## Synthesising Oscillators

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

### Re: Synthesising Oscillators

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.
`x = 106, y = 65, rule = B3/S2370bo\$71bo\$69b3o\$\$72bo\$66bobobbo24bo\$67boobb3o21bobo\$67bo27bobbo\$96boo\$bbo\$obo28boo28boo28boo\$boob3o23bobbo26bobbo6bo19bobbo\$4bo26bobo27bobo4bobo20bobo\$5bo26bo29bo6boo21bo\$103boo\$102bobbo\$102bobbo\$100booboo\$99bobbo\$99bobbo\$72bo27boo\$72boo\$71bobo3bo\$75boo\$76boo16\$10bo\$11bo\$9b3o\$\$12bo\$6bobobbo24bo29bo29bo\$7boobb3o21bobo27bobo27bobo\$7bo27bobbo26bobbo26bobbo\$36boo28boo28boo\$bbo\$obo28boo28boo28boo\$boob3o23bobbo26bobbo26bobbo\$4bo26bobo27bobo10bo16bobo\$5bo26bo29bo10bo18bo\$73b3o27boo\$77boo23bobbo\$77bobo22bobbo\$77bo22booboo\$68boo29bobbo\$67bobo29bobbo\$69bo30boo\$\$70b3o\$70bo\$71bo!`
mniemiec

Posts: 1026
Joined: June 1st, 2013, 12:00 am

### Re: Synthesising Oscillators

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):
`x = 53, y = 21, rule = B3/S2329bo\$30b2o\$29b2o6bo\$35bobo\$36b2o7bobo\$46b2o\$46bo\$2o\$b2o39b2o\$o3bobo36b2o\$4b2o36bo\$5bo44b2o\$49bo2bo\$49bo2bo\$47b2ob2o\$46bo2bo\$46bo2bo\$47b2o\$7b2o\$7bobo\$7bo!`

2718281828

Posts: 708
Joined: August 8th, 2017, 5:38 pm

### Re: Synthesising Oscillators

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):
`x = 53, y = 21, rule = B3/S2329bo\$30b2o\$29b2o6bo\$35bobo\$36b2o7bobo\$46b2o\$46bo\$2o\$b2o39b2o\$o3bobo36b2o\$4b2o36bo\$5bo44b2o\$49bo2bo\$49bo2bo\$47b2ob2o\$46bo2bo\$46bo2bo\$47b2o\$7b2o\$7bobo\$7bo!`

Jason's p6 in 14 gliders:
`x = 87, y = 73, rule = B3/S2321bo\$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!`
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: Synthesising Oscillators

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

These are all variants of burloaferimeter. Three non-burloaferimeter p7 oscillators have known syntheses:
`x = 51, y = 11, rule = B3/S239b2o\$9bo10b2o18b2o\$10bo9bo19bo\$2o7b2o14bo11bo7bo\$o7bo9b6obo11b7obo\$b4o2b4o7bo\$3bo7bo7b2ob2o3b2o10b2ob2o3b2o\$b2o7b2o8bobo4bobo10bobo4bobo\$bo18bobo6bo10bobo6bo\$2bo18bo7b2o10bo7b2o\$b2o!`

but what about the following p7 oscillators up to 29 bits?
`#C Row 1: 28 bits#C Row 2-3: 29 bitsx = 203, y = 63, rule = B3/S2358bobo\$8b2o17b2o29b2obo\$8bo18bo12b2o19bo2b2o\$10bo18bo10bo17b2obobobo\$2o7b2o8b2o7b2o15bo12bo2bo2bo\$o7bo10bo7bo10b6obo14bo\$b4o2b4o9b4o2b4o8bo23bo\$3bo7bo10bo7bo9bob2o3b2o11b3o\$b2o7b2o8b2o7b2o8b2obo4bobo\$bo18bo21bo6bo14b2o\$2bo19bo19b2o5b2o13bobo\$b2o18b2o43bo\$66b2o18\$28b2o98b2o\$11b2o15bo18bo21b2o17b2o21b2o15bo18bo21b2o17b2o\$10bobo16bo17b3o19bo18bo21bobo16bo17b3o19bo18bo\$10bo19bo19bo19bo19bo19bo19bo19bo19bo19bo\$2o7b2o9b2o7b2o9b2o7b2o9b2o7b2o9b2o7b2o9b2o7b2o9b2o7b2o9b2o7b2o9b2o7b2o9b2o7b2o\$o7bo11bo7bo11bo7bo11bo7bo11bo7bo11bo7bo11bo7bo11bo7bo11bo7bo11bo7bo\$b4o2b4o10b4o2b4o10b4o2b4o10b4o2b4o10b4o2b4o10b4o2b4o10b4o2b4o10b4o2b4o10b4o2b4o10b4o2b4o\$3bo7bo11bo7bo11bo7bo11bo7bo11bo7bo11bo7bo11bo7bo11bo7bo11bo7bo11bo7bo\$b2o7b2o9b2o7b2o9b2o7b2o9b2o7bobo8b2o7bobo8b2o7b2o9b2o7b2o9b2o7b2o9b2o7bobo8b2o7bobo\$bo19bo19bo19bo9bo9bo9bo9bo19bo19bo19bo9bo9bo9bo\$2bo19bo19bo19bo19bo20bo19bo19bo19bo19bo\$b2o18b2o18b2o18b2o18b2o19b2o18b2o18b2o18b2o18b2o8\$159bo\$141bobo14bobo\$141b2obo3bo9b2obo16b2o15b2o\$4b2o18b2o18b2o18b2o18b2o18b2o18b2o18bo2bobo11bo2b2o12bobob2o11bobob2obo\$4bo19bo19bo19bo19bo19bo19bo16b2obobobo9b2obobobo9b2obobobo2bo6b2obobobob2o\$9bo19bo19bo19bo19bo19bo19bo11bo2bo2bo10bo2bo2bo10bo2bo2bo2b2o6bo2bo2bo\$2b6obo10bob6obo12b6obo12b6obo12b6obo12b6obo12b6obo13bo16bo16bo16bo\$o2bo16b2obo18bo19bo18bo19bo19bo23bo16bo16bo16bo\$2o4b2o3b2o13b2o3b2o11bob2o3b2o10b2ob2o3b2o9b3ob2o3b2o9bobob2o3b2o9b3ob2o3b2o10b3o14b3o14b3o14b3o\$6bo4bobo12bo4bobo9b2obo4bobo10bobo4bobo10bobo4bobo9b2obo4bobo10bobo4bobo\$4bobo6bo10bobo6bo9bo2bo6bo9bo2bo6bo10bobo6bo12bo6bo12bo6bo13b2o15b2o15b2o15b2o\$4b2o7b2o9b2o7b2o9b2o7b2o9b2o7b2o10bo7b2o11b2o5b2o11b2o5b2o12bobo14bobo14bobo14bobo\$149bo16bo16bo16bo\$149b2o15b2o15b2o15b2o!`

