## 1-Dimensional Patterns

For discussion of specific patterns or specific families of patterns, both newly-discovered and well-known.

### 1-Dimensional Patterns

For all patterns that are only 1 cell thick!
Do all patterns have a 1-cell-thick-parent? (This includes junk that doesn't interfere with said pattern- for example, since a one cell thick is vertically symmetrical, what's above is the same as what's below.)
One-cell-thick patterns can cleanly create gliders for syntheses, etc, so I was thinking we could make a thread for the most interesting ones.

One-cell-thick infinite growth:
`x = 39, y = 1, rule = 23/38ob5o3b3o6b7ob5o!`

What do we want to accomplish with one-cell thick patterns?
To start, glider syntheses would work, so we have a few questions:
1) What is the smallest one-cell-thick pattern that creates gliders?
2) What is the smallest one-cell-thick pattern that is a PURE glider generator (that is, creates gliders and nothing else?)
twinb7

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Location: Ames, Iowa

### Re: 1-Dimensional Patterns

twinb7 wrote:1) What is the smallest one-cell-thick pattern that creates gliders?

Some research on this question is published here.

twinb7 wrote:2) What is the smallest one-cell-thick pattern that is a PURE glider generator (that is, creates gliders and nothing else?)

That's a tougher one -- at least I haven't seen very many one-cell-thick patterns that emit gliders without leaving piles of junk. Maybe Paul Callahan's 66-cell diehard could be adapted somehow to let a glider or spaceship out?

dvgrn
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### Re: 1-Dimensional Patterns

That's a tougher one -- at least I haven't seen very many one-cell-thick patterns that emit gliders without leaving piles of junk. Maybe Paul Callahan's 66-cell diehard could be adapted somehow to let a glider or spaceship out?

Mm, clearly we can take just half of that:

`x = 39, y = 1, rule = B3/S236ob4ob3ob7ob5ob4ob4o!`

to purely make gliders and LWSS's.

Adding a nice beehive predecessor to the right as shown:

`x = 61, y = 1, rule = B3/S236ob4ob3ob7ob5ob4ob4o18b4o!`

Could compact syntheses as it creates more gliders without the need for an entire new set of 33 cells.

Lastly, I give a real quick predecessor (5-1-5) of the pulsar. It may be obvious, though..
`x = 11, y = 1, rule = B3/S235ob5o!`
twinb7

Posts: 175
Joined: February 11th, 2014, 8:08 pm
Location: Ames, Iowa

### Re: 1-Dimensional Patterns

`x = 19, y = 1, rule = B3/S234o3b12o!`

A 16 cell, 19-wide pattern that produces a couple gliders- two heading diagonally to the upper left, and two heading diagonally downwards left from a good distance that may be used in syntheses.

