## Arrow (B3-jkn4a/S1e2-a3ijnry4n)

For discussion of other cellular automata.

### Arrow (B3-jkn4a/S1e2-a3ijnry4n)

This rule has a family of adjustable-speed rakes (3c/(12n+6) orthogonal, n≥6):
`x = 135, y = 27, rule = B3-jkn4a/S1e2-a3ijnry4n4bo13bo13bo13bo13bo13bo13bo13bo13bo13bo\$4bo13bo13bo13bo13bo13bo13bo13bo13bo13bo3\$2o5b2o5b2o5b2o5b2o5b2o5b2o5b2o5b2o5b2o5b2o5b2o5b2o5b2o5b2o5b2o5b2o5b2o5b2o5b2o2\$4bo13bo13bo13bo13bo13bo13bo13bo13bo13bo\$4bo13bo13bo13bo13bo13bo13bo13bo13bo13bo4\$3b3o\$4bo12b3o\$18bo12b3o\$32bo12b3o\$46bo12b3o\$4bo55bo12b3o\$4bo13bo55bo12b3o\$18bo13bo55bo12b3o\$32bo13bo55bo12b3o\$46bo13bo55bo12b3o\$60bo13bo55bo\$74bo13bo\$88bo13bo\$102bo13bo\$116bo13bo\$130bo!`

These make use of somewhat Snowflakes-esque push and pull reactions, and like Snowflakes, the spaceships can "pass through" each other. Here is an example of square root bounding box growth:
`x = 38, y = 3, rule = B3-jkn4a/S1e2-a3ijnry4n19bo\$2o16b2o16b2o\$19bo!`

These ships can be reflected in various ways, two of which are illustrated below; the right-hand one also functions as a period-doubling mechanism.
`x = 37, y = 5, rule = B3-jkn4a/S1e2-a3ijnry4n35b2o\$2o5bo\$4b2obo26b2o\$2o5bo\$35b2o!`

CGoL's c/4 diagonal glider is a c/2 orthogonal spaceship in this rule:
`x = 3, y = 3, rule = B3-jkn4a/S1e2-a3ijnry4nbo\$2bo\$3o!`

There are also 10c/20 spaceships, the most common of which is the following:
`x = 8, y = 15, rule = B3-jkn4a/S1e2-a3ijnry4nb3ob3o\$o\$o3bobo\$3o5\$b2o2\$2o\$bo\$3o\$obo\$3o!`

Apart from the adjustable-speed rakes, there is also this c/4 backrake:
`x = 5, y = 6, rule = B3-jkn4a/S1e2-a3ijnry4n2ob2o\$obobo\$b3o2\$2bo\$2bo!`

This backrake can be tethered. In the following pattern, the tether is broken by stray gliders after about 25000 generations, creating an interesting ripple effect in the backrake's output:
`x = 16, y = 16, rule = B3-jkn4a/S1e2-a3ijnry4n2b3obo2bo2b2obo\$5o3bo2bo2b2o\$b2o2bo3b4ob2o\$o2bo3bo2b2o3bo\$2ob6o6bo\$bo4bobo4b2o\$3b10obo\$2bob2ob2ob2obobo\$4obo2bo2bobobo\$o3bo2b2ob5o\$ob3obob2o4bo\$ob3obob2o5bo\$o3b3obo2bob3o\$o3b2o2bo2bob2o\$bo2b4obobob3o\$obobo3bob5o!`

There are also various small c/2 orthogonal puffers:

`x = 9, y = 8, rule = B3-jkn4a/S1e2-a3ijnry4n7bo\$7b2o\$7bo\$o2bo2bo\$o2bo2b2o\$o2bo2b3o\$6bobo\$8bo!`

`x = 15, y = 14, rule = B3-jkn4a/S1e2-a3ijnry4nbo3bo\$3ob3o\$3b3obo\$13bo\$9bo2b3o\$8b3o\$9bo3\$4b3o\$4bobo\$4b2o\$6bo\$6b3o!`

`x = 7, y = 7, rule = B3-jkn4a/S1e2-a3ijnry4nb2o\$2bo\$2bo3bo\$2bobobo\$2bo3bo\$2bo\$3o!`

`x = 7, y = 16, rule = B3-jkn4a/S1e2-a3ijnry4nbo3bo\$3ob3o\$b3o11\$4b3o\$6bo\$5bo!`

The name "Arrow" is derived from "adjustable rake rule" and inspired by names like Turro.