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:
`x = 37, y = 16, rule = B3/S2314b2o\$3bo11bo19b2o\$2bobo9bo20bo\$2bobo9b2o16b2obo\$b2ob2o11bo10b2o2bobo\$4bo9b3obo9bobobo\$4bo9bo15bobo\$2o2bobo9b2o11bo2b2o\$obo2b2o10b2o11b3o2bo\$2bo17bo\$2bo13bob3o\$b2ob2o11bo15b2o\$2bobo14b2o12bo\$2bobo15bo13b3o\$3bo15bo16bo\$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:
`x = 10, y = 13, rule = B3/S235bo\$5bo\$4b3o3\$5b2o\$2b2ob3o\$bobo\$bo4b4o\$2bo\$3bo\$3o\$o!`
-Matthias Merzenich
Sokwe
Moderator

Posts: 1473
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### Re: Synthesising Oscillators

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!
mniemiec

Posts: 1026
Joined: June 1st, 2013, 12:00 am

### Re: Synthesising Oscillators

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:
`x = 253, y = 121, rule = B3/S2386bo19bo39bo19bo\$5b2ob2o15b2ob2o15b2ob2o15b2ob2o15bobo17bobo17b2ob2o15bobo17bobo\$b2o3bobo2bo14bobo2bo12bobobo2bo14bobo2bo12bobobob2o12bobobo15bobobo2bo12bobobob2o12bobobo\$bo2bobobob2o9bo2bobobob2o12bobobob2o12bobobob2o12bobobob2o12bobobo15bobobob2o12bobobob2o12bobobo\$3b2o3bo12b4o3bo12b2obo3bo13b3o3bo12b2obo3bo12b2obo3bob2o9b2obo3bo12b2obo3bo12b2obo3bob2o\$8bo19bo12bobo4bo12bo6bo12bobo4bo12bobo4bob2o9bobo4bo12bobo4bo12bobo4bob2o\$3b5o15b5o16b4o14b6o16b4o16b4o16b4o16b4o16b4o\$3bo19bo\$5bo19bo18b2o18b2o18b2o18b2o20b2o18b2o18b2o\$4b2o18b2o18b2o18b2o18b2o18b2o20b2o18b2o18b2o21\$69bo19bo19bo19bo59bo19bo\$5b2ob2o15b2ob2o15b2ob2o15b2obobo14b2obobo14b2obobo14b2obobo14b2ob2o11b2o2b2ob2o15b2obobo14b2obobo14b2ob2o15b2ob2o\$b2o3bobo2bo14bobo2bo14bobo2bo9b2o3bobobo15bobobo13bobobobo15bobobo9b2o4bobo2bo10bo3bobo2bo9b2o3bobo2bo14bobo2bo9b2o3bobo2bo14bobo2bo\$bo2bobobob2o9bo2bobobob2o12bobobob2o9bo2bobobob2o9bo2bobobob2o12bobobob2o12bobobob2o8bobobobobob2o10bobobobob2o9bo2bobobob2o9bo2bobobob2o9bo2bobobob2o9bo2bobobob2o\$3b2o3bo12b4o3bo13b3o3bo14b2o3bo12b4o3bo12b2obo3bo13b3o3bo14b2o3bo14b2o3bo14b2o3bo12b4o3bo14b2o3bo12b4o3bo\$8bo19bo12bo6bo19bo19bo12bobo4bo12bo6bo19bo19bo19bo19bo19bo19bo\$3b5o15b5o13bob5o15b5o15b5o16b4o14b6o15b5o15b5o15b5o15b5o15b5o15b5o\$2bo19bo19bo20bo19bo59bo19bo19bo19bo18bo19bo\$3b3o17b3o17b3o19bo19bo18b2o18b2o19bo19bo19bo19bo17bobo17bobo\$5bo19bo19bo18b2o18b2o18b2o18b2o18b2o18b2o18b2o18b2o18b2o18b2o11\$109bo19bo16bo19bo39bo\$5b2ob2o15b2ob2o15b2ob2o15b2ob2o15b2ob2o15b2obobo14b2obobo14bobo17bobo15b2ob2o17bobo3bo13b2ob2o15b2ob2o\$6bobo2bo9b2o3bobo2bo12bobobo2bo9b2obobobo2bo14bobo2bo12bobobo2bo14bobo2bo12bobobob2o9b2obobobob2o12bobobob2o12bobobobobo11bobobo2bo14bobo2bo\$4bobobob2o9bo2bobobob2o8b2o2bobobob2o10bobobobob2o10bobobobob2o12bobobob2o12bobobob2o8b2o2bobobob2o10bobobobob2o12bobobob2o12bobobob2o12bobobob2o12bobobob2o\$2b3o3bo13b3o3bo11bobobo3bo13bobo3bo12bob2o3bo12b2obo3bo13b3o3bo11bobobo3bo13bobo3bo12b2obo3bo12b2obo3bo12b2obo3bo13b3o3bo\$bo6bo19bo14bo4bo14bo4bo12bo6bo12bobo4bo12bo6bo14bo4bo14bo4bo12bobo4bo12bobo4bo12bobo4bo12bo6bo\$bob5o16b4o16b4o16b4o14b6o16b4o14b6o16b4o16b4o16b4o16b4o16b4o14b6o\$2bo20bo\$3bobo17bobo18b2o18b2o18b2o18b2o18b2o18b2o18b2o18b2o18b2o18b2o18b2o\$4b2o18b2o18b2o18b2o18b2o18b2o18b2o18b2o18b2o18b2o18b2o17bobo17bobo\$224bo19bo10\$6bo19bo59bo59bo19bo79bo\$5bobo17bobo17b2ob2o15b2ob2o15bobo17b2ob2o15b2ob2o15bobo17bobo15b2ob2o17b2ob2o15b2ob2o15bobo\$4bobobob2o12bobobob2o12bobobo2bo14bobo2bo12bobobob2o9b2o3bobo17bobo15bobobo12b2obobobo15bobobo15bobobo17bobo15bobobo\$4bobobob2o12bobobobobo11bobobob2o12bobobob2o12bobobob2o9bo2bobobo12bo2bobobo11b2o2bobobo13bobobobo15bobobo15bobobo15bobobo15bobobo\$b2obo3bo12b2obo3bo2bo9b2obo3bo13b3o3bo12b2obo3bo14b2o3bob2o9b4o3bob2o8bobobo3bob2o10bobo3bob2o9b2obo3bob2o9b2obo3bob2o10b3o3bob2o9b2obo3bob2o\$bobo4bo12bobo4bo12bobo4bo12bo6bo12bobo4bo19bob2o16bob2o11bo4bob2o11bo4bob2o9bobo4bob2o9bobo4bob2o9bo6bob2o9bobo4bob2o\$4b4o16b4o16b4o14b6o16b4o15b5o15b5o16b4o16b4o16b4o16b4o14b6o16b4o\$103bo19bo\$4b2o18b2o18b2o18b2o18b2o19bo19bo18b2o18b2o18b2o18b2o18b2o18b2o\$3bobo18b2o18bobo17bobo17bobo17b2o18b2o18b2o18b2o18b2o18b2o18b2o17bobo\$4bo40bo19bo19bo158bo10\$6bo19bo22bo99bo16bo19bo39bo19bo\$5bobo17bobo17b2obobo14b2ob2o15b2ob2o15b2ob2o15b2ob2o15b2obobo14bobo17bobo15b2ob2o17bobo3bo13bobo\$4bobobo15bobobo15bobobobo13bobobo2bo9b2obobobo2bo9b2o3bobo2bo14bobo2bo12bobobo2bo12bobobob2o9b2obobobob2o12bobobob2o12bobobobobo11bobobob2o\$4bobobo15bobobo2bo12bobobob2o8b2o2bobobob2o10bobobobob2o9bo2bobobob2o9bo2bobobob2o12bobobob2o8b2o2bobobob2o10bobobobob2o12bobobob2o12bobobob2o12bobobobobo\$b2obo3bob2o9b2obo3bobobo8b2obo3bo11bobobo3bo13bobo3bo14b2o3bo12b4o3bo12b2obo3bo11bobobo3bo13bobo3bo12b2obo3bo12b2obo3bo12b2obo3bo2bo\$bobo4bob2o9bobo4bob2o9bobo4bo14bo4bo14bo4bo19bo19bo12bobo4bo14bo4bo14bo4bo12bobo4bo12bobo4bo12bobo4bo\$4b4o16b4o16b4o16b4o16b4o15b5o15b5o16b4o16b4o16b4o16b4o16b4o16b4o\$103bo19bo\$4b2o18b2o20b2o18b2o18b2o18b2o18b2o18b2o18b2o18b2o18b2o18b2o18b2o\$4bobo17b2o20b2o18b2o18b2o18b2o18b2o18b2o18b2o18b2o18b2o18b2o18b2o\$5bo10\$6bo19bo59bo39bo19bo19bo19bo39bo19bo\$5bobo17bobo15b2ob2o17b2ob2o15bobo17b2ob2o15bobo17bobo17bobo17bobo17b2ob2o15bobo17bobo\$4bobobo12b2obobobo15bobobo15bobobo15bobobo15bobobo2bo12bobobob2o12bobobo15bobobo15bobobo15bobobo2bo12bobobob2o12bobobo\$2o2bobobo13bobobobo15bobobo15bobobo15bobobo2bo12bobobob2o12bobobob2o12bobobo15bobobo15bobobo15bobobob2o12bobobob2o12bobobo\$obobo3bob2o10bobo3bob2o9b2obo3bob2o9b2obo3bob2o9b2obo3bobobo8b2obo3bo12b2obo3bo12b2obo3bob2o9b2obo3bob2o9b2obo3bob2o9b2obo3bo12b2obo3bo12b2obo3bob2o\$3bo4bob2o11bo4bob2o9bobo4bob2o9bobo4bob2o9bobo4bob2o9bobo4bo12bobo4bo12bobo4bob2o9bobo4bobobo8bobo4bobobo8bobo4bo12bobo4bo12bobo4bob2o\$4b4o16b4o16b4o16b4o16b4o16b4o16b4o16b4o16b4o3bo12b4o3bo12b4o16b4o16b4o2\$6b2o18b2o18b2o18b2o18b2o18b2o18b2o18b2o16b2o20b2o18b2o18b2o18b2o\$6b2o18b2o18b2o18b2o18b2o17bobo17bobo17bobo16b2o20b2o18bobo17bobo17bobo\$106bo19bo19bo60bo19bo19bo!`

