B2-ek3q4e/S03i4-ay5ace6en (CrossPlow)

[Disaster16439]

Welcome to CrossPlow. This is one of the “Plow” rules, a rule with at least the transitions B2-ek/S0.

First, meet the spaceship, the halfmoon:

Code: Select all

 x = 3, y = 4, rule = B2-ek3q4e/S03i4-ay5ace6en
o$2bo$2bo$o!

It is 2c/2.

The most useful still lifes, the family of bones:

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x = 18, y = 5, rule = B2-ek3q4e/S03i4-ay5ace6en
bo5bo6bo$3o3b3o4b3o$bo5b3o4b3o$8bo6b3o$16bo!

The left one is the Cross. The middle one is the Bone, and the right one is Long Bone, etc.

The bones can have replicator signals going along them:

Code: Select all

x = 7, y = 6, rule = B2-ek3q4e/S03i4-ay5ace6en
2bo$b3o$ob3o$3b3o$4b3o$5bo!

A good rule is that a normal bone cannot have signals on it forever. If we have a cross for supporting another one (seen later), and a signal unwantedly develops on it, we can try replacing it with a Bone. It isn’t guaranteed to work, but it might.

The next still life, the dot:

Code: Select all

x = 1, y = 1, rule = B2-ek3q4e/S03i4-ay5ace6en
o!

You sometimes see it in conduits. The first way is like so:

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x = 4, y = 3, rule = B2-ek3q4e/S03i4-ay5ace6en
o$bobo!

The second way is for the dot to block births. There are lots and lots of ways for this to happen, so I won’t go into detail. But there is one major thing:

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x = 8, y = 8, rule = B2-ek3q4e/S03i4-ay5ace6en
5bo2$6bo$5b3o$6bo$b2o$5bo$o2bo!

Remove one of the dots, and you have a starting point to have more catalyses.

REFLECTORS & STUFF

4 180° reflectors, 2 lane-shifters. None are interchangeable.

Code: Select all

x = 16, y = 54, rule = B2-ek3q4e/S03i4-ay5ace6en
10bo$6bo2b3o$5b3o2bo$6bo3$o8bo$2bo5b3o$2bo6bo$o8$2bo$4bo5bo$4bo$2bo8bo
$10b3o$11bo6$bo$3bo$3bo8bo$bo13bo$13bo$12b3o$13bo8$7bo$6b3o2bo$7bo2b3o
$11b3o$bo10bo$3bo$3bo9bo$bo$12bo$11b3o$10b3o$11bo!

We have this nice reaction:

Code: Select all

x = 12, y = 6, rule = B2-ek3q4e/S03i4-ay5ace6en
bo8bo$3o6b3o$bo8bo$5b2o$2bo6bo$4bo2bo!

However, the backward signal is uncatchable and is a big problem.

Still, we can change the “nozzle”:

Code: Select all

x = 69, y = 20, rule = B2-ek3q4e/S03i4-ay5ace6en
7bo$6b3o$7b3o32bo$8bo2bo29b3o$10b3o29bo13bo10bo$11b3o41b3o8b3o$12bo43b
o10bo4$bo8bo$3o6b3o$bo8bo21bo8bo$5b2o24b3o6b3o$2bo6bo22bo8bo15bo8bo$4b
o2bo28b2o18b3o6b3o$33bo6bo16bo8bo$35bo2bo22b2o$58bo6bo$60bo2bo!

Meet this almost-reflector, with a tantalizing dot:

Code: Select all

 x = 23, y = 10, rule = B2-ek3q4e/S03i4-ay5ace6en
o$2bo$2bo18bo$o19b3o$19b3o$5bo4bo7b3o$4b3o2b3o5b3o$5bo4b3o2bo2bo$11bo
2b3o$15bo!

Well, maybe if we attach the OTHER almost-reflector, the backwards halfmoon will annihilate with the dot. Miraculously, it does, with repeat time 40:

Code: Select all

 x = 23, y = 19, rule = B2-ek3q4e/S03i4-ay5ace6en
8bo8bo$7b3o6b3o$8bo8bo2$9bo6bo5$o$2bo$2bo18bo$o19b3o$19b3o$5bo4bo7b3o$
4b3o2b3o5b3o$5bo4b3o2bo2bo$11bo2b3o$15bo!