`x = 94, y = 1, rule = B3/S2313o2b12o25b9o4b8ob7o4b9o!`

A methuselah: At one point there's a pulsar.
twinb7

Posts: 175
Joined: February 11th, 2014, 8:08 pm
Location: Ames, Iowa

### Re: 1-Dimensional Patterns

oblique

Posts: 122
Joined: July 16th, 2013, 1:30 pm

### Re: 1-Dimensional Patterns

Oooo!
Oblique has pointed out a one-cell-thick quadratic growth pattern:
`x = 1013783, y = 1, rule = B3/S23105o298b25ob3o15828b41ob3o69b8o102b3ob41o91b105o161b105o101b4ob49o31930b41ob3o30b8o63b3ob41o13b105o3b105o101b4ob49o15906b41ob3o30b8o63b3ob41o13b105o14616b105o101b4ob49o1558b41ob3o30b8o63b3ob41o13b105o232b105o101b4ob49o1550b41ob3o30b8o63b3ob41o13b105o2b105o101b4ob49o1554b41ob3o30b8o63b3ob41o13b105o3b105o101b4ob49o1548b41ob3o30b8o63b3ob41o13b105o22b105o101b4ob49o1580b41ob3o30b8o63b3ob41o13b105o32367b105o101b4ob49o31822b41ob3o30b8o63b3ob41o13b105o221b105o101b4ob49o31836b41ob3o30b8o63b3ob41o13b105o239b105o101b4ob49o31836b41ob3o30b8o63b3ob41o13b105o397b105o298b25ob3o31764b41ob3o69b8o102b3ob41o91b105o2b105o101b4ob49o31970b41ob3o30b8o63b3ob41o13b105o503b105o298b25ob3o31842b41ob3o69b8o102b3ob41o91b105o3b105o101b4ob49o31876b41ob3o30b8o63b3ob41o13b105o3b105o101b4ob49o31870b41ob3o30b8o63b3ob41o13b105o2b105o101b4ob49o31882b41ob3o30b8o63b3ob41o13b105o3b105o101b4ob49o31876b41ob3o30b8o63b3ob41o13b105o2b105o101b4ob49o31872b41ob3o30b8o63b3ob41o13b105o397b105o101b4ob49o31902b41ob3o30b8o63b3ob41o13b105o7b105o13b41ob3o63b8o30b3ob41o31906b49ob4o101b105o3b105o91b41ob3o102b8o69b3ob41o31786b3ob25o298b105o116b105o13b41ob3o63b8o30b3ob41o31872b49ob4o101b105o32480b105o13b41ob3o63b8o30b3ob41o31866b49ob4o101b105o32858b105o13b41ob3o63b8o30b3ob41o31936b49ob4o101b105o2b105o91b41ob3o102b8o69b3ob41o31874b3ob25o298b105o158b105o91b41ob3o102b8o69b3ob41o31768b3ob25o298b105o3b105o91b41ob3o102b8o69b3ob41o31750b3ob25o298b105o2b105o91b41ob3o102b8o69b3ob41o31746b3ob25o298b105o2b105o91b41ob3o102b8o69b3ob41o31726b3ob25o298b105o3b105o13b41ob3o63b8o30b3ob41o1584b49ob4o101b105o2b105o13b41ob3o63b8o30b3ob41o1544b49ob4o101b105o1758b105o91b41ob3o102b8o69b3ob41o1464b3ob25o298b105o2b105o91b41ob3o102b8o69b3ob41o1462b3ob25o298b105o3b105o91b41ob3o102b8o69b3ob41o15820b3ob25o298b105o46826b105o383b3ob25o31701b41ob3o37b8o102b3ob41o63b105o!`
twinb7

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Joined: February 11th, 2014, 8:08 pm
Location: Ames, Iowa

### Re: 1-Dimensional Patterns

PURE gliders from 1D:
`x = 47, y = 1, rule = B3/S239ob10o4b7o5b3ob3ob3o!`
knightlife

Posts: 566
Joined: May 31st, 2009, 12:08 am

### Re: 1-Dimensional Patterns

knightlife wrote:PURE gliders from 1D...

Looks good... The really nice thing would be a couple of different pure *WSS generators, which could then be collided to produce a universal construction toolkit, along the lines of the solution for two-cells-thick patterns.

But I suppose the quadratic-growth pattern already has all the required pieces to solve the universal-construction problem -- just a lot messier than the 2xN case, is all...!

dvgrn
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Posts: 5718
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### Re: 1-Dimensional Patterns

knightlife wrote:PURE gliders from 1D:
`x = 47, y = 1, rule = B3/S239ob10o4b7o5b3ob3ob3o!`

Useful!

dvgrn wrote:But I suppose the quadratic-growth pattern already has all the required pieces to solve the universal-construction problem

Maybe. I'd still like more, I suppose. ^^
twinb7

Posts: 175
Joined: February 11th, 2014, 8:08 pm
Location: Ames, Iowa

### Re: 1-Dimensional Patterns

twinb7 wrote:
knightlife wrote:PURE gliders from 1D:
`x = 47, y = 1, rule = B3/S239ob10o4b7o5b3ob3ob3o!`

Useful!

dvgrn wrote:But I suppose the quadratic-growth pattern already has all the required pieces to solve the universal-construction problem

Maybe. I'd still like more, I suppose. ^^

How about using only PURE 1D glider generators for universal construction?

oblique

Posts: 122
Joined: July 16th, 2013, 1:30 pm

### Re: 1-Dimensional Patterns

oblique wrote:How about using only PURE 1D glider generators for universal construction?