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.
-Matthias Merzenich
Sokwe
Moderator

Posts: 1473
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### Re: Synthesising Oscillators

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:
`x = 90, y = 9, rule = B3/S234boo18boo18boo18boo18boo\$4bo19bo19bo19bo19bo\$6bo19bo19bo19bo19bo\$ob7o13b7o13b7o13b7o13b7o\$oobo5bo12bo6bo12bo6bo11bo7bo11bo7bo\$6b3o15bob3o14boob3o13b3ob3o13bobob3o\$6bo16boobo17bobo17bobo16boobo\$43bobbo\$44boo!`
mniemiec

Posts: 1026
Joined: June 1st, 2013, 12:00 am

### Re: Synthesising Oscillators

The new 28P7.3 in thirty gliders:
`x = 194, y = 50, rule = B3/S2325bo\$26b2o\$25b2o4\$33bobo\$33b2o135bo\$34bo135bobo\$170b2o\$31bo\$32b2o\$31b2o\$57bobo25bobo26bobo33bobo31bobo\$5b2o26bo3b2o18b2obo24b2obo25b2obo32b2obo30b2obo\$b2o2bobo25b2o3bo2bo18bo2bo24bo2bo25bo2bo18bo13bo2bo30bo2b2o\$obo2bo5bo20bobo3bobobo14b2obobobo20b2obobobo21b2obobobo18b2o8b2obobobo26b2obobobo\$2bo6b2o26b2ob2o15bo2bob2o21bo2bobobo21bo2bobobo17b2o9bo2bobobo26bo2bo2bo\$10b2o46b2o7bobo17b2ob2o24b2ob2o31b2ob2o29bo\$67b2o27bo14b2o40bo34bo\$68bo12bobo11bo14bo2bo37bobo32b3o\$82b2o11b3o12bo2bo7bo29b2o\$56b2o24bo28b2o3b2o2bobo67b2o\$8b3o44b2o9b2o24b3o20bobo2bobo67bobo\$8bo43b2o3bo7b2o14b2o9bo24bo3bo3bo66bo\$9bo43b2o12bo12bobo10bo16b3o11b2o66b2o\$52bo7b2o20bo29bo5bo5bobo\$59b2o50bo5b2o\$61bo55bobo47b3o\$114b2o51bo\$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:
`x = 137, y = 91, rule = B3/S2322bo6bo9bo15bo\$23b2o5b2o6bo17bo\$22b2o5b2o7b3o13b3o2\$57b2o\$57b2o2\$62b2o\$63bo\$60b3o2b3o30b2o35b2o\$19b2o10b2o27bo4bo32bo36bo\$18bo2bo10bo24b2obo5bo28b2obo8bobo22b2obo\$obobo13bo2bo7b3o21b2o2bobo31b2o2bobo9b2o19b2o2bobo\$14b3o2b2o8bo23bobobo23bo9bobobo12bo19bobobo\$16bo10bobo25bobo24b2o9bobo34bobo\$15bo11b2o26b2o24b2o10b2o34bo2b2o\$130b3o2bo\$27b2o26b2o36b2o\$26bobo25bobo35bobo\$27bo27bo37bo9b2o28b2o\$103bobo5bo21bo\$85b2o16bo6b2o22b3o\$84bobo23bobo23bo\$86bo2\$90bo\$90b2o\$89bobo2\$32b2o26b2o36b2o\$31bo2bo24bo2bo34bo2bo\$31bo2bo24bo2bo34bo2bo\$32b2o26b2o36b2o2\$100b2o\$100bobo\$100bo12\$27bo\$28b2o\$27b2o2\$29bo\$28bo\$28b3o3\$30bo\$28b2o\$29b2o5\$23bo28b2o35b2o35b2o\$22bobo5b2o21bo5b2o29bo5b2o9bobo17bo5b2o\$obobo18bo2b2obobo21bob2obobo29bob2obobo9b2o18bob2obobo\$27bobo24bobobo22bo9bobobo12bo19bobobo\$27bobo26bobo23b2o9bobo34bobo\$28bo27b2o4bo18b2o10b2o34bo2b2o\$60b2o68b3o2bo\$61b2o30b2o\$18b2o44b2o26bobo\$17bobo34b2o8bobo26bo9b2o28b2o\$19bo33bobo8bo38bobo5bo21bo\$24b2o29bo29b2o16bo6b2o22b3o\$23bobo7b2o49bobo23bobo23bo\$25bo7bobo50bo\$28b2o3bo\$29b2o59bo\$28bo61b2o\$89bobo2\$32b2o27b2o35b2o\$31bo2bo25bo2bo33bo2bo\$31bo2bo25bo2bo33bo2bo\$32b2o27b2o35b2o2\$100b2o\$100bobo\$100bo!`
I Like My Heisenburps! (and others)

Extrementhusiast

Posts: 1768
Joined: June 16th, 2009, 11:24 pm
Location: USA

### Re: Synthesising Oscillators

The p56 B-heptomino shuttle in 15 gliders:
`x = 59, y = 36, rule = B3/S2329bobo\$30b2o\$30bo5\$37bo\$16bobo16bobo\$17b2o17b2o\$17bo26bo\$42b2o\$43b2o\$o19bo\$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:
`x = 59, y = 36, rule = B3/S2329bobo\$30b2o\$30bo5\$37bo\$17bobo15bobo\$18b2o16b2o\$18bo25bo\$42b2o\$43b2o\$o20bo\$b2o18b2o\$2o3bo14bobo12bobo\$6b2o28b2o\$5b2o29bo2\$34b2o\$33b2o17b2o\$35bo15b2o\$53bo3b2o\$14b2o40b2o\$15b2o41bo\$14bo\$19b2o18b2o\$19bobo16b2o\$19bo20bo5\$26bo\$25b2o\$25bobo!`

2718281828

Posts: 708
Joined: August 8th, 2017, 5:38 pm

### Re: Synthesising Oscillators

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.
`x = 254, y = 175, rule = B3/S23163bo\$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\$141bo6\$136bo\$135b2o\$135bobo7\$44b3o\$46bo\$45bo5\$124b2o\$123b2o\$125bo5\$18b2o\$19b2o\$18bo14bo7b2o103b3o\$26b3o4b2o7b2o102bo\$28bo3bobo6bo105bo\$27bo116bo\$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.
mattiward