We can attach the nozzle in the ways shown. As an example, we have a p42 with an 180 degree reflector with the 90° nozzle facing cis:

Code: Select all

 x = 48, y = 32, rule = B2-ek3q4e/S03i4-ay5ace6en
7bo$6b3o2bo$4bo2bo2b3o4bo$3b3o2bo2b3o2b3o20bo$2b3obo5bo4bo20b3o$b3ob2o
3b2ob4o22b3o$3o3bobo28bo2bo2bo$bo15bo24b3o$3bo2bo6bo22bo6b3o$44bo2$35b
2o2b2o2$33bo8bo$6bo6bo18b4o4b4o$33bo8bo$5bo8bo21bo2bo$4b3o6b3o18bo2b2o
2bo$5bo8bo$37b2o3$3bo21bo$2b3o22bo11bo$3b3o21bo18bo$4bo2bo17bo19b3o$6b
3o35b3o$7b3o20bo4bo7b3o$8bo20b3o2b3o5b3o$30bo4b3o2bo2bo$36bo2b3o$40bo!

As to how I found it or how new conduits are found, it is useful to know how to place Crosses. They are pretty robust, so I place them rather randomly. However, there is an extremely common way for a Cross to fail. Look at the right Cross in the very first section of the reflector:

Code: Select all

x = 8, y = 8, rule = B2-ek3q4e/S03i4-ay5ace6en
4bo$6bo$6bo$4bo2$bo4bo$3o2b3o$bo4bo!

It fails because of a domino on the edge of the Cross. There are 3 ways to fix this by placing an extra cross:

Code: Select all

x = 20, y = 44, rule = B2-ek3q4e/S03i4-ay5ace6en
4bo$6bo$6bo$4bo2$bo4bo$3o2b3o2bo$bo4bo2b3o$10bo9$5bo$7bo$7bo$5bo2$2bo
4bo$b3o2b3o$2bo4bo2bo$9b3o$10bo10$11bo$13bo$13bo$11bo2$8bo4bo4bo$7b3o
2b3o2b3o$8bo4bo4bo!

We can also extend it to a bone, although in this case it doesn’t quite work.

OSCILLATORS

There are a bunch of random hasslers in this rule. The equivalent of a sparker in this rule is an object that provides a signal.

Some examples:

Code: Select all

 x = 51, y = 38, rule = B2-ek3q4e/S03i4-ay5ace6en
2b3o11b3o10b3o13bob3o$4bo9bobo12bobo13bo3bo$2b3o11b3o10b3o13bob3o$4bo
5bo7bobo8bobo13bo3bo$2b3o11b3o10b2obo12bob3o$30bo17bo3$49bo$33bo14b3o$
18bo13b3o12b3o$17b3o11b3o12b3o$2bobo11b3o11b3o12b3o$bob3o7bob3o9bob3o
10bob3o$3obo7b3obo9b3obo10b3obo$bo11bo13bo14bo$3bo11bo13bo14bo9$2b3o5b
3o$4bo5bo$2b3o2bo2b3o$2bo7bob2o$2b3o5b3o$11bo$3bo2$13bo$3bo8b3o$4bo4bo
b3o$3b3o4b3o$4bo6bo!

There are rephasing reflectors (p(2k+1)n where n is the period of sparker, n odd. Example is p39 with 13):

Code: Select all

  x = 59, y = 57, rule = B2-ek3q4e/S03i4-ay5ace6en
18bo$20bo$17bob3o$16b3obo$15b3obo$14b3o$13b3obo$12b3o$13bobo$11bo35bo$
10b3o25bo9bo$11bo28bo6b3o$10bo29bo7bo2bo$38bo11b3o$51b3o$52b3o$51bob3o
$11b2o41b3o$55bo2bo$11b2o43bo$10bo2bo41b3o$56bo14$2bo$b3o41bo2bo$2bo
43b2o$o2bo$2b3o41b2o$3b3obo$4b3o$5b3o$6b3o11bo$7bo2bo7bo29bo$9b3o6bo
28bo$10bo9bo25b3o$11bo35bo$43bobo$44b3o$41bob3o$42b3o$39bob3o$38bob3o$
37b3obo$38bo$40bo!

Except for the p3 reflector. It rephases and becomes 6n+5:

Code: Select all

 x = 35, y = 33, rule = B2-ek3q4e/S03i4-ay5ace6en
10bo$8bo$7b3obo$8bob3o$11bo$7bo19bo$6b3o9bo9bo$7bo12bo6b3o2bo$6bo13bo
7bo2b3o$18bo13bo$29bobo2bo$30b3o$31bo$7b2o2$7b2o$6bo2bo15bo2bo$26b2o2$
26b2o$3bo$2b3o$o2bobo$2bo13bo$b3o2bo7bo13bo$2bo2b3o6bo12bo$6bo9bo9b3o$
7bo19bo$23bo$22b3obo$23bob3o$26bo$24bo!