EDIT: a 5c/10 ship:
`x = 7, y = 14, rule = B3-jkn4a/S1e2-a3ijnry4no\$obo\$o\$2bo\$o\$o4bo\$2o3bo\$5bo\$2b3o3\$4bo\$4bobo\$4bo!`

77topaz

Posts: 1345
Joined: January 12th, 2018, 9:19 pm

### Re: Arrow (B3-jkn4a/S1e2-a3ijnry4n)

P11:
`x = 9, y = 9, rule = B3-jkn4a/S1e2-a3ijnry4n2b2o2bo\$2o4b2o\$4bo2b2o4\$4bo2b2o\$2o4b2o\$2b2o2bo!`

And some reaction:
`xx = 20, y = 3, rule = B3-jkn4a/S1e2-a3ijnry4n2o6bo5bo\$3b2obobo5bobob2o\$2o6bo5bo!`
Still drifting.
Bullet51

Posts: 518
Joined: July 21st, 2014, 4:35 am

### Re: Arrow (B3-jkn4a/S1e2-a3ijnry4n)

Nice find on the p11! That other pattern could be considered a variant of the square root bounding box growth pattern in my first post.

77topaz

Posts: 1345
Joined: January 12th, 2018, 9:19 pm

### Re: Arrow (B3-jkn4a/S1e2-a3ijnry4n)

Some of these may be new:

`x = 124, y = 13, rule = B3-jkn4a/S1e2-a3ijnry4n6b2o17b2o5bo7bo4b2o12bo16bobo10b2o3bobo3b2o4bo3bo4b2o2bo2b2o\$2o10b2o8bo9bo7bo6bo2b2o2b2obobo16bobo15bobo9bo3bo7bo\$4bob2obo6bo5bo10bo5bo4b2obo10bo16bobobo10b2o2bobo2b2o14b2o2bo2b2o\$2o10b2o2bo3b2o12bo3bo11b2o2b2o8b3ob3o4bobobo\$6b2o14bo2bo5bo2bo3bo2bo2b2o10b2o5b2o5b2o18b2o2bobo2b2o4b3ob3o\$25bo8bo3bo37bobo15bobo\$17b2obo3bob2o5bo5bo23b2o5b2o17b2o3bobo3b2o5b3o\$19bo12bo7bo23b3ob3o5bobo28bobo\$19bo2bo9bo7bo65bobobo\$23b2o3bo46bobobo24b2o5b2o\$22bo5bo46bobobo\$22bo53bobo\$18b2o56bobo!`
she/they // Please stop using my full name. Refer to me as dani.

"I'm always on duty, even when I'm off duty." -Cody Kolodziejzyk, Ph.D.

danny

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Joined: October 27th, 2017, 3:43 pm
Location: New Jersey, USA

### Re: Arrow (B3-jkn4a/S1e2-a3ijnry4n)

p216+32N T gun:
`x = 21, y = 13, rule = B3-jkn4a/S1e2-a3ijnry4n12bo\$12bob2o\$13bo3\$2o8bo\$4b2o3b2o7b3o\$2o8bo3\$13bo\$12bob2o\$12bo!`
Iteration of sigma(n)+tau(n)-n [sigma(n)+tau(n)-n : OEIS A163163] (e.g. 16,20,28,34,24,44,46,30,50,49,11,3,3, ...) :
965808 is period 336 (max = 207085118608).
AbhpzTa

Posts: 457
Joined: April 13th, 2016, 9:40 am
Location: Ishikawa Prefecture, Japan

### Re: Arrow (B3-jkn4a/S1e2-a3ijnry4n)

danny wrote:Some of these may be new:

`RLE`

Yeah, I think most of those are new. Good job! What did you use to find them?