Posts: 25
Joined: February 8th, 2018, 3:19 am

### Re: Synthesising Oscillators

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)
`x = 184, y = 131, rule = B3/S23obobo5boo18boo\$10bo19bo\$4bo6bobo17bobo\$20bo\$obobo7bobo3b3o11bobo\$12bo4bo14bo4boo\$4bo9bobobo15bobobo\$13boobboo14boobbo\$obobo33b3o\$40bo6\$o3bo6boo8boo9bo21boo15b3obobbobo12bo18boo17boo20booboo16boo\$11bobo4boobbo8boboo17bobo3boo12bobobobobbo10bobo10boo6boboo4bo10bobboo16booboo15bob3o\$o3bo7b3obo17boobboo11bo3bobobo21bo20boobo5bo7bobbo3boo4bobobbo35bo4bo\$14bo3b3o11bobobobbo12bo3bo17bo16bobboobobo7bo3boobboboboboboobbo5bobboo13b9o12boobo\$obobo13bo18boo35bobbobobobo7boo3bobbobobobboo8bo24bo9bobbo4bo11bo3bobobo\$15bobo16bobbo16b4obbo14bobobbob3o12bo4bo21bobo10boobb3o8bo4boo13b3o4bo\$4bo12bo19boo22bo63bo9boboobbo12bo19bob3o\$33bobo22bobo74bobo16bobo17bobo\$4bo28boo22boo76bo39bo\$135bo6\$obobo6bo19bo19bo19bo\$10bobb3o14bobb3o14bobb3o14bobb3o\$o11bo19bo19bo19bo\$13bobobbo14bobobbo14bobobbo14bobobbo\$obobo7boob4o13boob4o13boob4o13boob4o\$14bo4boo10bobbo16bobbo16bobbo\$4bo9bobobbo12bobobo15bobobo15bobboboo\$15bobobo13bobobo15bobobo15boo3bo\$obobo11bobo15bobbo16bobbo20bobo\$17bo17boo20boo20boo5\$18boo22boo12boo22boo\$obobo5boo6bo11boo11bo6boo4bo13boo9bo8boo18boo18boo18boo\$10bo10bo8bo9bo9bo8bo10bo7bo11bo19bo19bo19bo\$o10bobo6boo9bobo6boo9bobo4boo11bobo4boo11bobo17bobo17bobo17bobo\$\$obobo7bobo3b4o10bobo3b4o10bobo3b4o10bobo3b4o10bobo17bobo17bobo17bobo\$12bo4bo4bo9bo4bo4bo9bo4bo4bo9bo4bo4bo9bo4boo13bo4boo13bo4boo13bo4boo\$o3bo9bobobobboo11bobobobboo11bobobobboo11bobobobboo11bobobobboo11bobobobboo11bobobobboo11bobobobboo\$13boobboo14boobboo14boobboo14boobboo14boobbo4bo10boobbo4bo10boobbo4bo10boobbo4bo\$obobo93b4o16b4o16b4o16b4o\$\$100boo18boo18boo16boo\$101bo18bo20bo16bo\$98bo24bo14bo22bo\$98boo22boo14boo20boo6\$12booboo15booboo15booboo15booboo15booboo13boo5boo\$obobo5bobbobo14bobbobo14bobbobo3boo9bobbobobo12bobbobobo13bo6bo\$10boobo3bo12boobobobobbo9boobobobobbo9boobo3bo12boobo3bo13bobo4boboo\$4bo8bobb4o13bo3b4o12bo3boo14bobbooboo12bobbooboo11boo3boobo\$13bo6bo12bo19bo19bo4bobo12bo4bobo21bo\$4bo9b6o14b5o15b5o15b4o16b4o17bob6o\$38bo19bo56bo\$4bo11boo18bo19bo19boo16boo24bo\$16boo18boo18boo18boo16boo23boo\$4bo7\$obobo7bo19bo17bo3bo3bo13booboo15booboo15bo19bo\$10bobo17bobo37bobbobo17bobo15boboboo14boboboo\$o3bo6bobo17bobo16bo3bo3bo11boobo3bo15bo3bo13bobobo14bobbobo\$11bo19bo41bobb4o10boobobb4o10boobo3bo12boobo3bo\$obobo10bo19bo7boo5bo3bobobo14bo6bo9boobo6bo12bobb4o13bobb4o\$16bo19bo6bo30b5obo13b5obo12bo6bo12bo6bo\$o3bo7bo4bobboo10bo4bobboobo6bo7bo20bo19bo14b5obo13b5obo\$12boobobboboo10boobobbobooboo31bo19bo22bo19bo\$obobo11boo18boo12bo7bo17boo18boo18bo19bo\$116boo18boo\$22bo19bo\$20bobo17bobo\$21bobo17bobo\$21bo19bo7\$obobo6b3o5b3o10b3o16bo19b3o5b3o9boo18b3o17bo20b3o16boo\$15bobo12bo20bo23bobo12bobbo21bob3o11bo24bob3o9bobbo\$4bo5bo4bobo4bo7bo4bo15bo18bo4bobo4bo7bobobbo4b3o7bo4boboo12bo19bo4boboo10bobobbo\$14bo3bo12bo19boo21bo3bobbobo7bo4bobo15bo3boo11boo17bobobbo3boo10bo4bob3o\$obobo6boo7boo11boo3bo15bo4b3o9boo7bobbo12bobo4bo7boo5bo15bo15bobbo5bo16boboo\$11bo9bo12bo3bo11bo4bobo13bo9boo9b3o4bo11bo9boo7bo4bob3o11boo9boo8b3o4boo\$4bo6bo9bo12bo3bo16bobo4bo8bo29boo8bo6boobo13boboo20boobo16bo\$11bo9bo12bo3boo11b3o4bo12bo30bo8bo7bo11b3o4boo20bo21boo\$obobo36bo18boo40bo16bo18bo21bo18boobo\$37bo4bo18bo40bo38boo37bo\$42bo18bo76boobo38bo\$38b3o20bo77bo\$139bo8\$o3bo6boo7boo8bobobo3bobobo9boo\$10bobbo5bobbo29bo4boo\$o3bo5bobobbobobbobo11bo3bo3bo10bo3bobbo\$11bo9bo31boo4boo\$obobo7booboboboo9bobobo3bo3bo8bobbo\$14bo3bo31bo8boo\$4bo25bo7bo3bo7boo6bobbo\$56bobbobo\$4bo25bobobo3bobobo17bo\$56boboo\$57bo!`
Last edited by mniemiec on February 12th, 2018, 6:13 am, edited 1 time in total.
mniemiec

Posts: 1026
Joined: June 1st, 2013, 12:00 am

### Re: Synthesising Oscillators

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.

77topaz

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

### Re: Synthesising Oscillators

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

77topaz wrote:Mattiward himself posted a synthesis of one of the burloaferimeters just recently.

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).
mniemiec

Posts: 1026
Joined: June 1st, 2013, 12:00 am

### Re: Synthesising Oscillators

38P7.2 in 14 gliders:

`x = 45, y = 39, rule = B3/S234bo\$5b2o\$4b2o24bo\$30bobo\$30b2o2\$33bobo\$33b2o2b3o\$7bo26bo2bo\$8b2o28bo\$7b2o7\$44bo\$34b2ob2o3b2o\$29b2o3b2ob2o4b2o\$29bobo\$31bo\$31b2o7\$bo\$b2o29b3o\$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:

`x = 31, y = 22, rule = B3/S233bobo\$4b2o7bo\$4bo7bo12bobo\$12b3o2bo7b2o\$18bo7bo\$16b3o5\$15bo\$15bobo\$2o13b2o3b2o\$b2o17bobo\$o6bo14bo6b2o\$7b2o13b2o4b2o\$6bobo21bo3\$b2o11b2o\$2b2o11b2o\$bo12bo!`

Goldtiger997

Posts: 523
Joined: June 21st, 2016, 8:00 am
Location: 11.329903°N 142.199305°E

### Re: Synthesising Oscillators

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

`x = 31, y = 22, rule = B3/S233bobo\$4b2o7bo\$4bo7bo12bobo\$12b3o2bo7b2o\$18bo7bo\$16b3o5\$15bo\$15bobo\$2o13b2o3b2o\$b2o17bobo\$o6bo14bo6b2o\$7b2o13b2o4b2o\$6bobo21bo3\$b2o11b2o\$2b2o11b2o\$bo12bo!`