There are lots of oscillators, but here are the highlights that aren’t just boring billiard table-esque:

Code: Select all

 x = 53, y = 16, rule = B2-ek3q4e/S03i4-ay5ace6en
bo4bo16bo4bo$3o2b3o14b3o2b3o$bo4bo16bo4bo6$3b2o$5bo$5bobo34bo8bo$5bo
35b3o6b3o$4b3o15bobo2bobo12b3ob2ob3o$5bo15b3o4b3o12b3o2b3o$22b3o2b3o
14bo4bo$23bo4bo!

Left 2 are guns.
GOALS

Omniperiodicity: missing 10, 19, 21, 27, 31, 33, 37

[Disaster16439]

Unsorted oscillators based off of mostly a type of unbreachable wall:

Code: Select all

x = 181, y = 25, rule = B2-ek3q4e/S03i4-ay5ace6en
174bo$172bo$171b3obo$133bo36b3ob3o$106bo24bo37b3o3b3o$104bo25b3obo33b
3o2bo2b3o$38bo64b3obo21b3ob3o30bo2bo3bo3b3o$40bo22bo7bo30b3ob3o19b3obo
b3o31bo4bo4bo$37bob3o20b3o2bo2b3o28b3o3b3o19bo5bo31b3o7bo2bo$8bo27b3ob
3o18bobo2b3o2b3o26bobobobob3o57b3o5b3o$6bo28b3o3b3o16b3o2bobo2bobo26b
3obo3bob3o57b3o3b3o$5b3obo24b3o2bo2b3o13bo2bo9bo2bo22bo2bo4bo4bo59b3ob
3o$4bobob3o22b3obobo3b3o14bo9b3o26bo3bo3bobo2bo15bo3bo3bo34bob3o$3b3o
3bobo20b3o5b2o2bo14b3o7bobo26b3o3bobob3o16b3obobob3o36bo$2b3o5b3o17bo
2bobo7bo2bo13b3o2b2ob3o28b3o5b3o18b3o3b3o35bo$o2bo7b3o18bo7bob3o16b3ob
ob3o30b3o3bobo20b3o3bo$2bo6bo2bo2bo15b3obo5b3o18b3ob3o32b3ob3o22bo$b3o
6bo2bo18b3obobob3o20b3obo34bob3o$2b3o3bo3b3o18b3o3b3o22bo40bo$3b3o2bo
2bobo20b3ob3o25bo36bo$4bobo3b3o22b3obo$5b3obobo24bo$6bob3o27bo$9bo$7bo
!

None of the periods are new

Edit 1:

Teeny p6 gun found naturally:

Code: Select all

x = 6, y = 5, rule = B2-ek3q4e/S03i4-ay5ace6en
5bo$bo3bo$5o$bo$3bo!

Here’s a 2c/4 fuse/partial found by messing around with the gun (There are 2 tractor beam types, both of which the gun is really good at surviving. The partial was based on a different tractor beam)

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x = 4, y = 27, rule = B2-ek3q4e/S03i4-ay5ace6en
2bo2$bo2$2bo2$bo2$2bo2$bo2$2bo2$bo2$2bo2$bo2$b2o2$o2bo2$b2o2$o2bo!
[/code[

[I6_I6]

Idk, is this sublinear growth?

Code: Select all

x = 16, y = 5, rule = B2-ek3q4e/S03i4-ay5ace6en
5bo$bo3bo9bo$5o$bo$3bo!

Freaky adjustable p134:

Code: Select all

x = 30, y = 6, rule = B2-ek3q4e/S03i4-ay5ace6en
24bo3bo$4bobo20b3o$bo4bo21bo$3o$bo$3bo!

[NNlk05]

Idk, is this sublinear growth?

Code: Select all

x = 16, y = 5, rule = B2-ek3q4e/S03i4-ay5ace6en
5bo$bo3bo9bo$5o$bo$3bo!

Don’t look like one to me.
Let’s see… the puffer grows linearly, the rep pulls the dots closer, which is O(n), and the rep needs time to get to the dots. So each dot pulled is O(log n). So, the total growth is O(n - log n), and since log n gets very small compared to n at big n’s, so the total net effect is O(n).
This is strange though. I think it’s O(n/2).