AbhpzTa wrote:p216+32N T gun:
`RLE`

Awesome! From this gun, a sqrtgun can be trivially constructed by simply replacing the reflector on the left with a single domino:
`x = 17, y = 13, rule = B3-jkn4a/S1e2-a3ijnry4n8bo\$8bob2o\$9bo3\$6bo\$2o3b2o7b3o\$6bo3\$9bo\$8bob2o\$8bo!`

Also, a new 2c/4 ship:
`x = 3, y = 10, rule = B3-jkn4a/S1e2-a3ijnry4no\$obo\$3o\$b2o2\$2bo\$b2o\$2o\$obo\$o!`

EDIT: A new puffer:
`x = 12, y = 17, rule = B3-jkn4a/S1e2-a3ijnry4n3ob3o\$6bo\$bobo2bo\$4bo\$9bo\$9b2o\$9b3o\$5b2o7\$b3o2\$2bo!`

77topaz

Posts: 1345
Joined: January 12th, 2018, 9:19 pm

### Re: Arrow (B3-jkn4a/S1e2-a3ijnry4n)

New ships:
`x = 18, y = 5, rule = B3-jkn4a/S1e2-a3ijnry4n3o2b3o2b3o2b3o\$4b2o\$bob2obo4b6o\$12bo2bo\$11bo4bo!`
Still drifting.
Bullet51

Posts: 518
Joined: July 21st, 2014, 4:35 am

### Re: Arrow (B3-jkn4a/S1e2-a3ijnry4n)

A fourfold shuttle with unusual behaviour:
`x = 35, y = 35, rule = B3-jkn4a/S1e2-a3ijnry4n15bo3bo\$15bobobo\$17bo13\$2o14b3o14b2o\$15bobobo\$b2o12b2ob2o12b2o\$15bobobo\$2o14b3o14b2o13\$17bo\$15bobobo\$15bo3bo!`

EDIT: a D8_4-symmetric p7:
`x = 16, y = 16, rule = B3-jkn4a/S1e2-a3ijnry4n7b2o\$3bo8bo\$3bo8bo\$b2obobo2bobob2o\$3bo2bo2bo2bo2\$3b2o6b2o\$o14bo\$o14bo\$3b2o6b2o2\$3bo2bo2bo2bo\$b2obobo2bobob2o\$3bo8bo\$3bo8bo\$7b2o!`

And a small 2c/4 orthogonal spaceship:
`x = 8, y = 5, rule = B3-jkn4a/S1e2-a3ijnry4n3o2b3o2\$b6o\$2bo2bo\$bo4bo!`

And some new puffers:
`x = 40, y = 13, rule = B3-jkn4a/S1e2-a3ijnry4nb2o26bo9bo\$2o27bo3b3o3bo\$bo31bobo\$2bo11bobobo14b2obo\$b2o11bo3bo10bo5b2o\$3obo9bobobo6b4obo\$bo2b2o8b2o7b2o\$2b3o20bo6b5o\$3bo5bo9bo7bo8bo\$9bo9bo6bo5b5o\$bo8bo\$2o26bobo\$bo27bo!`

`x = 8, y = 21, rule = B3-jkn4a/S1e2-a3ijnry4nbo\$b2o\$b3o3\$o4b3o\$o6bo\$4bo2bo\$5bo\$7bo\$5bobo\$7bo\$5bo\$4bo2bo\$o6bo\$o4b3o3\$b3o\$b2o\$bo!`

EDIT 2: A shuttle that involves the t-like spaceship being transformed into the counterfeit glider and back again:
`x = 33, y = 7, rule = B3-jkn4a/S1e2-a3ijnry4n2o29b2o\$2b2o25b2o\$3bo25bo\$bobo25bobo\$bo29bo\$2bo27bo\$3b2o23b2o!`

The period is odd (23+4N), unlike the regular shuttles which have even periods, specifically p16+4N:
`x = 18, y = 3, rule = B3-jkn4a/S1e2-a3ijnry4n2o6bo7b2o\$4b2o2bo4b3o\$2o6bo7b2o!`