There's probably a better alternate teardrop but I didn't want to spend a lot of time slogging through the options:
`x = 32, y = 27, rule = B3/S23obo3bo\$b2o4bo\$bo3b3o5\$8bo17bobo\$7bobo8bo7b2o\$8bobo8bo7bo\$9b2o6b3o5\$16bo\$16bobo\$b2o13b2o3b2o\$2b2o17bobo\$bo6bo14bo6b2o\$8b2o13b2o4b2o\$7bobo21bo3\$2b2o11b2o\$3b2o11b2o\$2bo12bo!`
LifeWiki: Like Wikipedia but with more spaceships. [citation needed]

Posts: 1876
Joined: November 8th, 2014, 8:48 pm
Location: Getting a snacker from R-Bee's

### Re: Synthesising Oscillators

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

`x = 13, y = 15, rule = B3/S232o5b2o\$bo6bo\$bobo4bob2o\$2b2o3b2obo\$6bo5bo\$6bob5o\$5b2obo\$2bo6b2o\$obo7bo\$b2o2b2o3bobo\$4bobo4b2o\$3bobo\$4bo4b2o\$8bobo\$10bo!`

Reductions to the SL:
`x = 51, y = 11, rule = B3/S232b2o18b2o18b2o\$3bo19bo19bo\$3bob2o2bobo11bob2o16bob2o\$2b2obo3bobo10b2obobo14b2obobo\$bo4bo2bobo9bo4bo14bo4bo2bo\$bob3o15bob3o15bob3o3bo\$2obo16b2obo16b2obo6bo\$4b2o18b2o18b2o\$5bo19bo19bo\$5bobo17bobo17bobo\$6b2o18b2o18b2o!`
Tanner Jacobi

Kazyan

Posts: 830
Joined: February 6th, 2014, 11:02 pm

### Re: Synthesising Oscillators

90P25 honey farm hassler from 36 gliders.
`x = 115, y = 104, rule = B3/S239bo\$10b2o\$2bobo4b2o\$3b2o\$3bo7\$114bo\$112b2o\$22bo90b2o\$17bo2bobo4bo\$15bobo3b2o5b2o\$16b2o9b2o11\$50bo\$51bo\$49b3o9\$52bo\$53bo20bo\$51b3o4bo13b2o\$56bobo14b2o8bo\$57b2o7bo15bo4bobo\$65bo16b3o2b2o\$65b3o20bo2\$35bo\$36b2o27b3o\$35b2o10b2o16bo\$43bo4b2o7b2o7bo\$44bo2bo8bobo14b2o\$42b3o13bo13b2o\$74bo4\$60b2o\$59b2o\$61bo\$26bo\$26b2o2b3o16b2o\$25bobo4bo15bobo\$31bo18bo2\$42b3o\$44bo\$43bo17b2o\$35b2o24bobo\$36b2o23bo4b3o\$35bo30bo\$67bo3b2o\$71bobo\$71bo2\$46bo\$46b2o\$45bobo4\$70b2o\$70bobo\$70bo5\$86b2o9b2o\$85b2o5b2o3bobo\$87bo4bobo2bo\$2o90bo\$b2o\$o7\$111bo\$110b2o\$104b2o4bobo\$103b2o\$105bo!`
mattiward

Posts: 25
Joined: February 8th, 2018, 3:19 am

### Re: Synthesising Oscillators

mattiward wrote:90P25 honey farm hassler from 36 gliders.
`x = 115, y = 104, rule = B3/S239bo\$10b2o\$2bobo4b2o\$3b2o\$3bo7\$114bo\$112b2o\$22bo90b2o\$17bo2bobo4bo\$15bobo3b2o5b2o\$16b2o9b2o11\$50bo\$51bo\$49b3o9\$52bo\$53bo20bo\$51b3o4bo13b2o\$56bobo14b2o8bo\$57b2o7bo15bo4bobo\$65bo16b3o2b2o\$65b3o20bo2\$35bo\$36b2o27b3o\$35b2o10b2o16bo\$43bo4b2o7b2o7bo\$44bo2bo8bobo14b2o\$42b3o13bo13b2o\$74bo4\$60b2o\$59b2o\$61bo\$26bo\$26b2o2b3o16b2o\$25bobo4bo15bobo\$31bo18bo2\$42b3o\$44bo\$43bo17b2o\$35b2o24bobo\$36b2o23bo4b3o\$35bo30bo\$67bo3b2o\$71bobo\$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:
`x = 235, y = 38, rule = B3/S23136bo26bo\$137b2o25bo\$136b2o24b3o3bobo\$91bobo21bo53b2o11bo29bo9bo\$92b2o3bo16bo54bo10b3o29b3o5b3o\$92bo5b2o14b3o62bo35bo3bo\$97b2o37bo30b2o3b2o5b2o33b2o3b2o\$107bobo26bobo9b2o18b2obobo14b2o38b2o\$107b2o27b2o7b2o2bo17bo5bo11b2o2bo35b2o2bo\$108bo36bob2o36bob2o22bobo11bob2o\$102bo32bo8bo39bo20bo6b2o10bo\$100b2o34b2o6bo39bo21b2o4bo11bo\$101b2o5bo26b2o8bob2o36bob2o16b2o18bob2o\$107b2o36b2o2bo35b2o2bo26b3o6b2o2bo\$99bo7bobo38b2o38b2o26bo11b2o\$100bo102bo13bo\$98b3o13b3o86b2o\$114bo87bobo\$115bo\$bo21bobo\$2bo16bo3b2o207bobo\$3o14b2o5bo207b2o\$18b2o199bo13bo\$7bobo37b2o38b2o38b2o38b2o38b2o11bo\$8b2o37bo2b2o35bo2b2o35bo2b2o35bo2b2o35bo2b2o6b3o\$8bo39b2obo36b2obo36b2obo36b2obo36b2obo18b2o\$52bo39bo39bo39bo39bo11bo4b2o\$52bo39bo39bo39bo39bo10b2o6bo\$8bo39b2obo7bo28b2obo36b2obo36b2obo36b2obo11bobo\$8b2o37bo2b2o6bo28bo2b2o35bo2b2o35bo2b2o11bo5bo17bo2b2o\$7bobo37b2o9b3o26b2o38b2o38b2o14bobob2o18b2o\$18b2o76b2o38b2o38b2o5b2o3b2o26b2o3b2o\$3o14b2o38bo39bo39bo39bo39bo3bo\$2bo16bo36b2o36b3o37b3o37b3o10bo26b3o5b3o\$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.
-Matthias Merzenich
Sokwe
Moderator

Posts: 1473
Joined: July 9th, 2009, 2:44 pm

### Re: Synthesising Oscillators

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.

