Arrow (B3-jkn4a/S1e2-a3ijnry4n)

For discussion of other cellular automata.
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77topaz
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Arrow (B3-jkn4a/S1e2-a3ijnry4n)

Post by 77topaz » May 2nd, 2018, 7:53 pm

This rule has a family of adjustable-speed rakes (3c/(12n+6) orthogonal, n≥6):

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x = 135, y = 27, rule = B3-jkn4a/S1e2-a3ijnry4n
4bo13bo13bo13bo13bo13bo13bo13bo13bo13bo$4bo13bo13bo13bo13bo13bo13bo13b
o13bo13bo3$2o5b2o5b2o5b2o5b2o5b2o5b2o5b2o5b2o5b2o5b2o5b2o5b2o5b2o5b2o
5b2o5b2o5b2o5b2o5b2o2$4bo13bo13bo13bo13bo13bo13bo13bo13bo13bo$4bo13bo
13bo13bo13bo13bo13bo13bo13bo13bo4$3b3o$4bo12b3o$18bo12b3o$32bo12b3o$
46bo12b3o$4bo55bo12b3o$4bo13bo55bo12b3o$18bo13bo55bo12b3o$32bo13bo55bo
12b3o$46bo13bo55bo12b3o$60bo13bo55bo$74bo13bo$88bo13bo$102bo13bo$116bo
13bo$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:

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x = 38, y = 3, rule = B3-jkn4a/S1e2-a3ijnry4n
19bo$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.

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x = 37, y = 5, rule = B3-jkn4a/S1e2-a3ijnry4n
35b2o$2o5bo$4b2obo26b2o$2o5bo$35b2o!
CGoL's c/4 diagonal glider is a c/2 orthogonal spaceship in this rule:

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x = 3, y = 3, rule = B3-jkn4a/S1e2-a3ijnry4n
bo$2bo$3o!
There are also 10c/20 spaceships, the most common of which is the following:

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x = 8, y = 15, rule = B3-jkn4a/S1e2-a3ijnry4n
b3ob3o$o$o3bobo$3o5$b2o2$2o$bo$3o$obo$3o!
Apart from the adjustable-speed rakes, there is also this c/4 backrake:

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x = 5, y = 6, rule = B3-jkn4a/S1e2-a3ijnry4n
2ob2o$obobo$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:

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x = 16, y = 16, rule = B3-jkn4a/S1e2-a3ijnry4n
2b3obo2bo2b2obo$5o3bo2bo2b2o$b2o2bo3b4ob2o$o2bo3bo2b2o3bo$2ob6o6bo$bo
4bobo4b2o$3b10obo$2bob2ob2ob2obobo$4obo2bo2bobobo$o3bo2b2ob5o$ob3obob
2o4bo$ob3obob2o5bo$o3b3obo2bob3o$o3b2o2bo2bob2o$bo2b4obobob3o$obobo3bo
b5o!
There are also various small c/2 orthogonal puffers:

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x = 9, y = 8, rule = B3-jkn4a/S1e2-a3ijnry4n
7bo$7b2o$7bo$o2bo2bo$o2bo2b2o$o2bo2b3o$6bobo$8bo!

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x = 15, y = 14, rule = B3-jkn4a/S1e2-a3ijnry4n
bo3bo$3ob3o$3b3obo$13bo$9bo2b3o$8b3o$9bo3$4b3o$4bobo$4b2o$6bo$6b3o!

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x = 7, y = 7, rule = B3-jkn4a/S1e2-a3ijnry4n
b2o$2bo$2bo3bo$2bobobo$2bo3bo$2bo$3o!

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x = 7, y = 16, rule = B3-jkn4a/S1e2-a3ijnry4n
bo3bo$3ob3o$b3o11$4b3o$6bo$5bo!
The name "Arrow" is derived from "adjustable rake rule" and inspired by names like Turro.

EDIT: a 5c/10 ship:

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x = 7, y = 14, rule = B3-jkn4a/S1e2-a3ijnry4n
o$obo$o$2bo$o$o4bo$2o3bo$5bo$2b3o3$4bo$4bobo$4bo!

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

Post by Bullet51 » May 5th, 2018, 12:13 am

P11:

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x = 9, y = 9, rule = B3-jkn4a/S1e2-a3ijnry4n
2b2o2bo$2o4b2o$4bo2b2o4$4bo2b2o$2o4b2o$2b2o2bo!
And some reaction:

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xx = 20, y = 3, rule = B3-jkn4a/S1e2-a3ijnry4n
2o6bo5bo$3b2obobo5bobob2o$2o6bo5bo!
Still drifting.

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77topaz
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Re: Arrow (B3-jkn4a/S1e2-a3ijnry4n)

Post by 77topaz » May 5th, 2018, 8:36 am

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.

