Page **30** of **37**

### Re: Synthesising Oscillators

Posted: **December 22nd, 2017, 1:44 am**

by **mniemiec**

yoota wrote:Harbor in 23: ... Jason's p6 in 17: ...

Nice! The previous versions took 34 and 40 respectively. I found a way to make the constellation from 8 gliders. It's likely there is a 3-glider way to make the two loaves, which could reduce this to 15.

Code: Select all

```
x = 106, y = 65, rule = B3/S23
70bo$71bo$69b3o$$72bo$66bobobbo24bo$67boobb3o21bobo$67bo27bobbo$96boo$
bbo$obo28boo28boo28boo$boob3o23bobbo26bobbo6bo19bobbo$4bo26bobo27bobo
4bobo20bobo$5bo26bo29bo6boo21bo$103boo$102bobbo$102bobbo$100booboo$99b
obbo$99bobbo$72bo27boo$72boo$71bobo3bo$75boo$76boo16$10bo$11bo$9b3o$$
12bo$6bobobbo24bo29bo29bo$7boobb3o21bobo27bobo27bobo$7bo27bobbo26bobbo
26bobbo$36boo28boo28boo$bbo$obo28boo28boo28boo$boob3o23bobbo26bobbo26b
obbo$4bo26bobo27bobo10bo16bobo$5bo26bo29bo10bo18bo$73b3o27boo$77boo23b
obbo$77bobo22bobbo$77bo22booboo$68boo29bobbo$67bobo29bobbo$69bo30boo$$
70b3o$70bo$71bo!
```

### Re: Synthesising Oscillators

Posted: **December 22nd, 2017, 6:02 am**

by **2718281828**

mniemiec wrote: It's likely there is a 3-glider way to make the two loaves, which could reduce this to 15.

The two loafs with 3 gliders seems to be negative, but there is a 4 glider solution that works with the 3-glider bipond (so 7 gliders in total):

Code: Select all

```
x = 53, y = 21, rule = B3/S23
29bo$30b2o$29b2o6bo$35bobo$36b2o7bobo$46b2o$46bo$2o$b2o39b2o$o3bobo36b
2o$4b2o36bo$5bo44b2o$49bo2bo$49bo2bo$47b2ob2o$46bo2bo$46bo2bo$47b2o$7b
2o$7bobo$7bo!
```

### Re: Synthesising Oscillators

Posted: **December 25th, 2017, 4:50 am**

by **AbhpzTa**

2718281828 wrote:The two loafs with 3 gliders seems to be negative, but there is a 4 glider solution that works with the 3-glider bipond (so 7 gliders in total):

Code: Select all

```
x = 53, y = 21, rule = B3/S23
29bo$30b2o$29b2o6bo$35bobo$36b2o7bobo$46b2o$46bo$2o$b2o39b2o$o3bobo36b
2o$4b2o36bo$5bo44b2o$49bo2bo$49bo2bo$47b2ob2o$46bo2bo$46bo2bo$47b2o$7b
2o$7bobo$7bo!
```

Jason's p6 in 14 gliders:

Code: Select all

```
x = 87, y = 73, rule = B3/S23
21bo$22bo55bobo$20b3o55b2o$2bo76bo$obo3bobo$b2o4b2o8bo$7bo10bo$16b3o4$
17bobo$18b2o$18bo8$bo$2bo64bo$3o64bobo$67b2o2$50bo$8bo40bo$9b2o38b3o$
8b2o25$13b2o$12bobo$14bo7$20b3o57b2o$22bo57bobo$21bo58bo5$84b2o$84bobo
$84bo!
```

### Re: Synthesising Oscillators

Posted: **December 26th, 2017, 7:43 am**

by **Sokwe**

These are all variants of

burloaferimeter. Three non-burloaferimeter p7 oscillators have known syntheses:

Code: Select all

```
x = 51, y = 11, rule = B3/S23
9b2o$9bo10b2o18b2o$10bo9bo19bo$2o7b2o14bo11bo7bo$o7bo9b6obo11b7obo$b4o
2b4o7bo$3bo7bo7b2ob2o3b2o10b2ob2o3b2o$b2o7b2o8bobo4bobo10bobo4bobo$bo
18bobo6bo10bobo6bo$2bo18bo7b2o10bo7b2o$b2o!
```

but what about the following p7 oscillators up to 29 bits?

Code: Select all

```
#C Row 1: 28 bits
#C Row 2-3: 29 bits
x = 203, y = 63, rule = B3/S23
58bobo$8b2o17b2o29b2obo$8bo18bo12b2o19bo2b2o$10bo18bo10bo17b2obobobo$
2o7b2o8b2o7b2o15bo12bo2bo2bo$o7bo10bo7bo10b6obo14bo$b4o2b4o9b4o2b4o8bo
23bo$3bo7bo10bo7bo9bob2o3b2o11b3o$b2o7b2o8b2o7b2o8b2obo4bobo$bo18bo21b
o6bo14b2o$2bo19bo19b2o5b2o13bobo$b2o18b2o43bo$66b2o18$28b2o98b2o$11b2o
15bo18bo21b2o17b2o21b2o15bo18bo21b2o17b2o$10bobo16bo17b3o19bo18bo21bob
o16bo17b3o19bo18bo$10bo19bo19bo19bo19bo19bo19bo19bo19bo19bo$2o7b2o9b2o
7b2o9b2o7b2o9b2o7b2o9b2o7b2o9b2o7b2o9b2o7b2o9b2o7b2o9b2o7b2o9b2o7b2o$o
7bo11bo7bo11bo7bo11bo7bo11bo7bo11bo7bo11bo7bo11bo7bo11bo7bo11bo7bo$b4o
2b4o10b4o2b4o10b4o2b4o10b4o2b4o10b4o2b4o10b4o2b4o10b4o2b4o10b4o2b4o10b
4o2b4o10b4o2b4o$3bo7bo11bo7bo11bo7bo11bo7bo11bo7bo11bo7bo11bo7bo11bo7b
o11bo7bo11bo7bo$b2o7b2o9b2o7b2o9b2o7b2o9b2o7bobo8b2o7bobo8b2o7b2o9b2o
7b2o9b2o7b2o9b2o7bobo8b2o7bobo$bo19bo19bo19bo9bo9bo9bo9bo19bo19bo19bo
9bo9bo9bo$2bo19bo19bo19bo19bo20bo19bo19bo19bo19bo$b2o18b2o18b2o18b2o
18b2o19b2o18b2o18b2o18b2o18b2o8$159bo$141bobo14bobo$141b2obo3bo9b2obo
16b2o15b2o$4b2o18b2o18b2o18b2o18b2o18b2o18b2o18bo2bobo11bo2b2o12bobob
2o11bobob2obo$4bo19bo19bo19bo19bo19bo19bo16b2obobobo9b2obobobo9b2obobo
bo2bo6b2obobobob2o$9bo19bo19bo19bo19bo19bo19bo11bo2bo2bo10bo2bo2bo10bo
2bo2bo2b2o6bo2bo2bo$2b6obo10bob6obo12b6obo12b6obo12b6obo12b6obo12b6obo
13bo16bo16bo16bo$o2bo16b2obo18bo19bo18bo19bo19bo23bo16bo16bo16bo$2o4b
2o3b2o13b2o3b2o11bob2o3b2o10b2ob2o3b2o9b3ob2o3b2o9bobob2o3b2o9b3ob2o3b
2o10b3o14b3o14b3o14b3o$6bo4bobo12bo4bobo9b2obo4bobo10bobo4bobo10bobo4b
obo9b2obo4bobo10bobo4bobo$4bobo6bo10bobo6bo9bo2bo6bo9bo2bo6bo10bobo6bo
12bo6bo12bo6bo13b2o15b2o15b2o15b2o$4b2o7b2o9b2o7b2o9b2o7b2o9b2o7b2o10b
o7b2o11b2o5b2o11b2o5b2o12bobo14bobo14bobo14bobo$149bo16bo16bo16bo$149b
2o15b2o15b2o15b2o!
```

mniemiec wrote:14 P8 oscillators up to 32 bits

You only included stator variants of

R2D2. There are many stator variants up to 32 bits of the following three oscillators:

Code: Select all

```
x = 37, y = 16, rule = B3/S23
14b2o$3bo11bo19b2o$2bobo9bo20bo$2bobo9b2o16b2obo$b2ob2o11bo10b2o2bobo$
4bo9b3obo9bobobo$4bo9bo15bobo$2o2bobo9b2o11bo2b2o$obo2b2o10b2o11b3o2bo
$2bo17bo$2bo13bob3o$b2ob2o11bo15b2o$2bobo14b2o12bo$2bobo15bo13b3o$3bo
15bo16bo$19b2o!
```

I presume most of them do not have known syntheses. By the way, the sources of the second and third p8 are

here and

here respectively.

mniemiec wrote:7 P4 oscillators up to 25 bits

There is a new 25-bit p4 oscillator found by Tanner Jacobi:

Code: Select all

```
x = 10, y = 13, rule = B3/S23
5bo$5bo$4b3o3$5b2o$2b2ob3o$bobo$bo4b4o$2bo$3bo$3o$o!
```

### Re: Synthesising Oscillators

Posted: **December 26th, 2017, 8:31 am**

by **mniemiec**

I wrote:Here is my current list of small unbuildables ... 23 P7 oscillators up to 29 bits ...