You'd need a lot more clean 1D glider generators with slightly different timings, I think. As far as I can see, the current clean 1D reactions don't allow for putting gliders one behind another on nearby lanes, and it seems like that will be needed to produce clean *WSSes. At least I don't see how to do it with glider kickbacks...?

The usual trick is to collide gliders to produce lots of *WSSes on nearby lanes, and then collide those to make a couple of slow glider streams with arbitrary timing... and then collide those to build whatever object you want to build.

-- When I write it out, that sounds like a lot of work! But it's a lot harder if you can't build the *WSSes without leaving junk all over the place.

dvgrn
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### Re: 1-Dimensional Patterns

Four pure gliders:
`x = 56, y = 1, rule = B3/S234o5b8ob4ob3o4b3ob4ob8o5b4o!`

This uses a basic 3-4-8 pattern that needs cleanup.
knightlife

Posts: 566
Joined: May 31st, 2009, 12:08 am

### Re: 1-Dimensional Patterns

Two gliders for roughly half the size:
`x = 24, y = 1, rule = B3/S233o2b8ob5ob4o!`

Found it while randomizing a 100x1 rectangle at 80% density. (That 80% number can be varied somewhat.)
I Like My Heisenburps! (and others)

Extrementhusiast

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Joined: June 16th, 2009, 11:24 pm
Location: USA

### Re: 1-Dimensional Patterns

I tried to put two of these together and I realized that the distance between glider generators doesn't matter:

`x = 168, y = 1, rule = B3/S234o5b8ob4ob3o4b3ob4ob8o5b4o88b3o2b8ob5ob4o!`

`x = 94, y = 1, rule = B3/S234o5b8ob4ob3o4b3ob4ob8o5b4o14b3o2b8ob5ob4o!`

the gliders are the same distance from each other upon approach.
So, it's how long it takes for these gliders to be generated that's an important factor.
twinb7

Posts: 175
Joined: February 11th, 2014, 8:08 pm
Location: Ames, Iowa

### Re: 1-Dimensional Patterns

Diehard can be made any length:
`x = 149, y = 1, rule = B3/S235o5b4ob10ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3o8b4o!`
knightlife

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Joined: May 31st, 2009, 12:08 am

### Re: 1-Dimensional Patterns

`10o!`
Gpennder_____409

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Joined: February 27th, 2014, 11:55 pm

### Re: 1-Dimensional Patterns

Pure spaceship generator collection:
`x = 234, y = 529, rule = B3/S23obobo2\$4bo2\$4bo25b4o6b4ob5ob10ob6o2\$4bo2\$4bo32\$o3bobobo2\$o7bo2\$o3bobobo21b3o4b4ob5o2b3o4b3o51b3o2b8o3b5ob4o4b3o47b5o4b5o4b3ob4ob8o5b4o2\$o7bo2\$o3bobobo32\$obobo3bo2\$4bo3bo2\$obobo3bo21b5ob3o3b4o11b3o2\$o7bo2\$obobo3bo32\$obobo3bo3bo2\$4bo3bo3bo2\$obobo3bobobo17b10o7b5o3b3ob9o2b3o2\$o11bo2\$obobo7bo32\$obobo3bobobo2\$4bo7bo2\$obobo7bo17b3ob9ob3ob3o2\$o11bo2\$obobo7bo32\$obobo3bobobo2\$4bo3bo3bo2\$obobo3bobobo17b4o7b7ob3o6b4ob9ob3ob3o2\$o7bo3bo2\$obobo3bobobo32\$obobo3bo2\$4bo3bo2\$obobo3bo21b3o3b4o2b5o2b3ob3o2\$4bo3bo2\$obobo3bo32\$obobo3bobobo2\$4bo7bo2\$obobo3bobobo17b4ob5ob8o2b3o2\$4bo3bo2\$obobo3bobobo32\$o3bo3bo2\$o3bo3bo2\$obobo3bo21b9ob10o4b7o5b3ob3ob3o2\$4bo3bo2\$4bo3bo32\$obobo3bo3bo2\$o7bo3bo2\$obobo3bobobo17b12ob3ob4o3b3o2\$4bo7bo2\$obobo7bo32\$obobo3bobobo2\$o7bo3bo2\$obobo3bobobo17b3o2b3ob9ob3o2\$4bo7bo2\$obobo3bobobo32\$obobo3bobobo2\$o3bo7bo2\$obobo3bobobo17b3o3b4o2b5o2\$4bo3bo2\$obobo3bobobo32\$o3bo3bo3bo9bo\$20bo3bo\$o3bo3bo3bo9bo\$20bo3bo\$o3bobobo3bo9bo7b6ob4ob3ob7ob5ob4ob4o2\$o7bo3bo2\$o7bo3bo32\$obobo3bo3bobobo2\$4bo3bo3bo3bo2\$obobo3bo3bobobo13b5ob3o3b3ob4o9b10o2\$o7bo7bo2\$obobo3bo3bobobo!`

