4bo$bo$3bo!

Re: B2-a3i5/S2-a3

Posted: January 8th, 2021, 7:25 pm

by iNoMed

I found the c/4

Code: Select all

x = 42, y = 15, rule = B2-a3i5/S2-a3
19bobo11bo$3b2obo21bo6bo2bo$6bo15bo7bo3b2obob2o$5b3o13b3ob2obo3bo2bobo
b2o$9bo4bo4bobo9bo5bob2o$2bo10b2ob2o3bo5bo10bo2bo$3b2o5b5ob3o12bo7bo$
4o2b2ob2o2b2o2b2o2b2o16bobo$3b2o5b5ob3o12bo7bo$2bo10b2ob2o3bo5bo10bo2b
o$9bo4bo4bobo9bo5bob2o$5b3o13b3ob2obo3bo2bobob2o$6bo15bo7bo3b2obob2o$
3b2obo21bo6bo2bo$19bobo11bo!

Edit: also the c/4d

Code: Select all

x = 18, y = 18, rule = B2-a3i5/S2-a3
11bo$9bo2bo$9bo3bo$8bo3bo$5bo6bob2o$8bo2b3o2bo$3bo3b2o4b2o2bo2$7bo4b2o
bo$b3o8b2o$2o2bo3b2o2bo$3obo3bobobo$4o2bobo2b2o$b2o2bobo$5bo$6bobo2$6b
o!

Edit 2: also the c/5d to cap things off

Code: Select all

x = 26, y = 26, rule = B2-a3i5/S2-a3
19b3o$18bob4o$18bo2bob2o$24bo$23b3o$16bob2o4b2o$12b3obo2b2o4bo$12bo2bo
bo2bo2b2o$16bobo$12bo2bobob2o$6bobo4bo2bobo$6bo3b2o7bo$7bo3bobobo3bo$
10bo5bob2o$13b2o$12bobo$8b2o$6bo2bo5bo$13bo$3bo4bo5b2o$4bo$5bo$b3o2bo$
2b2o$o2bo$bo!

Re: B2-a3i5/S2-a3

Posted: January 8th, 2021, 9:11 pm

by goldenratio

Smaller c/4:

Code: Select all

x = 17, y = 18, rule = B2-a3i5/S2-a3
6bobobo$3b3o5b3o$3b3ob3ob3o$2bo3bo3bo3bo$3b3o5b3o2$2b3o7b3o$bo13bo$bo
13bo$4bo7bo$bob2o7b2obo$4bo7bo$4bo7bo$4bobo3bobo$2o3b2o3b2o3b2o$o3bo7b
o3bo$2bo11bo$o15bo!

Very small c/5:

Code: Select all

x = 11, y = 11, rule = B2-a3i5/S2-a3
4b3o$3b2ob2o$5bo$b3o3b3o$2bo5bo$2b2o3b2o$2o2b3o2b2o$3bo3bo$2o2bobo2b2o
$4bobo$5bo!

2c/5:

Code: Select all

x = 20, y = 16, rule = B2-a3i5/S2-a3
4b4o4b4o$4b4o4b4o$3bob2obo2bob2obo2$4b2ob2o2b2ob2o$6bo6bo$3bo3bo4bo3b
o$2bobo10bobo$4bo10bo$b4o10b4o$obo3bo6bo3bobo$4bo2bo4bo2bo$2bo2b2o6b2o
2bo$4bo2bo4bo2bo2$5bo8bo!

EDIT: long c/6 partial. C/6 seems to give long partials but with no spaceships yet.