77topaz

Posts: 1345
Joined: January 12th, 2018, 9:19 pm

### Re: Arrow (B3-jkn4a/S1e2-a3ijnry4n)

77topaz wrote:EDIT 2: A shuttle that involves the t-like spaceship being transformed into the counterfeit glider and back again:
`x = 33, y = 7, rule = B3-jkn4a/S1e2-a3ijnry4n2o29b2o\$2b2o25b2o\$3bo25bo\$bobo25bobo\$bo29bo\$2bo27bo\$3b2o23b2o!`

The period is odd (23+4N), unlike the regular shuttles which have even periods, specifically p16+4N:
`x = 18, y = 3, rule = B3-jkn4a/S1e2-a3ijnry4n2o6bo7b2o\$4b2o2bo4b3o\$2o6bo7b2o!`

I guess that's because the 2 ends of the shuttle are different
c(>^x^<c)~
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Most of all, Fluffy knows Natsuki best girl.

Redstoneboi

Posts: 329
Joined: May 14th, 2018, 3:57 am

### Re: Arrow (B3-jkn4a/S1e2-a3ijnry4n)

Redstoneboi wrote:I guess that's because the 2 ends of the shuttle are different

You don't say. The "ends" of the shuttle pretty much define it.

77topaz

Posts: 1345
Joined: January 12th, 2018, 9:19 pm

### Re: Arrow (B3-jkn4a/S1e2-a3ijnry4n)

New puffer:
`x = 20, y = 46, rule = B3-jkn4a/S1e2-a3ijnry4n8bo\$8bo\$9bo\$10b2o\$6bo\$6bo3\$2b2o3\$10bo\$10bo2\$15bo\$15bo3\$bo7bo\$o2bo5b2o2\$bo3bo6bob3o\$4b3o5bo\$10b4obo\$2b2obo6bobo\$b4o2bo6bobo\$2obo4bo3bo4b2o\$bo3bobo4bo\$6bo2bo3bobob3o\$9bo3bobo\$8bo4bo\$11bo\$7b2o\$6bobob2o3bo\$6b2o7bo\$8bo6bo\$8b7o2\$11bo2\$10b3o3\$14bo\$14b3o\$15bo!`

77topaz

Posts: 1345
Joined: January 12th, 2018, 9:19 pm

### Re: Arrow (B3-jkn4a/S1e2-a3ijnry4n)

Another new small c/2 puffer:
`x = 12, y = 8, rule = B3-jkn4a/S1e2-a3ijnry4n2b4o\$4b3o\$4b2o\$3o\$bo\$6b3o\$5b3ob3o\$6bo3bo!`

Also, I think there's a good chance this rule is omniperiodic, as there are shuttles of periods 16+4N, 23+4N and 57+4N (the fourfold shuttle with the small lake), leaving just one family of extendable shuttles (4N+2) plus a finite number of lower periods to be found.

EDIT: A thing which converts the output trails of the above puffer into gliders:
`x = 14, y = 53, rule = B3-jkn4a/S1e2-a3ijnry4n5bobo3bobo\$5bobo3bobo2\$6bo5bo\$6bo5bo3\$5b3o3b3o\$6bo5bo5\$6bo5bo\$6bo5bo11\$6bo5bo\$6bo5bo9\$9bo\$8b3o\$9bo\$9bo\$8b3o\$9bo\$5bo\$4b3o\$5bob2o\$8b2o\$6b3o\$7bo\$6bo\$b7o\$2bo2bo\$5bob3o\$6b3ob3o\$7bo3bo!`

77topaz

Posts: 1345
Joined: January 12th, 2018, 9:19 pm

### Re: Arrow (B3-jkn4a/S1e2-a3ijnry4n)

A new puffer:
`x = 15, y = 17, rule = B3-jkn4a/S1e2-a3ijnry4n3obo6b3o\$ob3obo4bo2bo\$3o3bo4bo2bo\$14bo\$12bo\$14bo\$12bobo\$14bo\$12bo\$11bo2bo\$2bo4bo6bo\$2bo2bobo4b3o\$2bo2bo2\$8b3o\$8b2o\$8bo!`