dvgrn
Moderator

Posts: 5705
Joined: May 17th, 2009, 11:00 pm

### Re: Synthesising Oscillators

`x = 59, y = 40, rule = LifeHistory16.27D\$16.D25.D\$16.D25.D\$16.D11.3D11.D\$2A14.D.2A7.D3.D7.2A.D14.2A\$A.A2.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.D25.D\$16.D25.D\$16.D25.D\$16.27D!`

PHPBB12345

Posts: 514
Joined: August 5th, 2015, 11:55 pm

### Re: Synthesising Oscillators

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.
mniemiec

Posts: 1026
Joined: June 1st, 2013, 12:00 am

### Re: Synthesising Oscillators

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:
`x = 909, y = 44, rule = B3/S23605bobo75bobo\$604bo78b2o\$604bo79bo\$604bo2bo\$465bo138b3o\$465bobo15bo190bobo\$20bo39bobo124bo277b2o16bobo188b2o\$21b2o40bo124bo290bo3b2o22bo105bo53bobo5bo4bo\$20b2o41bo122b3o272bo7bobo6bo26bobo105bobo20bo29bo13bobo52bo\$29bo30bo2bo398b2o5b2o7b3o25b2o87bo17b2o19bobo29bo3bo9b2o23bo29bobo\$27b2o32b3o93bo303b2o7bo58b2o64bobo37b2o29bo7b3o26bobo29b2o\$28b2o127bobo276bo39bo51b2o14bobo48b2o4bo5bobo56bo2bo4bo29b2o\$157b2o4bo236bo34bo30bo8bo48bobo3bo14b2o54bobo3b2o57b3o6bo99bo\$22bo139bo32bo84bo106bo12bobo32b3o26bobo8b3o5b3o39b2o18bo19bo35b2o5bo92bo70bo2bobo28bobo21bo\$23bo134bo3b3o31bo82bo106bo13b2o31bo31b2o15b5o38bo39bobo19bo53bo57bobo2bo25bo39bobo2b2o29b2o20bobo\$21b3o35bo3bobo92b2o34b3o82b3o73bo30b3o42bobo47b2ob3o70bo7b2o18bobo52bo59b2o2bobo24bo39b2o34bo17b2o2b2o31bo6bobo\$60bo3b2o91bobo39bo77bo75b2o77b2o48b2o74b2obo24b2o24bo27b3o61b2o23b3o94b2o35b2o4b2o\$bobo5bobo41bo4b3o3bo38bo95bobo73bobo76b2o13bo13bobo129b2o40b2o2bobo48bobo210bo36b2o6bo\$2b2o5b2o43b2o48bo90bo3b2o6bo62bo5b2o69bo15bo5bobo12b2o5bo66bo13bo42b2o44b2o49b2o29b2o31b2o49b2o40b2o95b2o\$2bo7bo42b2o47b3o91b2o9bobo3bo57b2o75b2o11b2o6b2o13bo6bobo47bo17b2o11bo4bo69bo4b2o76b2o2b2o7bobo18bo6b2o3bobo25b2o20bobo7b2ob2o27bobo2b2o19b2o3b2o27b2o35bo2bo\$80bo49b2o27b2o34b2o10b2o4bobo54b2o75b2o13b2o2b2o23b2o4bo6b2o34bobo15b2o3bobo6bo3bobo36b4o26bobo5bo42b2o5bo5b3o18bobo2bo7bo18bobo6bobo4bo23bo2bo22bo7bo3bo27bo5bo19bo2bo2bo4bobo20bo2bo34bo2bo\$3o7b3o24bobo26bo12bo49bobo26bobo30bo21b2o35b2o35b2o35b2o30b2o8bobo27bobo4b2o34bo2bo21b2o9bo2bo36bo3bo26b2o4bo43b2o3b3o5bo22b3o28b2o8b5o24b3o32b3o29b5o21b5o5b2o22b3o35b3o34b2ob2o\$2bo7bo13b2ob2o8b2o25b3o12b3o17bobo7bo20bo3bo24bo3bo28bo6b2o46b2o2bo32b2o2bo22bo9b2o2bo27b2o2bo8bo18bobo8bobo6bo27b2o4bobo22bo4b2o4bobo40bo24b2o6bo48bo9bo20bo40bo133bo97bo3bo\$bo9bo11bobobobo8bo24bo36b2o6bobo22bobo26bobo25b3o5bo2bo41b2obo33b2obo28bo7bo31bo33b2o6b2obo36bo2b2obo21bo7bo2b2obo40bob3o20bobo5bob3o31b2o11bob3o26bob3o36bob3o24b3o32b3o31b3o23b3o31b3o35b3o35b3o\$4b2ob2o14bobobobo33bob4o4bo26bo7bob3o15bo4bob3o24bob3o32bob3o6b2o32bobobobo30bobobobo22b3o7bobobo17bobo3b2o2bobobo29bo6bobo33bo4bobobo23b2o6bobobo42bobo2bo5b2o14bo5bobo2bo31b2o10bobo2bo25bobo2bo35bobo2bo22bobobo30bobobo29bobobo21bobobo9bo19bobobo28bobo2bobobo2bobo30bo\$4bo3bo15bo3bo4bobo28bo3bo4bobo2bo30bo3bo12bobo5bo3bo24bo3bo32bo3bo5bobo29bobobo3bo30bobo3bo29b2obo3bo18b2o3bobobo3bo35bo3bo16bobo11bobo5bo3bo21bobo7bo3bo5b3o34bo3bo4b2o22bo3bo30bo13bo3bo26bo3bo36bo3bo22bobobo30bobobo29bobobo21bobobo9bobo17bobobo29b2o2bobobo2b2o31bo\$5b3o17b3o5b2o30b3o5b2o2b2o18b3o10b3o14b2o6b3o26b3o27b2o5b3o6bo31b2o3b3o28b2obo2b3o20bo10bo2b3o19bo6bo2b3o37b3o9bo3b2o2b2o13b2o6b3o33b3o6bo37b3o7bo22b3o46b3o28b3o38b3o24b3o32b3o31b3o23b3o10b2o19b3o30bo4b3o4bo30b3o\$34bo21bo20bobo19bo30b2o28b2o25b3o3bobo82bo2bo26bo2b3o2bobo29bobo53b2o3bobo2bo16b2o35b2o12bo\$36bo19b2o40bo30bobo28b2o27bo5bo83b2o25b3o4bo2b2o30b2o54bobo2bo20bobo35b2o337bo55bo9bo\$5b3o17b3o7b2o18bobo7b3o42b3o18bo3b3o16b2o8b3o21bo12b3o43b3o34b3o25bo8b3o29b3o37b3o36bo3b3o23bo9b3o44b3o30b3o46b3o28b3o38b3o24b3o32b3o31b3o23b3o8b2o21b3o31b2o2b3o2b2o31b3o\$6bo19bo8bobo28bo44bo24bo16bobo9bo36bo29bobo13bo36bo36bo31bo39bo42bo24b2o9bo46bo32bo35bo12bo30bo40bo26bo34bo33bo25bo9bobo21bo31bobo3bo3bobo31bo\$6bo19bo39bo44bo24bo12b2o4bo9bo36bo30b2o2b2o9bo36bo36bo31bo39bo42bo19bo3bobo9bo27b2o17bo32bo34b3o11bo30bo30b2o8bo26bo34bo33bo25bo33bo37bo37bo\$5b3o17b3o37b3o42b3o22b3o10bobo13b3o34b3o29bo2bobo8b3o34b3o34b3o29b3o37b3o40b3o18b2o13b3o25bobo16b3o30b3o33bob2o9b3o28b3o28bobo7b3o24b3o32b3o31b3o23b3o31b3o35b3o35b3o\$150bo87bo217bobo43bo86b3o73bo\$589b2o\$5b3o17b3o37b3o42b3o22b3o26b3o34b3o43b3o34b3o34b3o29b3o37b3o40b3o33b3o44b3o30b3o46b3o28b3o38b3o24b3o32b3o31b3o23b3o31b3o35b3o35b3o\$6bo19bo39bo44bo24bo28bo36bo45bo36bo36bo31bo39bo42bo35bo46bo32bo48bo30bo40bo26bo34bo33bo25bo33bo37bo37bo\$6bo19bo39bo44bo24bo28bo36bo26b3o16bo36bo36bo31bo39bo42bo35bo46bo32bo48bo30bo40bo26bo34bo33bo25bo33bo37bo37bo\$5b3o17b3o37b3o42b3o22b3o26b3o34b3o27bo15b3o34b3o34b3o29b3o37b3o40b3o33b3o44b3o30b3o46b3o28b3o38b3o24b3o32b3o31b3o23b3o31b3o35b3o35b3o\$230bo2\$5b3o17b3o37b3o42b3o22b3o26b3o34b3o43b3o34b3o34b3o29b3o37b3o40b3o33b3o44b3o30b3o46b3o28b3o38b3o24b3o32b3o31b3o23b3o31b3o35b3o35b3o\$4bo3bo15bo3bo35bo3bo40bo3bo20bo3bo24bo3bo32bo3bo41bo3bo32bo3bo32bo3bo27bo3bo35bo3bo38bo3bo31bo3bo42bo3bo28bo3bo44bo3bo26bo3bo36bo3bo22bo3bo30bo3bo29bo3bo21bo3bo29bo3bo33bo3bo33bo3bo\$4b2ob2o15b2ob2o35b2ob2o40b2ob2o20b2ob2o24b2ob2o32b2ob2o41b2ob2o32b2ob2o32b2ob2o27b2ob2o35b2ob2o38b2ob2o31b2ob2o42b2ob2o28b2ob2o44b2ob2o26b2ob2o36b2ob2o22b2ob2o30b2ob2o29b2ob2o21b2ob2o29b2ob2o33b2ob2o33b2ob2o!`
I Like My Heisenburps! (and others)