Code: Select all

x = 17, y = 101, rule = B2-a3i5/S2-a3
4bo7bo2$3b3o5b3o$2bo3bo3bo3bo$bobobob3obobobo$2bob2o2bo2b2obo$2bo2bob
obobo2bo$4bobobobobo$5b3ob3o$5b3ob3o$2bobobo3bobobo$ob4obobob4obo$3bo
bo2bo2bobo$6b2ob2o$4bo7bo$6b2ob2o$7b3o2$7bobo$6bobobo$5b3ob3o$4b2o5b2o
$3b2o2bobo2b2o$3b3o5b3o$5b2o3b2o$3bo2bobobo2bo$bo2bobo3bobo2bo$3b2o3b
o3b2o$3bob3ob3obo$8bo$8bo$2bo2bo5bo2bo$4b2o2bo2b2o2$4bo7bo$4b2o2bo2b2o
$3bobo2bo2bobo$3b4o3b4o$bo13bo$2bob2ob3ob2obo$o2b3o2bo2b3o2bo$3b2o7b2o
$2b2ob2o3b2ob2o$2bo3bo3bo3bo$3bobobobobobo$2bo2bo5bo2bo$4b3o3b3o$5b2o
3b2o$3bo2bo3bo2bo$2b2o2bobobo2b2o$8bo$2b3o7b3o$8bo$8bo$8bo$4b3o3b3o$4b
obo3bobo3$6bobobo$3b3o2bo2b3o$8bo$8bo$6bobobo$4bo7bo$2bobo7bobo$2bo2b
3ob3o2bo$2b2obo5bob2o$5b3ob3o$7bobo$3b2obo3bob2o2$7bobo$5b2obob2o2$6b
o3bo$4bo7bo$6bo3bo$4b2o2bo2b2o$bo4b2ob2o4bo$b2obo7bob2o2$2bo11bo$8bo$
7bobo$4bo2b3o2bo$3bo3bobo3bo$8bo$4bo7bo$4bo7bo$2b2ob2o3b2ob2o$3bo2bo3b
o2bo$6bobobo$3b2o2bobo2b2o$4bob5obo$4bobo3bobo2$6b2ob2o3$5b7o!