Sokwe wrote:These are all variants of burloaferimeter. Three non-burloaferimeter p7 oscillators have known syntheses:

I know about these. I had 9 28-bit ones: 7 burloaferimeter stator variants plus 2 others (and now the new one found yesterday). I had 49 29-bit ones: 48 burloaferimeter stator variants plus 1 stator variant of one of the misc 29-bit ones (plus two new stator variants of yesterday's).

Sokwe wrote:but what about the following p7 oscillators up to 29 bits? ...

You're right! I forgot the obvious carrier, python, and eater variants of the symmetrical 28. (I feel embarrassed, because I usually enumerate those, because it's very easy). I didn't know about table version of the asymmetrical 28, and hadn't considered other ones either. I deduced the first two of yesterday's (and these have partial syntheses needing +2 and +3 gliders based on the 28-bit one), but I hadn't considered the last two.

I enumerate stator variants by hand, and it becomes easier to miss some the larger the list becomes. Is there a search program specifically geared towards finding stator variants? I think that would be much easier than searching for oscillators (i.e. given a rotor core, do an exhaustive search for all possible bushing cells, then for for one row around the bushing, casing cells that support that bushing, then a normal still-life search for the rest of casing).

I wrote:14 P8 oscillators up to 32 bits ...

Sokwe wrote:You only included stator variants of R2D2. There are many stator variants up to 32 bits of the following three oscillators: ... I presume most of them do not have known syntheses. By the way, the sources of the second and third p8 are here and here respectively.

I remember seeing the first one somewhere. I saw the second one and mostly ignored it, as I have only been attempting to systematically keep track of odd oscillators up to 32 bits, and/or ones for which syntheses are known. I have only the vaguest recollection of the third one.

I wrote:7 P4 oscillators up to 25 bits ...

Sokwe wrote:There is a new 25-bit p4 oscillator found by Tanner Jacobi: ...

Yes, I know about this one, but it was found very recently, and my post is much older than that. It's too bad that this one doesn't have a synthesis yet.

Thanks for bringing all of these to my attention!

### Re: Synthesising Oscillators

Posted: **December 26th, 2017, 9:20 am**

by **Sokwe**

mniemiec wrote:28-bit ones: 7 burloaferimeter stator variants...

29-bit ones: 48 burloaferimeter stator variants

There are 9 28-bit burloaferimeter variants and 65 29-bit variants:

Code: Select all

```
x = 253, y = 121, rule = B3/S23
86bo19bo39bo19bo$5b2ob2o15b2ob2o15b2ob2o15b2ob2o15bobo17bobo17b2ob2o
15bobo17bobo$b2o3bobo2bo14bobo2bo12bobobo2bo14bobo2bo12bobobob2o12bobo
bo15bobobo2bo12bobobob2o12bobobo$bo2bobobob2o9bo2bobobob2o12bobobob2o
12bobobob2o12bobobob2o12bobobo15bobobob2o12bobobob2o12bobobo$3b2o3bo
12b4o3bo12b2obo3bo13b3o3bo12b2obo3bo12b2obo3bob2o9b2obo3bo12b2obo3bo
12b2obo3bob2o$8bo19bo12bobo4bo12bo6bo12bobo4bo12bobo4bob2o9bobo4bo12bo
bo4bo12bobo4bob2o$3b5o15b5o16b4o14b6o16b4o16b4o16b4o16b4o16b4o$3bo19bo
$5bo19bo18b2o18b2o18b2o18b2o20b2o18b2o18b2o$4b2o18b2o18b2o18b2o18b2o
18b2o20b2o18b2o18b2o21$69bo19bo19bo19bo59bo19bo$5b2ob2o15b2ob2o15b2ob
2o15b2obobo14b2obobo14b2obobo14b2obobo14b2ob2o11b2o2b2ob2o15b2obobo14b
2obobo14b2ob2o15b2ob2o$b2o3bobo2bo14bobo2bo14bobo2bo9b2o3bobobo15bobob
o13bobobobo15bobobo9b2o4bobo2bo10bo3bobo2bo9b2o3bobo2bo14bobo2bo9b2o3b
obo2bo14bobo2bo$bo2bobobob2o9bo2bobobob2o12bobobob2o9bo2bobobob2o9bo2b
obobob2o12bobobob2o12bobobob2o8bobobobobob2o10bobobobob2o9bo2bobobob2o
9bo2bobobob2o9bo2bobobob2o9bo2bobobob2o$3b2o3bo12b4o3bo13b3o3bo14b2o3b
o12b4o3bo12b2obo3bo13b3o3bo14b2o3bo14b2o3bo14b2o3bo12b4o3bo14b2o3bo12b
4o3bo$8bo19bo12bo6bo19bo19bo12bobo4bo12bo6bo19bo19bo19bo19bo19bo19bo$
3b5o15b5o13bob5o15b5o15b5o16b4o14b6o15b5o15b5o15b5o15b5o15b5o15b5o$2bo
19bo19bo20bo19bo59bo19bo19bo19bo18bo19bo$3b3o17b3o17b3o19bo19bo18b2o
18b2o19bo19bo19bo19bo17bobo17bobo$5bo19bo19bo18b2o18b2o18b2o18b2o18b2o
18b2o18b2o18b2o18b2o18b2o11$109bo19bo16bo19bo39bo$5b2ob2o15b2ob2o15b2o
b2o15b2ob2o15b2ob2o15b2obobo14b2obobo14bobo17bobo15b2ob2o17bobo3bo13b
2ob2o15b2ob2o$6bobo2bo9b2o3bobo2bo12bobobo2bo9b2obobobo2bo14bobo2bo12b
obobo2bo14bobo2bo12bobobob2o9b2obobobob2o12bobobob2o12bobobobobo11bobo
bo2bo14bobo2bo$4bobobob2o9bo2bobobob2o8b2o2bobobob2o10bobobobob2o10bob
obobob2o12bobobob2o12bobobob2o8b2o2bobobob2o10bobobobob2o12bobobob2o
12bobobob2o12bobobob2o12bobobob2o$2b3o3bo13b3o3bo11bobobo3bo13bobo3bo
12bob2o3bo12b2obo3bo13b3o3bo11bobobo3bo13bobo3bo12b2obo3bo12b2obo3bo
12b2obo3bo13b3o3bo$bo6bo19bo14bo4bo14bo4bo12bo6bo12bobo4bo12bo6bo14bo
4bo14bo4bo12bobo4bo12bobo4bo12bobo4bo12bo6bo$bob5o16b4o16b4o16b4o14b6o
16b4o14b6o16b4o16b4o16b4o16b4o16b4o14b6o$2bo20bo$3bobo17bobo18b2o18b2o
18b2o18b2o18b2o18b2o18b2o18b2o18b2o18b2o18b2o$4b2o18b2o18b2o18b2o18b2o
18b2o18b2o18b2o18b2o18b2o18b2o17bobo17bobo$224bo19bo10$6bo19bo59bo59bo
19bo79bo$5bobo17bobo17b2ob2o15b2ob2o15bobo17b2ob2o15b2ob2o15bobo17bobo
15b2ob2o17b2ob2o15b2ob2o15bobo$4bobobob2o12bobobob2o12bobobo2bo14bobo
2bo12bobobob2o9b2o3bobo17bobo15bobobo12b2obobobo15bobobo15bobobo17bobo
15bobobo$4bobobob2o12bobobobobo11bobobob2o12bobobob2o12bobobob2o9bo2bo
bobo12bo2bobobo11b2o2bobobo13bobobobo15bobobo15bobobo15bobobo15bobobo$
b2obo3bo12b2obo3bo2bo9b2obo3bo13b3o3bo12b2obo3bo14b2o3bob2o9b4o3bob2o
8bobobo3bob2o10bobo3bob2o9b2obo3bob2o9b2obo3bob2o10b3o3bob2o9b2obo3bob
2o$bobo4bo12bobo4bo12bobo4bo12bo6bo12bobo4bo19bob2o16bob2o11bo4bob2o
11bo4bob2o9bobo4bob2o9bobo4bob2o9bo6bob2o9bobo4bob2o$4b4o16b4o16b4o14b
6o16b4o15b5o15b5o16b4o16b4o16b4o16b4o14b6o16b4o$103bo19bo$4b2o18b2o18b
2o18b2o18b2o19bo19bo18b2o18b2o18b2o18b2o18b2o18b2o$3bobo18b2o18bobo17b
obo17bobo17b2o18b2o18b2o18b2o18b2o18b2o18b2o17bobo$4bo40bo19bo19bo158b
o10$6bo19bo22bo99bo16bo19bo39bo19bo$5bobo17bobo17b2obobo14b2ob2o15b2ob
2o15b2ob2o15b2ob2o15b2obobo14bobo17bobo15b2ob2o17bobo3bo13bobo$4bobobo
15bobobo15bobobobo13bobobo2bo9b2obobobo2bo9b2o3bobo2bo14bobo2bo12bobob
o2bo12bobobob2o9b2obobobob2o12bobobob2o12bobobobobo11bobobob2o$4bobobo
15bobobo2bo12bobobob2o8b2o2bobobob2o10bobobobob2o9bo2bobobob2o9bo2bobo
bob2o12bobobob2o8b2o2bobobob2o10bobobobob2o12bobobob2o12bobobob2o12bob
obobobo$b2obo3bob2o9b2obo3bobobo8b2obo3bo11bobobo3bo13bobo3bo14b2o3bo
12b4o3bo12b2obo3bo11bobobo3bo13bobo3bo12b2obo3bo12b2obo3bo12b2obo3bo2b
o$bobo4bob2o9bobo4bob2o9bobo4bo14bo4bo14bo4bo19bo19bo12bobo4bo14bo4bo
14bo4bo12bobo4bo12bobo4bo12bobo4bo$4b4o16b4o16b4o16b4o16b4o15b5o15b5o
16b4o16b4o16b4o16b4o16b4o16b4o$103bo19bo$4b2o18b2o20b2o18b2o18b2o18b2o
18b2o18b2o18b2o18b2o18b2o18b2o18b2o$4bobo17b2o20b2o18b2o18b2o18b2o18b
2o18b2o18b2o18b2o18b2o18b2o18b2o$5bo10$6bo19bo59bo39bo19bo19bo19bo39bo
19bo$5bobo17bobo15b2ob2o17b2ob2o15bobo17b2ob2o15bobo17bobo17bobo17bobo
17b2ob2o15bobo17bobo$4bobobo12b2obobobo15bobobo15bobobo15bobobo15bobob
o2bo12bobobob2o12bobobo15bobobo15bobobo15bobobo2bo12bobobob2o12bobobo$
2o2bobobo13bobobobo15bobobo15bobobo15bobobo2bo12bobobob2o12bobobob2o
12bobobo15bobobo15bobobo15bobobob2o12bobobob2o12bobobo$obobo3bob2o10bo
bo3bob2o9b2obo3bob2o9b2obo3bob2o9b2obo3bobobo8b2obo3bo12b2obo3bo12b2ob
o3bob2o9b2obo3bob2o9b2obo3bob2o9b2obo3bo12b2obo3bo12b2obo3bob2o$3bo4bo
b2o11bo4bob2o9bobo4bob2o9bobo4bob2o9bobo4bob2o9bobo4bo12bobo4bo12bobo
4bob2o9bobo4bobobo8bobo4bobobo8bobo4bo12bobo4bo12bobo4bob2o$4b4o16b4o
16b4o16b4o16b4o16b4o16b4o16b4o16b4o3bo12b4o3bo12b4o16b4o16b4o2$6b2o18b
2o18b2o18b2o18b2o18b2o18b2o18b2o16b2o20b2o18b2o18b2o18b2o$6b2o18b2o18b
2o18b2o18b2o17bobo17bobo17bobo16b2o20b2o18bobo17bobo17bobo$106bo19bo
19bo60bo19bo19bo!
```

mniemiec wrote:Is there a search program specifically geared towards finding stator variants?

I use

JLS (in WLS the max cell count doesn't seem to work correctly when using fixed cells). I gave an explanation of basically how to do this

here. Only one thing needs to be added: under search->search options, "Processing" tab

- uncheck "Pause search after each solution"
- check "Append solutions to file"
- select a file location for the output

This should work well for finding stator variants that are no more than 3 bits larger than the minimum. If you allow for 4 bits above the minimum, you end up with a lot of "solutions" that are just the minimum solution and a nearby block. Nicolay's version of WLS might work to find larger stator variants.

### Re: Synthesising Oscillators

Posted: **December 26th, 2017, 2:17 pm**

by **mniemiec**

I wrote:28-bit ones: 7 burloaferimeter stator variants ...

29-bit ones: 48 burloaferimeter stator variants ...

Sokwe wrote:There are 9 28-bit burloaferimeter variants and 65 29-bit variants: ...

Thanks!

I was missing 2 related 28s: 1 and 2.

I was missing 17 29s: 1,2,4,5,8,9,10,11,12,13,32,33 related to the 2 above, and slightly different 15;

I was also inexplicably missing 23 and 50 (even though I had the related 36 and 55).

Sokwe wrote:This should work well for finding stator variants that are no more than 3 bits larger than the minimum. If you allow for 4 bits above the minimum, you end up with a lot of "solutions" that are just the minimum solution and a nearby block. Nicolay's version of WLS might work to find larger stator variants.

I'm perfectly happy with lots of spurious solutions; my object/pseudo-object/quasi-object/other filter can nicely separate these, and will yield the related pseudo-objects as a bonus. This method could verify (and/or correct) many of my larger lists of oscillators and pseudo-oscillators, all of which were generated by hand, and which consist mostly of boring stator variants.

EDIT: The 7 new 29-bit stator variants of 29P7.1 can trivially be synthesized from the following 5 as-yet-unsynthesized still-lifes:

Code: Select all

```
x = 90, y = 9, rule = B3/S23
4boo18boo18boo18boo18boo$4bo19bo19bo19bo19bo$6bo19bo19bo19bo19bo$ob7o
13b7o13b7o13b7o13b7o$oobo5bo12bo6bo12bo6bo11bo7bo11bo7bo$6b3o15bob3o
14boob3o13b3ob3o13bobob3o$6bo16boobo17bobo17bobo16boobo$43bobbo$44boo!
```

### Re: Synthesising Oscillators

Posted: **December 27th, 2017, 8:09 pm**

by **Extrementhusiast**

The new 28P7.3 in thirty gliders:

Code: Select all

```
x = 194, y = 50, rule = B3/S23
25bo$26b2o$25b2o4$33bobo$33b2o135bo$34bo135bobo$170b2o$31bo$32b2o$31b
2o$57bobo25bobo26bobo33bobo31bobo$5b2o26bo3b2o18b2obo24b2obo25b2obo32b
2obo30b2obo$b2o2bobo25b2o3bo2bo18bo2bo24bo2bo25bo2bo18bo13bo2bo30bo2b
2o$obo2bo5bo20bobo3bobobo14b2obobobo20b2obobobo21b2obobobo18b2o8b2obob
obo26b2obobobo$2bo6b2o26b2ob2o15bo2bob2o21bo2bobobo21bo2bobobo17b2o9bo
2bobobo26bo2bo2bo$10b2o46b2o7bobo17b2ob2o24b2ob2o31b2ob2o29bo$67b2o27b
o14b2o40bo34bo$68bo12bobo11bo14bo2bo37bobo32b3o$82b2o11b3o12bo2bo7bo
29b2o$56b2o24bo28b2o3b2o2bobo67b2o$8b3o44b2o9b2o24b3o20bobo2bobo67bobo
$8bo43b2o3bo7b2o14b2o9bo24bo3bo3bo66bo$9bo43b2o12bo12bobo10bo16b3o11b
2o66b2o$52bo7b2o20bo29bo5bo5bobo$59b2o50bo5b2o$61bo55bobo47b3o$114b2o
51bo$113bobo26bo17b2o6bo$115bo26b2o15b2o$141bobo17bo$157b2o$156bobo$
158bo4$172bo$171b2o$171bobo6$176b3o$176bo$177bo!
```

All steps but the second are pretty well-known; the second step probably isn't required, as there are likely other more familiar (but more expensive) ways to get to the result thereof.