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

Post by danny » May 5th, 2018, 12:24 pm

Some of these may be new:

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x = 124, y = 13, rule = B3-jkn4a/S1e2-a3ijnry4n
6b2o17b2o5bo7bo4b2o12bo16bobo10b2o3bobo3b2o4bo3bo4b2o2bo2b2o$2o10b2o8b
o9bo7bo6bo2b2o2b2obobo16bobo15bobo9bo3bo7bo$4bob2obo6bo5bo10bo5bo4b2ob
o10bo16bobobo10b2o2bobo2b2o14b2o2bo2b2o$2o10b2o2bo3b2o12bo3bo11b2o2b2o
8b3ob3o4bobobo$6b2o14bo2bo5bo2bo3bo2bo2b2o10b2o5b2o5b2o18b2o2bobo2b2o
4b3ob3o$25bo8bo3bo37bobo15bobo$17b2obo3bob2o5bo5bo23b2o5b2o17b2o3bobo
3b2o5b3o$19bo12bo7bo23b3ob3o5bobo28bobo$19bo2bo9bo7bo65bobobo$23b2o3bo
46bobobo24b2o5b2o$22bo5bo46bobobo$22bo53bobo$18b2o56bobo!
she/her // danielle

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

Post by AbhpzTa » May 5th, 2018, 1:59 pm

p216+32N T gun:

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x = 21, y = 13, rule = B3-jkn4a/S1e2-a3ijnry4n
12bo$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).

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77topaz
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Re: Arrow (B3-jkn4a/S1e2-a3ijnry4n)

Post by 77topaz » May 5th, 2018, 5:28 pm

danny wrote:Some of these may be new:

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RLE
Yeah, I think most of those are new. Good job! What did you use to find them?
AbhpzTa wrote:p216+32N T gun:

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RLE
Awesome! :D From this gun, a sqrtgun can be trivially constructed by simply replacing the reflector on the left with a single domino:

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x = 17, y = 13, rule = B3-jkn4a/S1e2-a3ijnry4n
8bo$8bob2o$9bo3$6bo$2o3b2o7b3o$6bo3$9bo$8bob2o$8bo!
Also, a new 2c/4 ship:

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x = 3, y = 10, rule = B3-jkn4a/S1e2-a3ijnry4n
o$obo$3o$b2o2$2bo$b2o$2o$obo$o!
EDIT: A new puffer:

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x = 12, y = 17, rule = B3-jkn4a/S1e2-a3ijnry4n
3ob3o$6bo$bobo2bo$4bo$9bo$9b2o$9b3o$5b2o7$b3o2$2bo!

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

Post by Bullet51 » May 8th, 2018, 5:27 am

New ships:

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x = 18, y = 5, rule = B3-jkn4a/S1e2-a3ijnry4n
3o2b3o2b3o2b3o$4b2o$bob2obo4b6o$12bo2bo$11bo4bo!
Still drifting.

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77topaz
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Re: Arrow (B3-jkn4a/S1e2-a3ijnry4n)

Post by 77topaz » May 29th, 2018, 5:56 pm

A fourfold shuttle with unusual behaviour:

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x = 35, y = 35, rule = B3-jkn4a/S1e2-a3ijnry4n
15bo3bo$15bobobo$17bo13$2o14b3o14b2o$15bobobo$b2o12b2ob2o12b2o$15bobobo$2o14b
3o14b2o13$17bo$15bobobo$15bo3bo!
EDIT: a D8_4-symmetric p7:

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x = 16, y = 16, rule = B3-jkn4a/S1e2-a3ijnry4n
7b2o$3bo8bo$3bo8bo$b2obobo2bobob2o$3bo2bo2bo2bo2$3b2o6b2o$o14bo$o14bo$3b2o6b
2o2$3bo2bo2bo2bo$b2obobo2bobob2o$3bo8bo$3bo8bo$7b2o!
And a small 2c/4 orthogonal spaceship:

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x = 8, y = 5, rule = B3-jkn4a/S1e2-a3ijnry4n
3o2b3o2$b6o$2bo2bo$bo4bo!
And some new puffers:

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x = 40, y = 13, rule = B3-jkn4a/S1e2-a3ijnry4n
b2o26bo9bo$2o27bo3b3o3bo$bo31bobo$2bo11bobobo14b2obo$b2o11bo3bo10bo5b
2o$3obo9bobobo6b4obo$bo2b2o8b2o7b2o$2b3o20bo6b5o$3bo5bo9bo7bo8bo$9bo9b
o6bo5b5o$bo8bo$2o26bobo$bo27bo!