EDIT2: ntzfind's going to reach the depth limit soon if this keeps going

Code: Select all

x = 17, y = 275, rule = B2-a3i5/S2-a3
4bo7bo2$3b3o5b3o$2bo3bo3bo3bo$bobobob3obobobo$2bob2o2bo2b2obo$2bo2bob
obobo2bo$4bobobobobo$5b3ob3o$5b3ob3o$2bobobo3bobobo$ob4obobob4obo$3bo
bo2bo2bobo$6b2ob2o$4bo7bo$6b2ob2o$7b3o2$7bobo$6bobobo$5b3ob3o$4b2o5b2o
$3b2o2bobo2b2o$3b3o5b3o$5b2o3b2o$3bo2bobobo2bo$bo2bobo3bobo2bo$3b2o3b
o3b2o$3bob3ob3obo$8bo$8bo$2bo2bo5bo2bo$4b2o2bo2b2o2$4bo7bo$4b2o2bo2b2o
$3bobo2bo2bobo$3b4o3b4o$bo13bo$2bob2ob3ob2obo$o2b3o2bo2b3o2bo$3b2o7b2o
$2b2ob2o3b2ob2o$2bo3bo3bo3bo$3bobobobobobo$2bo2bo5bo2bo$4b3o3b3o$5b2o
3b2o$3bo2bo3bo2bo$2b2o2bobobo2b2o$8bo$2b3o7b3o$8bo$8bo$8bo$4b3o3b3o$4b
obo3bobo3$6bobobo$3b3o2bo2b3o$8bo$8bo$6bobobo$4bo7bo$2bobo7bobo$2bo2b
3ob3o2bo$2b2obo5bob2o$5b3ob3o$7bobo$3b2obo3bob2o2$7bobo$5b2obob2o2$6b
o3bo$4bo7bo$6bo3bo$4b2o2bo2b2o$bo4b2ob2o4bo$b2obo7bob2o2$2bo11bo$8bo$
7bobo$4bo2b3o2bo$3bo3bobo3bo$8bo$4bo7bo$4bo7bo$2b2ob2o3b2ob2o$3bo2bo3b
o2bo$6bobobo$3b2o2bobo2b2o$4bob5obo$4bobo3bobo2$6b2ob2o3$5b7o$5bo5bo$
5b2o3b2o$8bo$2bo2bobobobo2bo$2bo5bo5bo$3b2o7b2o$bo5b3o5bo$obo3bobobo3b
obo$2bo4b3o4bo$2bo2b7o2bo$4b3obob3o$8bo$7b3o$4b3obob3o2$6bobobo$6b5o$
6bo3bo$6bo3bo$8bo$7bobo$7b3o$5b3ob3o$5b2o3b2o$2bo2bobobobo2bo$2bo2bob
obobo2bo$3b2obo3bob2o$3b2o2bobo2b2o$2bo3bobobo3bo$b2obo3bo3bob2o$bob2o
b2ob2ob2obo$3b2o2bobo2b2o$3bo4bo4bo$4bo3bo3bo$5bo5bo$3bo3bobo3bo$6b5o
$7bobo$4b2obobob2o$5bo5bo2$4bo2bobo2bo$5bo2bo2bo$5bobobobo$2b2o2b2ob2o
2b2o$2b3o7b3o$bo4bobobo4bo$7bobo$3bob7obo$6b5o2$8bo2$6b2ob2o$4bo7bo$3b
o2bobobo2bo$7bobo2$obobo2bobo2bobobo$bob3o5b3obo$bo2b2o5b2o2bo$4b2o5b
2o$8bo$4bob2ob2obo$7b3o$6bobobo$7b3o$8bo$8bo$6bobobo$5bob3obo$5b7o$5b
7o$4b2o2bo2b2o$3bo2bo3bo2bo$2bob2obobob2obo2$3bo2bobobo2bo$6bo3bo$2bo
3b2ob2o3bo2$5bo5bo$3b2o7b2o$5b2o3b2o$4b3obob3o$6bobobo$5b2o3b2o$5b2ob
ob2o$7b3o$8bo$3b5ob5o$6b2ob2o$8bo$2bo2bo5bo2bo$2bo3bobobo3bo$5bo2bo2b
o$4bo3bo3bo$6bo3bo$5b7o$6b5o$3bo3b3o3bo$3b2o7b2o$3bo9bo2$2b2obo5bob2o
$bob2o7b2obo$5b2obob2o$ob2o4bo4b2obo$2bo2b2obob2o2bo$3b3o5b3o$3bobobo
bobobo$7bobo2$5bo2bo2bo$4bo2b3o2bo$4bo7bo$4bo7bo$4bo7bo$3bo4bo4bo$6b2o
b2o2$2bob4ob4obo$4b9o$7bobo$6bo3bo2$6b2ob2o$7b3o$2bo2bo2bo2bo2bo$bobo
bo2bo2bobobo$5bo5bo$b3ob2obob2ob3o$3bobo2bo2bobo3$4b9o$4b2o5b2o$4bo7b
o$5bobobobo$3bo3bobo3bo$5b2o3b2o$2bo3b2ob2o3bo$2bo3bo3bo3bo$3b2o7b2o$
7bobo$5bo5bo$7b3o$5bo5bo$2bobobobobobobo$4bobo3bobo$b3o3b3o3b3o$5bo2b
o2bo$5b2obob2o$7b3o$b2ob2ob3ob2ob2o$b2o2b2obob2o2b2o$bo2bo7bo2bo$obo11b
obo$3bo2bobobo2bo$7b3o$2b2o2bo3bo2b2o2$3b2o3bo3b2o$5bobobobo$4b2o5b2o
$4b2obobob2o$3bo2bobobo2bo2$3b2ob2ob2ob2o$b2o5bo5b2o$b2o2bo2bo2bo2b2o
2$3bobo2bo2bobo$o3b2obobob2o3bo!

EDIT3: Yep, it just did.
Also, 15^2th post

Re: B2-a3i5/S2-a3

Posted: January 9th, 2021, 7:47 am

by iNoMed

The 2c/5 can trivially be chopped in half and it'll still work just fine!