EDIT: The 29-bit P8 (which actually comes in two variants) from trivial junk:

Code: Select all

```
x = 137, y = 91, rule = B3/S23
22bo6bo9bo15bo$23b2o5b2o6bo17bo$22b2o5b2o7b3o13b3o2$57b2o$57b2o2$62b2o
$63bo$60b3o2b3o30b2o35b2o$19b2o10b2o27bo4bo32bo36bo$18bo2bo10bo24b2obo
5bo28b2obo8bobo22b2obo$obobo13bo2bo7b3o21b2o2bobo31b2o2bobo9b2o19b2o2b
obo$14b3o2b2o8bo23bobobo23bo9bobobo12bo19bobobo$16bo10bobo25bobo24b2o
9bobo34bobo$15bo11b2o26b2o24b2o10b2o34bo2b2o$130b3o2bo$27b2o26b2o36b2o
$26bobo25bobo35bobo$27bo27bo37bo9b2o28b2o$103bobo5bo21bo$85b2o16bo6b2o
22b3o$84bobo23bobo23bo$86bo2$90bo$90b2o$89bobo2$32b2o26b2o36b2o$31bo2b
o24bo2bo34bo2bo$31bo2bo24bo2bo34bo2bo$32b2o26b2o36b2o2$100b2o$100bobo$
100bo12$27bo$28b2o$27b2o2$29bo$28bo$28b3o3$30bo$28b2o$29b2o5$23bo28b2o
35b2o35b2o$22bobo5b2o21bo5b2o29bo5b2o9bobo17bo5b2o$obobo18bo2b2obobo
21bob2obobo29bob2obobo9b2o18bob2obobo$27bobo24bobobo22bo9bobobo12bo19b
obobo$27bobo26bobo23b2o9bobo34bobo$28bo27b2o4bo18b2o10b2o34bo2b2o$60b
2o68b3o2bo$61b2o30b2o$18b2o44b2o26bobo$17bobo34b2o8bobo26bo9b2o28b2o$
19bo33bobo8bo38bobo5bo21bo$24b2o29bo29b2o16bo6b2o22b3o$23bobo7b2o49bob
o23bobo23bo$25bo7bobo50bo$28b2o3bo$29b2o59bo$28bo61b2o$89bobo2$32b2o
27b2o35b2o$31bo2bo25bo2bo33bo2bo$31bo2bo25bo2bo33bo2bo$32b2o27b2o35b2o
2$100b2o$100bobo$100bo!
```

### Re: Synthesising Oscillators

Posted: **January 9th, 2018, 4:48 am**

by **2718281828**

The p56 B-heptomino shuttle in 15 gliders:

Code: Select all

```
x = 59, y = 36, rule = B3/S23
29bobo$30b2o$30bo5$37bo$16bobo16bobo$17b2o17b2o$17bo26bo$42b2o$43b2o$o
19bo$b2o17b2o$2o3bo13bobo13bobo$6b2o28b2o$5b2o29bo2$34b2o$33b2o17b2o$
35bo15b2o$53bo3b2o$14b2o40b2o$15b2o41bo$14bo$19b2o18b2o$19bobo16b2o$
19bo20bo5$26bo$25b2o$25bobo!
```

It uses 2x5 gliders for the blockers, 3 gliders for B+block and 2 gliders for the remaining block.

In the same way the 'asymmetric' version with one block shifted:

Code: Select all

```
x = 59, y = 36, rule = B3/S23
29bobo$30b2o$30bo5$37bo$17bobo15bobo$18b2o16b2o$18bo25bo$42b2o$43b2o$o
20bo$b2o18b2o$2o3bo14bobo12bobo$6b2o28b2o$5b2o29bo2$34b2o$33b2o17b2o$
35bo15b2o$53bo3b2o$14b2o40b2o$15b2o41bo$14bo$19b2o18b2o$19bobo16b2o$
19bo20bo5$26bo$25b2o$25bobo!
```

### Re: Synthesising Oscillators

Posted: **February 12th, 2018, 3:16 am**

by **mattiward**

The other missing p6 at the bottom of page 14 happens to be the p6 with block and head.

Here it is from 40G and 1LWSS.

Code: Select all

```
x = 254, y = 175, rule = B3/S23
163bo$161b2o$162b2o$7bo$o7b2o$b2o4b2o$2o10$150bo$150bobo$150b2o$26bobo
$27b2o$27bo2$14bo$12bobo7bo$13b2o8b2o$22b2o3$30bo$31b2o$30b2o4$128bo$
128bobo$128b2o$44bo$45b2o$39bo4b2o$37bobo$38b2o5$143bo$141b2o$142b2o5$
128bobo$128b2o$129bo16$55bo59bo$53bobo58bo$54b2o37bo20b3o$91bobo$92b2o
$60bobo$61b2o$61bo3$94b2o$95b2o$94bo4$103bo146bo2bo$104b2ob3o139bo$
103b2o2bo141bo3bo$108bo8b2o130b4o$117bobo$117bo17$140b2o$139b2o$141bo
6$136bo$135b2o$135bobo7$44b3o$46bo$45bo5$124b2o$123b2o$125bo5$18b2o$
19b2o$18bo14bo7b2o103b3o$26b3o4b2o7b2o102bo$28bo3bobo6bo105bo$27bo116b
o$143b2o$23b2o118bobo$22bobo16b2o$24bo15bobo$42bo6$3b3o$5bo$4bo$7b3o$
9bo$8bo$17b2o$18b2o$17bo2$4b2o$5b2o$4bo10b3o152b3o$17bo152bo$16bo154bo
$175b2o$175bobo$175bo!
```

I wish that Mark D. Niemiec would update his game of life website more often.

### Re: Synthesising Oscillators

Posted: **February 12th, 2018, 5:27 am**

by **mniemiec**

mattiward wrote:The other missing p6 at the bottom of page 14 happens to be the p6 with block and head.

Here it is from 40G and 1LWSS. ...

Nice! That's a substantial improvement over Extrementhusiast's original 79-glider one (which took 45 gliders to get to the wing and block on side still-life).

mattiward wrote:I wish that Mark D. Niemiec would update his game of life website more often.

I'm sorry about that. It's getting there, slowly but surely. OCD+ADD sometimes synergize well (e.g. I can't remember where I put my keys, but it's OK because I always put them in the same place). Sometimes they synergize poorly (things aren't ready until they're perfect, but I find it hard to getting around to finishing them perfectly).