EDIT: 9 more:
`x = 98, y = 329, rule = B3/S23obobo2\$o2\$obobo25b3ob5o2b6o3b7o6b5ob5o2\$4bo2\$obobo32\$o3bobobo2\$o7bo2\$o3bobobo21b3o3b4ob4o3b3o2b5ob5o5b4o2\$o3bo2\$o3bobobo32\$obobo3bobobo2\$4bo3bo2\$obobo3bobobo17b3o7b3ob3ob10o2b3o2b7o3b3o2\$o11bo2\$obobo3bobobo32\$obobo3bobobo2\$4bo3bo2\$obobo3bobobo17b5ob5o6b7o3b9ob3o2\$o7bo3bo2\$obobo3bobobo32\$obobo3bobobo2\$4bo7bo2\$obobo3bobobo17b3o5b5ob4o11b10ob3o6b3o2\$4bo7bo2\$obobo3bobobo32\$obobo3bobobo2\$o7bo3bo2\$obobo3bobobo17b6ob5o7b5o5b7o3b3o3b4o6b4ob3o2b3o2\$4bo3bo3bo2\$obobo3bobobo32\$obobo3bo2\$o7bo2\$obobo3bo21b3ob4o8b4ob4ob6o4b3o8b3ob3o2\$o3bo3bo2\$obobo3bo32\$obobo3bobobo2\$o11bo2\$obobo3bobobo17b3ob4o8b4ob4o2b6o3b3o8b3ob3o2\$o3bo7bo2\$obobo3bobobo32\$o3bobobo3bobobo2\$o7bo7bo2\$o3bobobo3bobobo13b4o2b3o9b3ob4ob3ob10o2\$o3bo7bo2\$o3bobobo3bobobo!`

EDIT2: 3 more:
`x = 73, y = 89, rule = B3/S23obobo3bo2\$4bo3bo2\$obobo3bo21b5ob3o3b4ob6o2b4o10b4o2\$o7bo2\$obobo3bo32\$obobo3bobobo2\$4bo3bo2\$obobo3bobobo17b6ob4o2b5ob3o6b8o2\$4bo7bo2\$obobo3bobobo32\$obobo3bobobo2\$o11bo2\$obobo3bobobo17b4o14b3ob5ob3ob4o3b3o2\$4bo3bo2\$obobo3bobobo!`

EDIT3: T17:
`x = 105, y = 9, rule = B3/S23o3bobobo2\$o7bo2\$o7bo21b3o2b3o4b7o9b13o2b3o3b3o6b5o2b4o3b3o2\$o7bo2\$o7bo!`

EDIT4: T6, T47 and T57:
`x = 227, y = 129, rule = B3/S23obobo2\$o2\$obobo15b4o7b7ob3ob3o3b5ob4o6b6o2b3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3o2b3o5b5ob4o5b4ob3ob10ob4o9b5o2b4o3b3o2\$o3bo2\$obobo52\$o3bo3bobobo2\$o3bo7bo2\$obobo7bo7b6o3b5ob3o3b3o2b4ob8o2b3ob5o3b3o3b5o2b4o3b3o2\$4bo7bo2\$4bo7bo52\$obobo3bobobo2\$o11bo2\$obobo7bo7b3o3b4o2b5o14b3o4b4o2b3ob4ob3ob5o3b6o2\$4bo7bo2\$obobo7bo!`