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x = 8, y = 21, rule = B3-jkn4a/S1e2-a3ijnry4n
bo$b2o$b3o3$o4b3o$o6bo$4bo2bo$5bo$7bo$5bobo$7bo$5bo$4bo2bo$o6bo$o4b3o
3$b3o$b2o$bo!
EDIT 2: A shuttle that involves the t-like spaceship being transformed into the counterfeit glider and back again:

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x = 33, y = 7, rule = B3-jkn4a/S1e2-a3ijnry4n
2o29b2o$2b2o25b2o$3bo25bo$bobo25bobo$bo29bo$2bo27bo$3b2o23b2o!
The period is odd (23+4N), unlike the regular shuttles which have even periods, specifically p16+4N:

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x = 18, y = 3, rule = B3-jkn4a/S1e2-a3ijnry4n
2o6bo7b2o$4b2o2bo4b3o$2o6bo7b2o!

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

Post by Redstoneboi » May 29th, 2018, 7:34 pm

77topaz wrote: EDIT 2: A shuttle that involves the t-like spaceship being transformed into the counterfeit glider and back again:

Code: Select all

x = 33, y = 7, rule = B3-jkn4a/S1e2-a3ijnry4n
2o29b2o$2b2o25b2o$3bo25bo$bobo25bobo$bo29bo$2bo27bo$3b2o23b2o!
The period is odd (23+4N), unlike the regular shuttles which have even periods, specifically p16+4N:

Code: Select all

x = 18, y = 3, rule = B3-jkn4a/S1e2-a3ijnry4n
2o6bo7b2o$4b2o2bo4b3o$2o6bo7b2o!
I guess that's because the 2 ends of the shuttle are different
c(>^w^<c)~*
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「Fluffy」is my sutando.
「Fluffy」has the ability to engineer r e p l i c a t o r s.
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Re: Arrow (B3-jkn4a/S1e2-a3ijnry4n)

Post by 77topaz » May 30th, 2018, 12:38 am

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.

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

Post by 77topaz » June 21st, 2018, 3:31 am

New puffer:

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x = 20, y = 46, rule = B3-jkn4a/S1e2-a3ijnry4n
8bo$8bo$9bo$10b2o$6bo$6bo3$2b2o3$10bo$10bo2$15bo$15bo3$bo7bo$o2bo5b2o
2$bo3bo6bob3o$4b3o5bo$10b4obo$2b2obo6bobo$b4o2bo6bobo$2obo4bo3bo4b2o$b
o3bobo4bo$6bo2bo3bobob3o$9bo3bobo$8bo4bo$11bo$7b2o$6bobob2o3bo$6b2o7bo
$8bo6bo$8b7o2$11bo2$10b3o3$14bo$14b3o$15bo!

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77topaz
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Re: Arrow (B3-jkn4a/S1e2-a3ijnry4n)

Post by 77topaz » June 23rd, 2018, 11:20 pm

Another new small c/2 puffer:

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x = 12, y = 8, rule = B3-jkn4a/S1e2-a3ijnry4n
2b4o$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:

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x = 14, y = 53, rule = B3-jkn4a/S1e2-a3ijnry4n
5bobo3bobo$5bobo3bobo2$6bo5bo$6bo5bo3$5b3o3b3o$6bo5bo5$6bo5bo$6bo5bo
11$6bo5bo$6bo5bo9$9bo$8b3o$9bo$9bo$8b3o$9bo$5bo$4b3o$5bob2o$8b2o$6b3o$
7bo$6bo$b7o$2bo2bo$5bob3o$6b3ob3o$7bo3bo!

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77topaz
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Re: Arrow (B3-jkn4a/S1e2-a3ijnry4n)

Post by 77topaz » October 2nd, 2018, 7:17 am

A new puffer:

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x = 15, y = 17, rule = B3-jkn4a/S1e2-a3ijnry4n
3obo6b3o$ob3obo4bo2bo$3o3bo4bo2bo$14bo$12bo$14bo$12bobo$14bo$12bo$11bo
2bo$2bo4bo6bo$2bo2bobo4b3o$2bo2bo2$8b3o$8b2o$8bo!

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

Post by muzik » January 2nd, 2019, 5:08 pm

Random stuff:

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x = 33, y = 23, rule = B3-jkn4a/S1e2-a3ijnry4n
6bo$6bo4b2o3b2o3b2o3b2o3b2o4$bo$bo4b2o18bo$26bo5bo$32bo$31bo$bo9bo19bo
$bo8b3o3b2o3b2o$11bo3$6bo$2o4bo14bo$21bo4$5b2o3b2o3b2o4bo$21bo!
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77topaz
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Re: Arrow (B3-jkn4a/S1e2-a3ijnry4n)

Post by 77topaz » January 2nd, 2019, 10:53 pm

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?