I am only aware of the following remaining oscillators above P2 up to 32 bits without syntheses:

2 P3s up to 21 bits (larger ones uncounted; there are several known 22-bit ones without syntheses; more larger).

9 P4s up to 26 bits (there are many trivial 25+-bit molds based on 19+-bit still-lifes with loaves; more larger).

4 P5s up to 28 bits (all Elkies's P5s; more larger; also 2 30-bit tied pseudo-barber-poles).

9 P6s up to 29 bits (all trivial P2 components added to the 2 unknown P3s; more larger).

6 P7s up to 28 bits (1 28P7.1 and several burloaferimeters; 46 29s; more larger).

2 P8s up to 32 bits (28-bit blocker w/sparks suppressed by clocks, and 32-bit same w/table).

4 P14s up to 29 bits (all burloaferimeters; 9 30s; more larger).

I am also only aware of the following non-trivial pseudo-oscillators above P2 up to 32 bits without syntheses (excluding the trivial ones with a small simple object on a large unsynthesized oscillator):

9 P3s (all pairs of caterers and/or jams)

1 P4 (mold on mold)

1 P20 (mold on Silver's P5)

Code: Select all

```
x = 184, y = 131, rule = B3/S23
obobo5boo18boo$10bo19bo$4bo6bobo17bobo$20bo$obobo7bobo3b3o11bobo$12bo
4bo14bo4boo$4bo9bobobo15bobobo$13boobboo14boobbo$obobo33b3o$40bo6$o3bo
6boo8boo9bo21boo15b3obobbobo12bo18boo17boo20booboo16boo$11bobo4boobbo
8boboo17bobo3boo12bobobobobbo10bobo10boo6boboo4bo10bobboo16booboo15bob
3o$o3bo7b3obo17boobboo11bo3bobobo21bo20boobo5bo7bobbo3boo4bobobbo35bo
4bo$14bo3b3o11bobobobbo12bo3bo17bo16bobboobobo7bo3boobboboboboboobbo5b
obboo13b9o12boobo$obobo13bo18boo35bobbobobobo7boo3bobbobobobboo8bo24bo
9bobbo4bo11bo3bobobo$15bobo16bobbo16b4obbo14bobobbob3o12bo4bo21bobo10b
oobb3o8bo4boo13b3o4bo$4bo12bo19boo22bo63bo9boboobbo12bo19bob3o$33bobo
22bobo74bobo16bobo17bobo$4bo28boo22boo76bo39bo$135bo6$obobo6bo19bo19bo
19bo$10bobb3o14bobb3o14bobb3o14bobb3o$o11bo19bo19bo19bo$13bobobbo14bob
obbo14bobobbo14bobobbo$obobo7boob4o13boob4o13boob4o13boob4o$14bo4boo
10bobbo16bobbo16bobbo$4bo9bobobbo12bobobo15bobobo15bobboboo$15bobobo
13bobobo15bobobo15boo3bo$obobo11bobo15bobbo16bobbo20bobo$17bo17boo20b
oo20boo5$18boo22boo12boo22boo$obobo5boo6bo11boo11bo6boo4bo13boo9bo8boo
18boo18boo18boo$10bo10bo8bo9bo9bo8bo10bo7bo11bo19bo19bo19bo$o10bobo6b
oo9bobo6boo9bobo4boo11bobo4boo11bobo17bobo17bobo17bobo$$obobo7bobo3b4o
10bobo3b4o10bobo3b4o10bobo3b4o10bobo17bobo17bobo17bobo$12bo4bo4bo9bo4b
o4bo9bo4bo4bo9bo4bo4bo9bo4boo13bo4boo13bo4boo13bo4boo$o3bo9bobobobboo
11bobobobboo11bobobobboo11bobobobboo11bobobobboo11bobobobboo11bobobobb
oo11bobobobboo$13boobboo14boobboo14boobboo14boobboo14boobbo4bo10boobbo
4bo10boobbo4bo10boobbo4bo$obobo93b4o16b4o16b4o16b4o$$100boo18boo18boo
16boo$101bo18bo20bo16bo$98bo24bo14bo22bo$98boo22boo14boo20boo6$12boob
oo15booboo15booboo15booboo15booboo13boo5boo$obobo5bobbobo14bobbobo14bo
bbobo3boo9bobbobobo12bobbobobo13bo6bo$10boobo3bo12boobobobobbo9boobobo
bobbo9boobo3bo12boobo3bo13bobo4boboo$4bo8bobb4o13bo3b4o12bo3boo14bobb
ooboo12bobbooboo11boo3boobo$13bo6bo12bo19bo19bo4bobo12bo4bobo21bo$4bo
9b6o14b5o15b5o15b4o16b4o17bob6o$38bo19bo56bo$4bo11boo18bo19bo19boo16b
oo24bo$16boo18boo18boo18boo16boo23boo$4bo7$obobo7bo19bo17bo3bo3bo13boo
boo15booboo15bo19bo$10bobo17bobo37bobbobo17bobo15boboboo14boboboo$o3bo
6bobo17bobo16bo3bo3bo11boobo3bo15bo3bo13bobobo14bobbobo$11bo19bo41bobb
4o10boobobb4o10boobo3bo12boobo3bo$obobo10bo19bo7boo5bo3bobobo14bo6bo9b
oobo6bo12bobb4o13bobb4o$16bo19bo6bo30b5obo13b5obo12bo6bo12bo6bo$o3bo7b
o4bobboo10bo4bobboobo6bo7bo20bo19bo14b5obo13b5obo$12boobobboboo10boobo
bbobooboo31bo19bo22bo19bo$obobo11boo18boo12bo7bo17boo18boo18bo19bo$
116boo18boo$22bo19bo$20bobo17bobo$21bobo17bobo$21bo19bo7$obobo6b3o5b3o
10b3o16bo19b3o5b3o9boo18b3o17bo20b3o16boo$15bobo12bo20bo23bobo12bobbo
21bob3o11bo24bob3o9bobbo$4bo5bo4bobo4bo7bo4bo15bo18bo4bobo4bo7bobobbo
4b3o7bo4boboo12bo19bo4boboo10bobobbo$14bo3bo12bo19boo21bo3bobbobo7bo4b
obo15bo3boo11boo17bobobbo3boo10bo4bob3o$obobo6boo7boo11boo3bo15bo4b3o
9boo7bobbo12bobo4bo7boo5bo15bo15bobbo5bo16boboo$11bo9bo12bo3bo11bo4bob
o13bo9boo9b3o4bo11bo9boo7bo4bob3o11boo9boo8b3o4boo$4bo6bo9bo12bo3bo16b
obo4bo8bo29boo8bo6boobo13boboo20boobo16bo$11bo9bo12bo3boo11b3o4bo12bo
30bo8bo7bo11b3o4boo20bo21boo$obobo36bo18boo40bo16bo18bo21bo18boobo$37b
o4bo18bo40bo38boo37bo$42bo18bo76boobo38bo$38b3o20bo77bo$139bo8$o3bo6b
oo7boo8bobobo3bobobo9boo$10bobbo5bobbo29bo4boo$o3bo5bobobbobobbobo11bo
3bo3bo10bo3bobbo$11bo9bo31boo4boo$obobo7booboboboo9bobobo3bo3bo8bobbo$
14bo3bo31bo8boo$4bo25bo7bo3bo7boo6bobbo$56bobbobo$4bo25bobobo3bobobo
17bo$56boboo$57bo!
```

### Re: Synthesising Oscillators

Posted: **February 12th, 2018, 5:34 am**

by **77topaz**

mniemiec wrote:4 P14s up to 29 bits (all burloaferimiters; 9 30s; more larger).

Mattiward himself posted

a synthesis of one of the burloaferimeters just recently.

### Re: Synthesising Oscillators

Posted: **February 12th, 2018, 6:11 am**

by **mniemiec**

mniemiec wrote:4 P14s up to 29 bits (all burloaferimeters; 9 30s; more larger). ...

Dave Buckingham discovered the burloaferimeter in the 1970s. He first synthesized that version with the tub on top in the 1990s. I extrapolated that into trivial syntheses of 3 other 28-bit ones and 29 other 29-bit ones. However, there are also 5 other 28-bit ones and 36 other 29-bit ones without the tub at the top that do not yet have syntheses. There are also trivial P14 variants that add a separate P2 rotor, either as a 1-beacon as part of the stator, or as an inducting beacon - 1 28-bit and 2 29-bit (without syntheses), and 25 30-bit (9 without syntheses).