EDIT5: T152+18n:
`x = 79, y = 41, rule = B3/S235o5b4ob10ob3ob3ob3ob3o2b3o11b4o3b3o40\$5o5b4ob10ob3ob3ob3ob3ob3ob3ob3o2b3o11b4o3b3o!`

2 pure LWSS generators:
`x = 172, y = 91, rule = B3/S236ob4ob3ob7ob5ob4ob4o14b5o5b4ob10ob3ob3ob3ob3o2b3o11b4o3b3o90\$6ob4ob3ob7ob5ob4ob4o24b5ob4o6b4o6b5ob3o7b5o5b4ob10ob3ob3ob3ob3o2b3o11b4o3b3o!`
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

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### Re: 1-Dimensional Patterns

1-cell-thick (double) glider gun synth:
`x = 11313, y = 1, rule = B3/S233o3b4o11b3o2b3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob10ob4o5b5o5b6ob4ob3ob7ob5ob4ob4o14b5o5b4ob10ob3ob3ob3ob3o2b3o11b4o3b3o30b6ob4ob3ob7ob5ob4ob4o14b5o5b4ob10ob3ob3ob3ob3o2b3o11b4o3b3o3b6ob4ob3ob7ob5ob4ob4o14b5o5b4ob10ob3ob3ob3ob3o2b3o11b4o3b3o4b6ob4ob3ob7ob5ob4ob4o14b5o5b4ob10ob3ob3ob3ob3o2b3o11b4o3b3o30b6ob4ob3ob7ob5ob4ob4o14b5o5b4ob10ob3ob3ob3ob3o2b3o11b4o3b3o3b6ob4ob3ob7ob5ob4ob4o14b5o5b4ob10ob3ob3ob3ob3o2b3o11b4o3b3o3b6ob4ob3ob7ob5ob4ob4o14b5o5b4ob10ob3ob3ob3ob3o2b3o11b4o3b3o50b6ob4ob3ob7ob5ob4ob4o14b5o5b4ob10ob3ob3ob3ob3o2b3o11b4o3b3o3b6ob4ob3ob7ob5ob4ob4o14b5o5b4ob10ob3ob3ob3ob3o2b3o11b4o3b3o51b6ob4ob3ob7ob5ob4ob4o14b5o5b4ob10ob3ob3ob3ob3o2b3o11b4o3b3o30b6ob4ob3ob7ob5ob4ob4o14b5o5b4ob10ob3ob3ob3ob3o2b3o11b4o3b3o3b6ob4ob3ob7ob5ob4ob4o14b5o5b4ob10ob3ob3ob3ob3o2b3o11b4o3b3o3b6ob4ob3ob7ob5ob4ob4o14b5o5b4ob10ob3ob3ob3ob3o2b3o11b4o3b3o228b6ob4o2b5ob3o6b8o293b3o3b4o11b3o2b3ob3ob3ob3ob10ob4o5b5o14b4ob4ob5ob7ob3ob4ob6o51b3o3b4o11b3o2b3ob3ob3ob3ob10ob4o5b5o14b4ob4ob5ob7ob3ob4ob6o4b3o3b4o11b3o2b3ob3ob3ob3ob10ob4o5b5o14b4ob4ob5ob7ob3ob4ob6o4b3o3b4o11b3o2b3ob3ob3ob3ob10ob4o5b5o14b4ob4ob5ob7ob3ob4ob6o4b3o3b4o11b3o2b3ob3ob3ob3ob10ob4o5b5o14b4ob4ob5ob7ob3ob4ob6o4b3o3b4o11b3o2b3ob3ob3ob3ob10ob4o5b5o14b4ob4ob5ob7ob3ob4ob6o4b3o3b4o11b3o2b3ob3ob3ob3ob10ob4o5b5o14b4ob4ob5ob7ob3ob4ob6o72b3o3b4o11b3o2b3ob3ob3ob3ob10ob4o5b5o14b4ob4ob5ob7ob3ob4ob6o4b3o3b4o11b3o2b3ob3ob3ob3ob10ob4o5b5o14b4ob4ob5ob7ob3ob4ob6o4b3o3b4o11b3o2b3ob3ob3ob3ob10ob4o5b5