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

Post by 77topaz » January 3rd, 2019, 5:03 pm

Create your own reflector:

Code: Select all

x = 16, y = 16, rule = B3-jkn4a/S1e2-a3ijnry4n
bo2b2o2b2obo2b2o$3obobo3bob3o$o2bob5obo3bo$3bo2bo2b3ob3o$4b2ob3ob2obo$
b2o2bo7b2o$b4ob2o5b3o$4b2ob2o2bo2bo$4ob3ob2obob2o$bob2ob2ob2o$3b2ob3ob
obo2bo$2obobobo2bo3b2o$3o2bo2bobob3o$b2obo2bo5b2o$2b4o2b2o2b2obo$3o4bo
b5obo!
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.

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

Post by Rhombic » January 3rd, 2019, 5:32 pm

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.

Code: Select all

x = 390, y = 3, rule = B3-jkn4a/S1e2-a3ijnry4n
o8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo
8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo4b3ob3o7bo8bo$2o7b
2o7b2o7b2o7b2o7b2o7b2o7b2o7b2o7b2o7b2o7b2o7b2o7b2o7b2o7b2o7b2o7b2o7b2o
7b2o7b2o7b2o7b2o7b2o7b2o7b2o7b2o7b2o7b2o7b2o7b2o7b2o7b2o7b2o7b2o7b2o7b
2o7b2o7b2o7b2o7b2o3bobobobo7b2o7b2o$o8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo
8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo8bo
8bo8bo8bo8bo8bo8bo4b3ob3o7bo8bo!
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Re: Arrow (B3-jkn4a/S1e2-a3ijnry4n)

Post by 77topaz » January 3rd, 2019, 7:12 pm

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.

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

Post by Hdjensofjfnen » January 3rd, 2019, 7:36 pm

p4 :D

Code: Select all

x = 3, y = 10, rule = B3-jkn4a/S1e2-a3ijnry4n
bo$obo$bo2$3o$bo2$bo$obo$bo!
EDIT: Annoying:

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x = 8, y = 7, rule = B3-jkn4a/S1e2-a3ijnry4n
2o$2bo$2o$5b2o$5bobo$5bo$b2o!
EDIT: Fixed:

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x = 8, y = 8, rule = B3-jkn4a/S1e2-a3ijnry4n
4bo$2bobo$2bo2$5b2o$5bobo$5bo$b2o!
EDIT: p6 :D

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x = 4, y = 5, rule = B3-jkn4a/S1e2-a3ijnry4n
2bo$2b2o$3bo$o$o!
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Code: Select all

x = 7, y = 5, rule = B3/S2-i3-y4i
4b3o$6bo$o3b3o$2o$bo!

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77topaz
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Re: Arrow (B3-jkn4a/S1e2-a3ijnry4n)

Post by 77topaz » January 3rd, 2019, 8:58 pm

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

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

Post by danny » January 4th, 2019, 2:50 am

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/her // danielle

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

Post by 77topaz » January 4th, 2019, 4:19 am

A new spaceship/t-ship-tagalong (6c/12) found by Danny using apgsearch:

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x = 7, y = 11, rule = B3-jkn4a/S1e2-a3ijnry4n
2bo$b2o$2bo2$b2o$3ob3o$bob2obo$5b2o$bo$bobo$bo!
EDIT: A new puffer:

Code: Select all

x = 8, y = 11, rule = B3-jkn4a/S1e2-a3ijnry4n
o$obo$o$2bo$o2bo$o2bo2b2o$o2bo$2bo$o$obo$2o!

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

Post by AbhpzTa » January 5th, 2019, 2:48 pm

T to T+R, recovery time 40:

Code: Select all

x = 57, y = 14, rule = B3-jkn4a/S1e2-a3ijnry4n
51bo$51bo4$o19bo28b2o$2o18b2o$o19bo$55bo$49bo5bo$49bo2$54bobo$54bobo!
T to 2T, recovery time 40:

Code: Select all

x = 57, y = 14, rule = B3-jkn4a/S1e2-a3ijnry4n
51bo$51bo4$o19bo28b2o$2o18b2o$o19bo$55bo$49bo5bo$40bobobo4bo$40bobobo$
54bobo$54bobo!
R to 2T, recovery time 105:

Code: Select all

x = 90, y = 18, rule = B3-jkn4a/S1e2-a3ijnry4n
2bo51bo29b2o$obo51b2o$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).

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77topaz
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Joined: January 12th, 2018, 9:19 pm

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

Post by 77topaz » January 5th, 2019, 4:16 pm

Impressive! :D 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.

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77topaz
Posts: 1366
Joined: January 12th, 2018, 9:19 pm

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

Post by 77topaz » January 6th, 2019, 5:45 pm

A new puffer:

Code: Select all

x = 11, y = 5, rule = B3-jkn4a/S1e2-a3ijnry4n
4b2o$3b2ob2o2bo$3b4ob3o$3o2bo3bo$bo!
It has a period of 8, making it the shortest-period puffer known in Arrow so far.

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