### Re: Synthesising Oscillators

Posted: **February 12th, 2018, 6:19 am**

by **Goldtiger997**

38P7.2 in 14 gliders:

Code: Select all

```
x = 45, y = 39, rule = B3/S23
4bo$5b2o$4b2o24bo$30bobo$30b2o2$33bobo$33b2o2b3o$7bo26bo2bo$8b2o28bo$
7b2o7$44bo$34b2ob2o3b2o$29b2o3b2ob2o4b2o$29bobo$31bo$31b2o7$bo$b2o29b
3o$obo29bo$33bo2$15bo$15b2o$2bo11bobo$2b2o$bobo!
```

This could have been much cheaper, if not for the annoying symmetry which meant gliders would rewind into each other

. I wonder if anyone can reduce it.

**Edit:** Just realized the same method can be used to synthesize the trans version of the oscillator. It shouldn't be "too hard" to complete one out of this "pseuosynthesis", but I'm out of time for now:

Code: Select all

```
x = 31, y = 22, rule = B3/S23
3bobo$4b2o7bo$4bo7bo12bobo$12b3o2bo7b2o$18bo7bo$16b3o5$15bo$15bobo$2o
13b2o3b2o$b2o17bobo$o6bo14bo6b2o$7b2o13b2o4b2o$6bobo21bo3$b2o11b2o$2b
2o11b2o$bo12bo!
```

### Re: Synthesising Oscillators

Posted: **February 12th, 2018, 8:54 am**

by **BlinkerSpawn**

Goldtiger997 wrote:It shouldn't be "too hard" to complete one out of this "pseudosynthesis", but I'm out of time for now:

Code: Select all

```
x = 31, y = 22, rule = B3/S23
3bobo$4b2o7bo$4bo7bo12bobo$12b3o2bo7b2o$18bo7bo$16b3o5$15bo$15bobo$2o
13b2o3b2o$b2o17bobo$o6bo14bo6b2o$7b2o13b2o4b2o$6bobo21bo3$b2o11b2o$2b
2o11b2o$bo12bo!
```

There's probably a better alternate teardrop but I didn't want to spend a lot of time slogging through the options:

Code: Select all

```
x = 32, y = 27, rule = B3/S23
obo3bo$b2o4bo$bo3b3o5$8bo17bobo$7bobo8bo7b2o$8bobo8bo7bo$9b2o6b3o5$16b
o$16bobo$b2o13b2o3b2o$2b2o17bobo$bo6bo14bo6b2o$8b2o13b2o4b2o$7bobo21bo
3$2b2o11b2o$3b2o11b2o$2bo12bo!
```

### Re: Synthesising Oscillators

Posted: **February 12th, 2018, 11:31 pm**

by **Kazyan**

One of those P7s is pretty easy if the base still life can be made:

Code: Select all

```
x = 13, y = 15, rule = B3/S23
2o5b2o$bo6bo$bobo4bob2o$2b2o3b2obo$6bo5bo$6bob5o$5b2obo$2bo6b2o$obo7bo
$b2o2b2o3bobo$4bobo4b2o$3bobo$4bo4b2o$8bobo$10bo!
```

Reductions to the SL:

Code: Select all

```
x = 51, y = 11, rule = B3/S23
2b2o18b2o18b2o$3bo19bo19bo$3bob2o2bobo11bob2o16bob2o$2b2obo3bobo10b2ob
obo14b2obobo$bo4bo2bobo9bo4bo14bo4bo2bo$bob3o15bob3o15bob3o3bo$2obo16b
2obo16b2obo6bo$4b2o18b2o18b2o$5bo19bo19bo$5bobo17bobo17bobo$6b2o18b2o
18b2o!
```

### Re: Synthesising Oscillators

Posted: **February 13th, 2018, 1:00 am**

by **mattiward**

90P25 honey farm hassler from 36 gliders.

Code: Select all

```
x = 115, y = 104, rule = B3/S23
9bo$10b2o$2bobo4b2o$3b2o$3bo7$114bo$112b2o$22bo90b2o$17bo2bobo4bo$15bo
bo3b2o5b2o$16b2o9b2o11$50bo$51bo$49b3o9$52bo$53bo20bo$51b3o4bo13b2o$
56bobo14b2o8bo$57b2o7bo15bo4bobo$65bo16b3o2b2o$65b3o20bo2$35bo$36b2o
27b3o$35b2o10b2o16bo$43bo4b2o7b2o7bo$44bo2bo8bobo14b2o$42b3o13bo13b2o$
74bo4$60b2o$59b2o$61bo$26bo$26b2o2b3o16b2o$25bobo4bo15bobo$31bo18bo2$
42b3o$44bo$43bo17b2o$35b2o24bobo$36b2o23bo4b3o$35bo30bo$67bo3b2o$71bob
o$71bo2$46bo$46b2o$45bobo4$70b2o$70bobo$70bo5$86b2o9b2o$85b2o5b2o3bobo
$87bo4bobo2bo$2o90bo$b2o$o7$111bo$110b2o$104b2o4bobo$103b2o$105bo!
```

### Re: Synthesising Oscillators

Posted: **February 13th, 2018, 3:01 am**

by **Sokwe**

mattiward wrote:90P25 honey farm hassler from 36 gliders.

Code: Select all

```
x = 115, y = 104, rule = B3/S23
9bo$10b2o$2bobo4b2o$3b2o$3bo7$114bo$112b2o$22bo90b2o$17bo2bobo4bo$15bo
bo3b2o5b2o$16b2o9b2o11$50bo$51bo$49b3o9$52bo$53bo20bo$51b3o4bo13b2o$
56bobo14b2o8bo$57b2o7bo15bo4bobo$65bo16b3o2b2o$65b3o20bo2$35bo$36b2o
27b3o$35b2o10b2o16bo$43bo4b2o7b2o7bo$44bo2bo8bobo14b2o$42b3o13bo13b2o$
74bo4$60b2o$59b2o$61bo$26bo$26b2o2b3o16b2o$25bobo4bo15bobo$31bo18bo2$
42b3o$44bo$43bo17b2o$35b2o24bobo$36b2o23bo4b3o$35bo30bo$67bo3b2o$71bob
o$71bo2$46bo$46b2o$45bobo4$70b2o$70bobo$70bo5$86b2o9b2o$85b2o5b2o3bobo
$87bo4bobo2bo$2o90bo$b2o$o7$111bo$110b2o$104b2o4bobo$103b2o$105bo!
```

I have enjoyed your recent syntheses! Just a note, it is often nicer (and easier) to display a synthesis step-by-step. For example, here is the 88-bit p25 in steps:

Code: Select all

```
x = 235, y = 38, rule = B3/S23
136bo26bo$137b2o25bo$136b2o24b3o3bobo$91bobo21bo53b2o11bo29bo9bo$92b2o
3bo16bo54bo10b3o29b3o5b3o$92bo5b2o14b3o62bo35bo3bo$97b2o37bo30b2o3b2o
5b2o33b2o3b2o$107bobo26bobo9b2o18b2obobo14b2o38b2o$107b2o27b2o7b2o2bo
17bo5bo11b2o2bo35b2o2bo$108bo36bob2o36bob2o22bobo11bob2o$102bo32bo8bo
39bo20bo6b2o10bo$100b2o34b2o6bo39bo21b2o4bo11bo$101b2o5bo26b2o8bob2o
36bob2o16b2o18bob2o$107b2o36b2o2bo35b2o2bo26b3o6b2o2bo$99bo7bobo38b2o
38b2o26bo11b2o$100bo102bo13bo$98b3o13b3o86b2o$114bo87bobo$115bo$bo21bo
bo$2bo16bo3b2o207bobo$3o14b2o5bo207b2o$18b2o199bo13bo$7bobo37b2o38b2o
38b2o38b2o38b2o11bo$8b2o37bo2b2o35bo2b2o35bo2b2o35bo2b2o35bo2b2o6b3o$
8bo39b2obo36b2obo36b2obo36b2obo36b2obo18b2o$52bo39bo39bo39bo39bo11bo4b
2o$52bo39bo39bo39bo39bo10b2o6bo$8bo39b2obo7bo28b2obo36b2obo36b2obo36b
2obo11bobo$8b2o37bo2b2o6bo28bo2b2o35bo2b2o35bo2b2o11bo5bo17bo2b2o$7bob
o37b2o9b3o26b2o38b2o38b2o14bobob2o18b2o$18b2o76b2o38b2o38b2o5b2o3b2o
26b2o3b2o$3o14b2o38bo39bo39bo39bo39bo3bo$2bo16bo36b2o36b3o37b3o37b3o
10bo26b3o5b3o$bo54bobo35bo39bo39bo11b2o26bo9bo$186bobo3b3o$192bo$193bo
!
```

This is just a small modification of your synthesis of the 90-bit version.