Code: Select all

x = 9, y = 16, rule = B2-a3i5/S2-a3
4b4o$4b4o$3bob2obo2$4b2ob2o$6bo$3bo3bo$2bobo$4bo$b4o$obo3bo$4bo2bo$2bo
2b2o$4bo2bo2$5bo!

Edit: c/5 pushalong that can support itself infinitely:

Code: Select all

x = 56, y = 13, rule = B2-a3i5/S2-a3
3bo30bo13bo$14b2o2b3o9bo2bo3bo10bobobo$4bo11b2ob5o7b3o2b3o5bobob2o$2bo
2bobo10bo4bo6bo2bo4b2o7bo2bobobo$3bob2o6bo2bo4bobo9b2o3bo9b2o3bobo$3ob
ob2o2bo7bo5bo10b2o2bo6b2o2bo$2ob3o2bo2bob2ob2o3bo2bo2bo2bobobo3b3o5bob
3o2bobo$3obob2o2bo7bo5bo10b2o2bo6b2o2bo$3bob2o6bo2bo4bobo9b2o3bo9b2o3b
obo$2bo2bobo10bo4bo6bo2bo4b2o7bo2bobobo$4bo11b2ob5o7b3o2b3o5bobob2o$
14b2o2b3o9bo2bo3bo10bobobo$3bo30bo13bo!

Re: B2-a3i5/S2-a3

Posted: January 9th, 2021, 10:53 am

by creeperman7002

What I believe is the smallest possible c/3o:

Code: Select all

x = 13, y = 10, rule = B2-a3i5/S2-a3
2bobo$6bo$bobob3o$o2bo$bo2bo$2bo$2bo2bo$3b3o4bobo$5b4obobo$8bobo!

In rlifesrc, I have searched widths 12-16 with max pop 27 and no success so far.

EDIT: There are actually 2 slightly different 28-bit c/3s:

Code: Select all

x = 32, y = 10, rule = B2-a3i5/S2-a3
8bobo13bo$6bo17bobobobo$5b3obobo11b3o2bobo$9bo2bo15bob2o$8bo2bo12bo4b
2o$10bo17bo$7bo2bo16b3o$obo4b3o9bobo4bobo$obob4o12b3o2b2o$2bobo19bo!

EDIT 2: Whoops, the latter actually has 29 cells:

Code: Select all

x = 13, y = 10, rule = B2-a3i5/S2-a3
8bobo$6bo$5b3obobo$9bo2bo$8bo2bo$10bo$bo5bo2bo$2bo4b3o$3ob4o$2bobo!

Re: B2-a3i5/S2-a3

Posted: January 9th, 2021, 1:32 pm

by goldenratio

Surprised nobody's tried to apgsearch this yet. Unfortunately it's quite slow due to the c/2 puffer causing lots of zz_LINEARs (not even D4_+4 or D8_4 is seachable at a decent speed).
Anyways a p115:

Code: Select all

x = 34, y = 5, rule = B2-a3i5/S2-a3
3bo26bo$3o28b3o$o32bo$3o28b3o$3bo26bo!

a p6 consisting of a duoplet/shiplet torturing a B2n p3 to make it work:

Code: Select all

x = 7, y = 7, rule = B2-a3i5/S2-a3
3bo$2bob2o$3b3o$3b2obo$5bo$o$bo!

What's the second smallest still life? Is it this?

Code: Select all

x = 6, y = 6, rule = B2-a3i5/S2-a3
b2o$bob2o$o3bo$bo3bo$b2ob2o$3bo!

Re: B2-a3i5/S2-a3

Posted: January 9th, 2021, 1:43 pm

by creeperman7002

goldenratio wrote: January 9th, 2021, 1:32 pm What's the second smallest still life? Is it this?
Code: Select all
x = 6, y = 6, rule = B2-a3i5/S2-a3
b2o$bob2o$o3bo$bo3bo$b2ob2o$3bo!

This is actually the second-smallest still life (12 bits):

Code: Select all

x = 5, y = 5, rule = B2-a3i5/S2-a3
2b2o$2obo$o3bo$bob2o$b2o!