77topaz

Posts: 1345
Joined: January 12th, 2018, 9:19 pm

### Re: Arrow (B3-jkn4a/S1e2-a3ijnry4n)

Random stuff:
`x = 33, y = 23, rule = B3-jkn4a/S1e2-a3ijnry4n6bo\$6bo4b2o3b2o3b2o3b2o3b2o4\$bo\$bo4b2o18bo\$26bo5bo\$32bo\$31bo\$bo9bo19bo\$bo8b3o3b2o3b2o\$11bo3\$6bo\$2o4bo14bo\$21bo4\$5b2o3b2o3b2o4bo\$21bo!`
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muzik

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Location: Scotland

### Re: Arrow (B3-jkn4a/S1e2-a3ijnry4n)

Nice! It's a track that's not reburnable, but not that far from it either - I wonder if waveguides could be used (as with AbhpzTa's gun) to stabilise that track and allow the creation of loop oscillators?

77topaz

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Joined: January 12th, 2018, 9:19 pm

### Re: Arrow (B3-jkn4a/S1e2-a3ijnry4n)

`x = 16, y = 16, rule = B3-jkn4a/S1e2-a3ijnry4nbo2b2o2b2obo2b2o\$3obobo3bob3o\$o2bob5obo3bo\$3bo2bo2b3ob3o\$4b2ob3ob2obo\$b2o2bo7b2o\$b4ob2o5b3o\$4b2ob2o2bo2bo\$4ob3ob2obob2o\$bob2ob2ob2o\$3b2ob3obobo2bo\$2obobobo2bo3b2o\$3o2bo2bobob3o\$b2obo2bo5b2o\$2b4o2b2o2b2obo\$3o4bob5obo!`

EDIT: Some clarifying information: this pattern features a long line of t-ships with a reflector (part of a backrake's disturbed output) pushing a single domino for about 50k generations until it reaches a pair of dominos to create another reflector, finally stabilising the ships into an oscillator.
Last edited by 77topaz on January 3rd, 2019, 7:10 pm, edited 1 time in total.

77topaz

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Joined: January 12th, 2018, 9:19 pm

### Re: Arrow (B3-jkn4a/S1e2-a3ijnry4n)

The ripple effect is in fact a t-ship travelling through an opposite-direction t-ship stream. It goes through without being altered in any way.
`x = 390, y = 3, rule = B3-jkn4a/S1e2-a3ijnry4no8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo4b3ob3o7bo8bo\$2o7b2o7b2o7b2o7b2o7b2o7b2o7b2o7b2o7b2o7b2o7b2o7b2o7b2o7b2o7b2o7b2o7b2o7b2o7b2o7b2o7b2o7b2o7b2o7b2o7b2o7b2o7b2o7b2o7b2o7b2o7b2o7b2o7b2o7b2o7b2o7b2o7b2o7b2o7b2o7b2o3bobobobo7b2o7b2o\$o8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo4b3ob3o7bo8bo!`
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Rhombic

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### Re: Arrow (B3-jkn4a/S1e2-a3ijnry4n)

Rhombic wrote:The ripple effect is in fact a t-ship travelling through an opposite-direction t-ship stream. It goes through without being altered in any way.

Indeed, and in the example in the OP it's a stream from a backrake hitting a reflector and thus passing back through itself; a long chain of the ripples in your example is created, because you have two continuous streams in opposite directions passing through each other.

77topaz

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Joined: January 12th, 2018, 9:19 pm

### Re: Arrow (B3-jkn4a/S1e2-a3ijnry4n)

p4
`x = 3, y = 10, rule = B3-jkn4a/S1e2-a3ijnry4nbo\$obo\$bo2\$3o\$bo2\$bo\$obo\$bo!`

EDIT: Annoying:
`x = 8, y = 7, rule = B3-jkn4a/S1e2-a3ijnry4n2o\$2bo\$2o\$5b2o\$5bobo\$5bo\$b2o!`

EDIT: Fixed:
`x = 8, y = 8, rule = B3-jkn4a/S1e2-a3ijnry4n4bo\$2bobo\$2bo2\$5b2o\$5bobo\$5bo\$b2o!`

EDIT: p6
`x = 4, y = 5, rule = B3-jkn4a/S1e2-a3ijnry4n2bo\$2b2o\$3bo\$o\$o!`
Life is hard. Deal with it.
My favorite oscillator of all time:
`x = 7, y = 5, rule = B3/S2-i3-y4i4b3o\$6bo\$o3b3o\$2o\$bo!`

Hdjensofjfnen

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Location: r cis θ

### Re: Arrow (B3-jkn4a/S1e2-a3ijnry4n)

Those p4 and p6 mechanisms were known from Catagolue, but I suppose no-one posted them in this thread before.