There is also a script (by chris_c?) that can build a continuous synthesis from the step-by-step synthesis, but I can't seem to find it right now. Hopefully someone else can link to it.

### Re: Synthesising Oscillators

Posted: **February 13th, 2018, 3:08 am**

by **dvgrn**

Sokwe wrote:There is also a script (by chris_c?) that can build a continuous synthesis from the step-by-step synthesis, but I can't seem to find it right now. Hopefully someone else can link to it.

Here's an

indirect link, to a post with some warnings about what can go wrong when you try to use the script. Basically, make your pattern and choose your selection in such a way that the incremental pieces are split cleanly into width-N blocks.

Also make sure that there aren't any placeholder stages (like in Mark Niemiec's incremental syntheses, where there's a "before" and "after" picture for each stage).

Also make sure to line things up so that each intermediate pattern is exactly N ticks from the previous one. A slight left/right/up/down shift at any point in the chain will cause mysterious disasters.

### Re: Synthesising Oscillators

Posted: **February 13th, 2018, 6:40 am**

by **PHPBB12345**

Code: Select all

```
x = 59, y = 40, rule = LifeHistory
16.27D$16.D25.D$16.D25.D$16.D11.3D11.D$2A14.D.2A7.D3.D7.2A.D14.2A$A.A
2.A2.A2.A2.A.DA.A11.D7.A.AD.A2.A2.A2.A2.A.A$2.4A2.4A2.2ACA12.D10.AD.
4A2.4A2.A$A.A2.A2.A2.A2.A.DA.A9.D9.A.AD.A2.A2.A2.A2.A.A$2A14.D.2A19.
2A.D14.2A$16.D12.D12.D$16.D25.D$16.D25.D$16.27D3$28.3D$28.3D$28.3D$
28.3D$28.3D$28.3D$26.7D$27.5D$28.3D$29.D3$16.27D$16.D25.D$16.D25.D$
16.D25.D$2A14.D25.D14.2A$A.A2.A2.A2.A2.A.DA2.A2.A2.A2.A2.A2.A2.A2.AD.
A2.A2.A2.A2.A.A$2.4A2.4A2.2ACA2.4A2.4A2.4A2.4AD.4A2.4A2.A$A.A2.A2.A2.
A2.A.DA2.A2.A2.A2.A2.A2.A2.A2.AD.A2.A2.A2.A2.A.A$2A14.D25.D14.2A$16.D
25.D$16.D25.D$16.D25.D$16.27D!
```

### Re: Synthesising Oscillators

Posted: **February 13th, 2018, 7:02 am**

by **mniemiec**

PHPBB12345 wrote:...

There are known mechanisms for creating pistons of any odd length from scratch, and for shorening a piston of any length by one segment, but I am not aware of any way of growing a piston, nor of splicing two together in the middle. Also, in general, syntheses that splice two existing objects tend to be much more difficult than ones that merely extend one object. The easiest way to do what you are requesting is to create a piston one section longer than what you are looking for, from scratch, and then shorten it by one segment.

### Re: Synthesising Oscillators

Posted: **February 13th, 2018, 1:11 pm**

by **Extrementhusiast**

mniemiec wrote:[...] but I am not aware of any way of growing a piston, [...]

From page 17:

Extrementhusiast wrote:General procedure for lengthening a piston:

Code: Select all

```
x = 909, y = 44, rule = B3/S23
605bobo75bobo$604bo78b2o$604bo79bo$604bo2bo$465bo138b3o$465bobo15bo
190bobo$20bo39bobo124bo277b2o16bobo188b2o$21b2o40bo124bo290bo3b2o22bo
105bo53bobo5bo4bo$20b2o41bo122b3o272bo7bobo6bo26bobo105bobo20bo29bo13b
obo52bo$29bo30bo2bo398b2o5b2o7b3o25b2o87bo17b2o19bobo29bo3bo9b2o23bo
29bobo$27b2o32b3o93bo303b2o7bo58b2o64bobo37b2o29bo7b3o26bobo29b2o$28b
2o127bobo276bo39bo51b2o14bobo48b2o4bo5bobo56bo2bo4bo29b2o$157b2o4bo
236bo34bo30bo8bo48bobo3bo14b2o54bobo3b2o57b3o6bo99bo$22bo139bo32bo84bo
106bo12bobo32b3o26bobo8b3o5b3o39b2o18bo19bo35b2o5bo92bo70bo2bobo28bobo
21bo$23bo134bo3b3o31bo82bo106bo13b2o31bo31b2o15b5o38bo39bobo19bo53bo
57bobo2bo25bo39bobo2b2o29b2o20bobo$21b3o35bo3bobo92b2o34b3o82b3o73bo
30b3o42bobo47b2ob3o70bo7b2o18bobo52bo59b2o2bobo24bo39b2o34bo17b2o2b2o
31bo6bobo$60bo3b2o91bobo39bo77bo75b2o77b2o48b2o74b2obo24b2o24bo27b3o
61b2o23b3o94b2o35b2o4b2o$bobo5bobo41bo4b3o3bo38bo95bobo73bobo76b2o13bo
13bobo129b2o40b2o2bobo48bobo210bo36b2o6bo$2b2o5b2o43b2o48bo90bo3b2o6bo
62bo5b2o69bo15bo5bobo12b2o5bo66bo13bo42b2o44b2o49b2o29b2o31b2o49b2o40b
2o95b2o$2bo7bo42b2o47b3o91b2o9bobo3bo57b2o75b2o11b2o6b2o13bo6bobo47bo
17b2o11bo4bo69bo4b2o76b2o2b2o7bobo18bo6b2o3bobo25b2o20bobo7b2ob2o27bob
o2b2o19b2o3b2o27b2o35bo2bo$80bo49b2o27b2o34b2o10b2o4bobo54b2o75b2o13b
2o2b2o23b2o4bo6b2o34bobo15b2o3bobo6bo3bobo36b4o26bobo5bo42b2o5bo5b3o
18bobo2bo7bo18bobo6bobo4bo23bo2bo22bo7bo3bo27bo5bo19bo2bo2bo4bobo20bo
2bo34bo2bo$3o7b3o24bobo26bo12bo49bobo26bobo30bo21b2o35b2o35b2o35b2o30b
2o8bobo27bobo4b2o34bo2bo21b2o9bo2bo36bo3bo26b2o4bo43b2o3b3o5bo22b3o28b
2o8b5o24b3o32b3o29b5o21b5o5b2o22b3o35b3o34b2ob2o$2bo7bo13b2ob2o8b2o25b
3o12b3o17bobo7bo20bo3bo24bo3bo28bo6b2o46b2o2bo32b2o2bo22bo9b2o2bo27b2o
2bo8bo18bobo8bobo6bo27b2o4bobo22bo4b2o4bobo40bo24b2o6bo48bo9bo20bo40bo
133bo97bo3bo$bo9bo11bobobobo8bo24bo36b2o6bobo22bobo26bobo25b3o5bo2bo
41b2obo33b2obo28bo7bo31bo33b2o6b2obo36bo2b2obo21bo7bo2b2obo40bob3o20bo
bo5bob3o31b2o11bob3o26bob3o36bob3o24b3o32b3o31b3o23b3o31b3o35b3o35b3o$
4b2ob2o14bobobobo33bob4o4bo26bo7bob3o15bo4bob3o24bob3o32bob3o6b2o32bob
obobo30bobobobo22b3o7bobobo17bobo3b2o2bobobo29bo6bobo33bo4bobobo23b2o
6bobobo42bobo2bo5b2o14bo5bobo2bo31b2o10bobo2bo25bobo2bo35bobo2bo22bobo
bo30bobobo29bobobo21bobobo9bo19bobobo28bobo2bobobo2bobo30bo$4bo3bo15bo
3bo4bobo28bo3bo4bobo2bo30bo3bo12bobo5bo3bo24bo3bo32bo3bo5bobo29bobobo
3bo30bobo3bo29b2obo3bo18b2o3bobobo3bo35bo3bo16bobo11bobo5bo3bo21bobo7b
o3bo5b3o34bo3bo4b2o22bo3bo30bo13bo3bo26bo3bo36bo3bo22bobobo30bobobo29b
obobo21bobobo9bobo17bobobo29b2o2bobobo2b2o31bo$5b3o17b3o5b2o30b3o5b2o
2b2o18b3o10b3o14b2o6b3o26b3o27b2o5b3o6bo31b2o3b3o28b2obo2b3o20bo10bo2b
3o19bo6bo2b3o37b3o9bo3b2o2b2o13b2o6b3o33b3o6bo37b3o7bo22b3o46b3o28b3o
38b3o24b3o32b3o31b3o23b3o10b2o19b3o30bo4b3o4bo30b3o$34bo21bo20bobo19bo
30b2o28b2o25b3o3bobo82bo2bo26bo2b3o2bobo29bobo53b2o3bobo2bo16b2o35b2o
12bo$36bo19b2o40bo30bobo28b2o27bo5bo83b2o25b3o4bo2b2o30b2o54bobo2bo20b
obo35b2o337bo55bo9bo$5b3o17b3o7b2o18bobo7b3o42b3o18bo3b3o16b2o8b3o21bo
12b3o43b3o34b3o25bo8b3o29b3o37b3o36bo3b3o23bo9b3o44b3o30b3o46b3o28b3o
38b3o24b3o32b3o31b3o23b3o8b2o21b3o31b2o2b3o2b2o31b3o$6bo19bo8bobo28bo
44bo24bo16bobo9bo36bo29bobo13bo36bo36bo31bo39bo42bo24b2o9bo46bo32bo35b
o12bo30bo40bo26bo34bo33bo25bo9bobo21bo31bobo3bo3bobo31bo$6bo19bo39bo
44bo24bo12b2o4bo9bo36bo30b2o2b2o9bo36bo36bo31bo39bo42bo19bo3bobo9bo27b
2o17bo32bo34b3o11bo30bo30b2o8bo26bo34bo33bo25bo33bo37bo37bo$5b3o17b3o
37b3o42b3o22b3o10bobo13b3o34b3o29bo2bobo8b3o34b3o34b3o29b3o37b3o40b3o
18b2o13b3o25bobo16b3o30b3o33bob2o9b3o28b3o28bobo7b3o24b3o32b3o31b3o23b
3o31b3o35b3o35b3o$150bo87bo217bobo43bo86b3o73bo$589b2o$5b3o17b3o37b3o
42b3o22b3o26b3o34b3o43b3o34b3o34b3o29b3o37b3o40b3o33b3o44b3o30b3o46b3o
28b3o38b3o24b3o32b3o31b3o23b3o31b3o35b3o35b3o$6bo19bo39bo44bo24bo28bo
36bo45bo36bo36bo31bo39bo42bo35bo46bo32bo48bo30bo40bo26bo34bo33bo25bo
33bo37bo37bo$6bo19bo39bo44bo24bo28bo36bo26b3o16bo36bo36bo31bo39bo42bo
35bo46bo32bo48bo30bo40bo26bo34bo33bo25bo33bo37bo37bo$5b3o17b3o37b3o42b
3o22b3o26b3o34b3o27bo15b3o34b3o34b3o29b3o37b3o40b3o33b3o44b3o30b3o46b
3o28b3o38b3o24b3o32b3o31b3o23b3o31b3o35b3o35b3o$230bo2$5b3o17b3o37b3o
42b3o22b3o26b3o34b3o43b3o34b3o34b3o29b3o37b3o40b3o33b3o44b3o30b3o46b3o
28b3o38b3o24b3o32b3o31b3o23b3o31b3o35b3o35b3o$4bo3bo15bo3bo35bo3bo40bo
3bo20bo3bo24bo3bo32bo3bo41bo3bo32bo3bo32bo3bo27bo3bo35bo3bo38bo3bo31bo
3bo42bo3bo28bo3bo44bo3bo26bo3bo36bo3bo22bo3bo30bo3bo29bo3bo21bo3bo29bo
3bo33bo3bo33bo3bo$4b2ob2o15b2ob2o35b2ob2o40b2ob2o20b2ob2o24b2ob2o32b2o
b2o41b2ob2o32b2ob2o32b2ob2o27b2ob2o35b2ob2o38b2ob2o31b2ob2o42b2ob2o28b
2ob2o44b2ob2o26b2ob2o36b2ob2o22b2ob2o30b2ob2o29b2ob2o21b2ob2o29b2ob2o
33b2ob2o33b2ob2o!
```

### Re: Synthesising Oscillators

Posted: **February 13th, 2018, 6:06 pm**

by **mniemiec**

Extrementhusiast wrote:General procedure for lengthening a piston: ...

Thanks! Now that you mention it, I to vaguely recall seeing this. However, I don't have it recorded in any of my syntheses since it's not actually necessary, as it's usually cheaper to just build the longer piston from the start.

Given how complex such a seemingly simple operation turns out to be should illustrate just how much harder it would likely be to try to glue two pistons together in the middle!

### Re: Synthesising Oscillators

Posted: **February 13th, 2018, 6:36 pm**

by **Extrementhusiast**

The last 16-bit P2 in about the least likely way imaginable (in two slight variants):

Code: Select all

```
x = 125, y = 76, rule = B3/S23
97bo$97bobo$90bo6b2o$90bobo$90b2o4$82bo$82bobo$82b2o$76bo12bo$77b2o10b
obo$76b2o11b2o2$81bo$80bobob2o$80bobob2o$75b2o4bo$67b2o5bo2bo$66b4o4bo
2bo9b2o$66b2ob2o4b2o4b3o4bo$68b2o15bobo$73b2o7bobo$72bobo6bo4b3o$74bo
2b2o2b2o$78bo$77bo$77b2o$72b2o$71bobo6b3o$73bo6bo$4bo76bo$3bo72b2o$3b
3o70bobo$76bo$obo$b2o7bo$bo9b2o$10b2o$32b2o83b2o4b2o$4bo21b3o4bo83bobo
4bo$4b2o6bobo15bobo9bobobo74bobo$3bobo6b2o13bobo87bo2bo$13bo12bo4b3o
84bo3b3o$26b2o42bo22bo24bo$6b2o60bobo22bobo$5b2o9bo52b2o22b2o$7bo7b2o
66bobo$15bobo65b2o$84bo$12b3o61bo12bo$14bo62b2o10bobo$13bo62b2o11b2o2$
81bo$80bobob2o$80bobob2o$75b2o4bo$67b2o5bo2bo$66b4o4bo2bo9b2o$66b2ob2o
4b2o4b3o4bo$68b2o15bobo$73b2o7bobo$72bobo6bo4b3o$74bo2b2o2b2o$78bo$77b
o$77b2o$72b2o$71bobo6b3o$73bo6bo$81bo$76b2o$76bobo$76bo!
```

The corresponding 17-bit P2 can be made the same way far more cheaply:

Code: Select all

```
x = 44, y = 28, rule = B3/S23
b2o$2b2o$bo3bobo$5b2o$6bo5$35b2o$18b2o15bo6b2o$12b3o4bo16bobo4bo$16bob
o21bobo$13bobo20bo2bo$2b2o8bo4b3o17bo3b3o$3b2o7b2o23bo$2bo4$b2o$obo$2b
o2$14b3o$3b2o9bo$2bobo10bo$4bo!
```

Unfortunately, the usual barberpole-shortening technique doesn't work here.

### Re: Synthesising Oscillators

Posted: **February 13th, 2018, 8:51 pm**

by **Kazyan**

Nice work! Those disjoint-bits objects are hard.

Half of an idea for a general solution to all those p3 variants:

Code: Select all

```
x = 15, y = 17, rule = LifeHistory
.A5.A$.A$3.A4.3A$3.A$5.2A.A$6.2A$5.2C7.A$A.A2.C2.C3.3A$A.A4.2CB.A$A.A
5.CBA.A$8.CB.2A$7.2C2$4.3A$6.A.3A$5.A2.A$9.A!
```