o14b4ob4ob5ob7ob3ob4ob6o19b3o3b4o11b3o2b3ob3ob3ob3ob10ob4o5b5o14b4ob4ob5ob7ob3ob4ob6o4b3o3b4o11b3o2b3ob3ob3ob3ob10ob4o5b5o14b4ob4ob5ob7ob3ob4ob6o4b3o3b4o11b3o2b3ob3ob3ob3ob10ob4o5b5o14b4ob4ob5ob7ob3ob4ob6o4b6ob4ob3ob7ob5ob4ob4o14b5o5b4ob10ob3ob3ob3ob3o2b3o11b4o3b3o280b6ob4ob3ob7ob5ob4ob4o14b5o5b4ob10ob3ob3ob3ob3o2b3o11b4o3b3o4b6ob4ob3ob7ob5ob4ob4o14b5o5b4ob10ob3ob3ob3ob3o2b3o11b4o3b3o4b6ob4ob3ob7ob5ob4ob4o14b5o5b4ob10ob3ob3ob3ob3o2b3o11b4o3b3o4b6ob4ob3ob7ob5ob4ob4o14b5o5b4ob10ob3ob3ob3ob3o2b3o11b4o3b3o4b6ob4ob3ob7ob5ob4ob4o14b5o5b4ob10ob3ob3ob3ob3o2b3o11b4o3b3o4b6ob4ob3ob7ob5ob4ob4o14b5o5b4ob10ob3ob3ob3ob3o2b3o11b4o3b3o116b6ob4ob3ob7ob5ob4ob4o14b5o5b4ob10ob3ob3ob3ob3o2b3o11b4o3b3o4b6ob4ob3ob7ob5ob4ob4o14b5o5b4ob10ob3ob3ob3ob3o2b3o11b4o3b3o4b6ob4ob3ob7ob5ob4ob4o14b5o5b4ob10ob3ob3ob3ob3o2b3o11b4o3b3o12b6ob4ob3ob7ob5ob4ob4o14b5o5b4ob10ob3ob3ob3ob3o2b3o11b4o3b3o4b6ob4ob3ob7ob5ob4ob4o14b5o5b4ob10ob3ob3ob3ob3o2b3o11b4o3b3o4b6ob4ob3ob7ob5ob4ob4o14b5o5b4ob10ob3ob3ob3ob3o2b3o11b4o3b3o2b3o2b8ob5ob4o13b3o3b4o11b3o2b3ob3ob3ob3ob10ob4o5b5o14b4ob4ob5ob7ob3ob4ob6o3b3o3b4o11b3o2b3ob3ob3ob3ob10ob4o5b5o14b4ob4ob5ob7ob3ob4ob6o30b3o3b4o11b3o2b3ob3ob3ob3ob10ob4o5b5o14b4ob4ob5ob7ob3ob4ob6o3b3o3b4o11b3o2b3ob3ob3ob3ob10ob4o5b5o14b4ob4ob5ob7ob3ob4ob6o3b3o3b4o11b3o2b3ob3ob3ob3ob10ob4o5b5o14b4ob4ob5ob7ob3ob4ob6o54b3o3b4o11b3o2b3ob3ob3ob3ob10ob4o5b5o14b4ob4ob5ob7ob3ob4ob6o3b3o3b4o11b3o2b3ob3ob3ob3ob10ob4o5b5o14b4ob4ob5ob7ob3ob4ob6o3b3o3b4o11b3o2b3ob3ob3ob3ob10ob4o5b5o14b4ob4ob5ob7ob3ob4ob6o30b3o3b4o11b3o2b3ob3ob3ob3ob10ob4o5b5o14b4ob4ob5ob7ob3ob4ob6o19b3o3b4o11b3o2b3ob3ob3ob3ob10ob4o5b5o14b4ob4ob5ob7ob3ob4ob6o3b3o3b4o11b3o2b3ob3ob3ob3ob10ob4o5b5o14b4ob4ob5ob7ob3ob4ob6o30b3o3b4o11b3o2b3ob3ob3ob3ob10ob4o5b5o14b4ob4ob5ob7ob3ob4ob6o297b3o3b4o11b3o2b3ob3ob3ob3ob10ob4o5b5o14b4ob4ob5ob7ob3ob4ob6o5b5o5b4ob10ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3o2b3o11b4o3b3o!`
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: 468
Joined: April 13th, 2016, 9:40 am
Location: Ishikawa Prefecture, Japan