77topaz

Posts: 1345
Joined: January 12th, 2018, 9:19 pm

### Re: Arrow (B3-jkn4a/S1e2-a3ijnry4n)

I feel like the 'passing through' mechanism could be used to make really cool constructs while only using one channel instead of a reflector loop.
she/they // Please stop using my full name. Refer to me as dani.

"I'm always on duty, even when I'm off duty." -Cody Kolodziejzyk, Ph.D.

danny

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### Re: Arrow (B3-jkn4a/S1e2-a3ijnry4n)

A new spaceship/t-ship-tagalong (6c/12) found by Danny using apgsearch:
`x = 7, y = 11, rule = B3-jkn4a/S1e2-a3ijnry4n2bo\$b2o\$2bo2\$b2o\$3ob3o\$bob2obo\$5b2o\$bo\$bobo\$bo!`

EDIT: A new puffer:
`x = 8, y = 11, rule = B3-jkn4a/S1e2-a3ijnry4no\$obo\$o\$2bo\$o2bo\$o2bo2b2o\$o2bo\$2bo\$o\$obo\$2o!`

77topaz

Posts: 1345
Joined: January 12th, 2018, 9:19 pm

### Re: Arrow (B3-jkn4a/S1e2-a3ijnry4n)

T to T+R, recovery time 40:
`x = 57, y = 14, rule = B3-jkn4a/S1e2-a3ijnry4n51bo\$51bo4\$o19bo28b2o\$2o18b2o\$o19bo\$55bo\$49bo5bo\$49bo2\$54bobo\$54bobo!`

T to 2T, recovery time 40:
`x = 57, y = 14, rule = B3-jkn4a/S1e2-a3ijnry4n51bo\$51bo4\$o19bo28b2o\$2o18b2o\$o19bo\$55bo\$49bo5bo\$40bobobo4bo\$40bobobo\$54bobo\$54bobo!`

R to 2T, recovery time 105:
`x = 90, y = 18, rule = B3-jkn4a/S1e2-a3ijnry4n2bo51bo29b2o\$obo51b2o\$b2o50b2o29b2o2\$84b2o2\$85b3o\$88bo\$85b2o2bo\$89bo\$86b3o2\$88b2o3\$79bo\$72bo6bo\$72bo!`
Iteration of sigma(n)+tau(n)-n [sigma(n)+tau(n)-n : OEIS A163163] (e.g. 16,20,28,34,24,44,46,30,50,49,11,3,3, ...) :
965808 is period 336 (max = 207085118608).
AbhpzTa

Posts: 457
Joined: April 13th, 2016, 9:40 am
Location: Ishikawa Prefecture, Japan

### Re: Arrow (B3-jkn4a/S1e2-a3ijnry4n)

Impressive! I think the T-to-2T in particular could be used to create another family of adjustable-period oscillators, by placing four of them in a loop and eating the second T so the mechanism acts as a Snark. Would that allow all oscillators periods greater than 40, or would it still be limited to a subset?

Also, leaving one or more of the second Ts uneaten would give a family of adjustable-period guns.

77topaz

Posts: 1345
Joined: January 12th, 2018, 9:19 pm

### Re: Arrow (B3-jkn4a/S1e2-a3ijnry4n)

A new puffer:
`x = 11, y = 5, rule = B3-jkn4a/S1e2-a3ijnry4n4b2o\$3b2ob2o2bo\$3b4ob3o\$3o2bo3bo\$bo!`

It has a period of 8, making it the shortest-period puffer known in Arrow so far.

77topaz

Posts: 1345
Joined: January 12th, 2018, 9:19 pm

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