Extrementhusiast

Posts: 1768
Joined: June 16th, 2009, 11:24 pm
Location: USA

### Re: Synthesising Oscillators

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!
mniemiec

Posts: 1026
Joined: June 1st, 2013, 12:00 am

### Re: Synthesising Oscillators

The last 16-bit P2 in about the least likely way imaginable (in two slight variants):
`x = 125, y = 76, rule = B3/S2397bo\$97bobo\$90bo6b2o\$90bobo\$90b2o4\$82bo\$82bobo\$82b2o\$76bo12bo\$77b2o10bobo\$76b2o11b2o2\$81bo\$80bobob2o\$80bobob2o\$75b2o4bo\$67b2o5bo2bo\$66b4o4bo2bo9b2o\$66b2ob2o4b2o4b3o4bo\$68b2o15bobo\$73b2o7bobo\$72bobo6bo4b3o\$74bo2b2o2b2o\$78bo\$77bo\$77b2o\$72b2o\$71bobo6b3o\$73bo6bo\$4bo76bo\$3bo72b2o\$3b3o70bobo\$76bo\$obo\$b2o7bo\$bo9b2o\$10b2o\$32b2o83b2o4b2o\$4bo21b3o4bo83bobo4bo\$4b2o6bobo15bobo9bobobo74bobo\$3bobo6b2o13bobo87bo2bo\$13bo12bo4b3o84bo3b3o\$26b2o42bo22bo24bo\$6b2o60bobo22bobo\$5b2o9bo52b2o22b2o\$7bo7b2o66bobo\$15bobo65b2o\$84bo\$12b3o61bo12bo\$14bo62b2o10bobo\$13bo62b2o11b2o2\$81bo\$80bobob2o\$80bobob2o\$75b2o4bo\$67b2o5bo2bo\$66b4o4bo2bo9b2o\$66b2ob2o4b2o4b3o4bo\$68b2o15bobo\$73b2o7bobo\$72bobo6bo4b3o\$74bo2b2o2b2o\$78bo\$77bo\$77b2o\$72b2o\$71bobo6b3o\$73bo6bo\$81bo\$76b2o\$76bobo\$76bo!`

The corresponding 17-bit P2 can be made the same way far more cheaply:
`x = 44, y = 28, rule = B3/S23b2o\$2b2o\$bo3bobo\$5b2o\$6bo5\$35b2o\$18b2o15bo6b2o\$12b3o4bo16bobo4bo\$16bobo21bobo\$13bobo20bo2bo\$2b2o8bo4b3o17bo3b3o\$3b2o7b2o23bo\$2bo4\$b2o\$obo\$2bo2\$14b3o\$3b2o9bo\$2bobo10bo\$4bo!`

Unfortunately, the usual barberpole-shortening technique doesn't work here.
I Like My Heisenburps! (and others)

Extrementhusiast

Posts: 1768
Joined: June 16th, 2009, 11:24 pm
Location: USA

### Re: Synthesising Oscillators

Nice work! Those disjoint-bits objects are hard.

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

`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.A5.CBA.A\$8.CB.2A\$7.2C2\$4.3A\$6.A.3A\$5.A2.A\$9.A!`
Tanner Jacobi

Kazyan

Posts: 830
Joined: February 6th, 2014, 11:02 pm

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