### Re: 1-Dimensional Patterns

I've been censusing B3/S23 in 1x256X2+1(two axes of symmetry, one from the 1-cell-thick nature of the pattern, and one artificial), does anyone want to help me? There's a VERY HIGH OBJECCT YIELD!
https://catagolue.appspot.com/census/b3s23/1x256X2+1

wwei23

Posts: 935
Joined: May 22nd, 2017, 6:14 pm
Location: The (Life?) Universe

### Re: 1-Dimensional Patterns

Following Wojowu's post here, a nontrivial unidimensional pattern that evolves into another.

`x = 77, y = 1, rule = B3/S2311ob4o2b4ob3o6b6ob3o2b9ob3ob3o7b5ob3o![[ STOP 128 ]]`

I spent about a week searching for this purposefully, by way of near-brute force, after figuring out how to make some VERY amateur modifications to bgolly and a pair of similarly amateur C++ "search" programs: one to find an inward-bound glider pair generator (right), and the other to find an appropriately-timed blinker edge-shooter (left). This final result, however, came about by virtue of sheer dumb luck (and a frantic few minutes of manual fiddling in Golly), and as such I'm sure there's a more optimized solution to be found if one were interested enough to properly search for it.
gamer54657 wrote:God save us all.
God save humanity.

hgkhjfgh

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M. I. Wright

Posts: 371
Joined: June 13th, 2015, 12:04 pm

### Re: 1-Dimensional Patterns

M. I. Wright wrote:Following Wojowu's post here, a nontrivial unidimensional pattern that evolves into another.

`x = 77, y = 1, rule = B3/S2311ob4o2b4ob3o6b6ob3o2b9ob3ob3o7b5ob3o![[ STOP 128 ]]`

I spent about a week searching for this purposefully, by way of near-brute force, after figuring out how to make some VERY amateur modifications to bgolly and a pair of similarly amateur C++ "search" programs: one to find an inward-bound glider pair generator (right), and the other to find an appropriately-timed blinker edge-shooter (left). This final result, however, came about by virtue of sheer dumb luck (and a frantic few minutes of manual fiddling in Golly), and as such I'm sure there's a more optimized solution to be found if one were interested enough to properly search for it.

But it's at 90 degrees!

wwei23

Posts: 935
Joined: May 22nd, 2017, 6:14 pm
Location: The (Life?) Universe

### Re: 1-Dimensional Patterns

wwei23 wrote:But it's at 90 degrees!

Still evolves into a 1-cell thick pattern. If you want one that's parallel, here's one (See generation 9):
`x = 48, y = 1, rule = B3/S233ob6o3b6o2b6o2b6o3b6ob3o!`

From this post.
It can be extended, too:
`x = 80, y = 1, rule = B3/S233ob6o3b6o2b6o2b6o2b6o2b6o2b6o2b6o3b6ob3o!`
`x = 11, y = 5, rule = B2ck3-ij5n78/S01e2ei3-k5ai8b2o\$2o3b2o\$bo4bo3bo\$2bo2b2o\$o7bo!`

(Check Gen 2)

toroidalet

Posts: 967
Joined: August 7th, 2016, 1:48 pm
Location: my computer

### Re: 1-Dimensional Patterns

toroidalet wrote:
`x = 48, y = 1, rule = B3/S233ob6o3b6o2b6o2b6o3b6ob3o!`
From this post.

Oh!
I definitely saw this when you posted it (back when I visited these forums regularly). This time around I had a faint memory of it, but after finding no mention of it on the wiki page
Wiki (~1 year out of date as of Aug 21) wrote:A weaker problem is to find a unidimensional pattern that is the predecessor of another non-trivial unidimensional pattern.
– and no results from the forum search, I chalked it up to misremembering Wojowu's speculation as a full solution and went ahead with my own search.
Congratulations, however! I suppose my find is still interesting as a novelty, if nothing else...
gamer54657 wrote:God save us all.
God save humanity.

hgkhjfgh

nutshelltlifeDiscord 'Conwaylife Lounge'
M. I. Wright

Posts: 371
Joined: June 13th, 2015, 12:04 pm