ConwayLife.com • First Known Oscillators for Each Period

Page 1 of 1

First Known Oscillators for Each Period

Posted: July 11th, 2021, 6:57 am

by Sokwe

This thread is meant to collect discussion of the first known oscillators for each period. It is a parallel to the discussion of the smallest known oscillators for each period.

Unfortunately, in many cases the resources needed to determine the first known oscillators and the details of their discovery is either lost or not publicly available, so I don't expect this thread to get much use, nor do I expect to get a definitive answer for each period.

Re: First Known Oscillators for Each Period

Posted: July 11th, 2021, 7:05 am

by Sokwe

I'll begin the discussion with a detailed account of the discovery of early traffic jam-based oscillators that I compiled recently. Traffic jam loops allowed the construction of oscillators of all periods above 100 that are multiples of 4, 6, or 10.

14 Oct. 1994:
- Noam Elkies builds p50 traffic jam using toasters instead of Octogon II and 4 traffic lights instead of 3.
- In response, Bill Gosper notes that p36 traffic jam can be built with HWSS emulators and T-nosed p4s.
- Noam Elkies posts a spark combination for p40 traffic jam, but it doesn't quite work as posted.
15 Oct. 1994:
- Noam Elkies posts the 3-traffic light version of p50 traffic jam and the base reaction for p100 traffic jam. He also posts a corrected and complete p40 traffic jam.
- Dean Hickerson gives reductions for the p36, p40, and p100 traffic jams and notes that the traffic jam reaction can reflect a glider and notes that glider loops of periods 36n, 40n, and 50n can be constructed.
- Bill Gosper builds a p400 traffic jam loop using the 75-generation traffic jam corner and notes that periods 400+50n are achievable.
16 Oct. 1994:
- Bill Gosper builds a p200 traffic jam loop using the 25-generation traffic jam corner.
- Noam Elkies notes that the toasters in the p50 and related traffic jams can be replaced with Octagon II.

17 Oct. 1994:

Bill Gosper builds a p110 traffic jam loop using the 25-generation corner and notes that using the 75-generation corner would give a smaller example. Here is the original p110 traffic jam:

Code: Select all

x = 161, y = 78, rule = B3/S23
26b2o4b2o$26bobo2bobo$28bo2bo$27b2o2b2o$26b3o2b3o$28bo2bo5b4o$36bob2ob
o92b2o4b2o$36b2o2b2o92bobo2bobo$36b2o2b2o94bo2bo$36bob2obo93b2o2b2o$
30b3o4b4o93b3o2b3o$11b4o121bo2bo5b4o$10bob2obo12bo5bo109bob2obo$10b2o
2b2o12bo5bo109b2o2b2o$10b2o2b2o12bo5bo109b2o2b2o$10bob2obo128bob2obo$
11b4o15b3o105b3o4b4o$18bo$18bo117bo5bo$5b2o2bo8bo35bo13b2o4b2o60bo5bo$
5bo2b2o44bo10b3ob2o2bo2bo59bo5bo$6b5o3b3o3b3o3b3o12b3o10bo8bob4o3b2ob
2o12b3o10bo$26bobo34bo2bobo4bobo2bo23bo35b3o$18bo7b3o10bo5bo4b3o3b3o4b
o2bobo4bobo2bo8bo5bo8bo10b3o$6b5o7bo20bo5bo19b2ob2o3b4obo8bo5bo28b3o$
5bo2b2o8bo20bo5bo8bo10bo2bo2b2ob3o10bo5bo4b3o3b3o4bo5bo$5b2o2bo44bo11b
2o4b2o37bo5bo2bo5bo$41b3o10bo34b3o10bo8bo5bo2bo5bo29bo2b2o$102bo17bo5b
o7b3o10bo8b2o2bo$102bo10b3o31bo7b5o$122b3o7bo5bo8bo$132bo5bo$132bo5bo
4b3o3b3o3b5o$156b2o2bo$134b3o10bo8bo2b2o$6b4o137bo$5bob2obo14b3o119bo$
5b2o2b2o14bobo123b4o$5b2o2b2o14b3o122bob2obo$5bob2obo123bo15b2o2b2o$6b
4o124bo15b2o2b2o$134bo15bob2obo$25bo125b4o$2o2bo20bo104b3o3b3o$o2b2o8b
o11bo$b5o5b2ob2o118bo$13bo7b3o3b3o104bo$33b3o10bo87bo$b5o19bo20bo14bo$
o2b2o20bo5bo5bo8bo14bo8bo58b3o$2o2bo20bo5bo5bo23bo8bo$31bo5bo4b3o3b3o
13bo5bo10b3o10bo18bobo2b3o6bo5bo17bo2b2o$57b3o3b3ob2o25bo11bo7b7o6bo5b
o17b2o2bo$33b3o10bo16b2ob3o3b3o4bo5bo8bo10bo8b4obob2o4bo5bo7b3o6b5o$
21bo24bo14bo5bo11bo5bo19b2obob4o8bo$21bo24bo14bo8bo8bo5bo4b3o3b3o8b7o
7bo7b3o7bo5bo$21bo39bo8bo36b3o2bobo24bo5bo4b5o$70bo10b3o10bo44bo5bo5b
2o2bo$17b3o3b3o68bo56bo2b2o$94bo46b3o$21bo107bo$12b4o5bo107bo16b4o$11b
ob2obo4bo107bo15bob2obo$11b2o2b2o128b2o2b2o$11b2o2b2o108b3o3b3o11b2o2b
2o$11bob2obo128bob2obo$12b4o5bo2bo104bo16b4o$19b3o2b3o93b4o5bo$20b2o2b
2o93bob2obo4bo$21bo2bo94b2o2b2o$19bobo2bobo92b2o2b2o$19b2o4b2o92bob2ob
o$120b4o5bo2bo$127b3o2b3o$128b2o2b2o$129bo2bo$127bobo2bobo$127b2o4b2o!

Dean Hickerson notes that the method in the p110 traffic jam can be used to construct oscillators of all periods greater than or equal to 100 that are multiples of 4 or 10.

19 Oct. 1994:
- Noam Elkies notes that a dot spark can cause the traffic jam reaction to release a glider:
  Code: Select all
```
x = 48, y = 18, rule = B3/S23
30bo$2ob2o38b2ob2o$o24b5o3b2o12bo$b2o2bo6b3o8b2o4bob2o2bo6bo2b2o$2b3o
26b2ob3o6b3o$2b3o5bo5bo4b2o4b2o3bobobo6b3o$b2o2bo4bo5bo6bobobo3b2o4b2o
3bo2b2o$o9bo5bo6b3ob2o18bo$2ob2o19bo2b2obo4b2o6b2ob2o$12b3o10b2o3b5o$
7b2o30b2o$6bo2bo28bo2bo$5bo4bo26bo4bo$4bo6bo24bo6bo$4bo6bo24bo6bo$5bo
4bo26bo4bo$6bo2bo28bo2bo$7b2o30b2o!
```
- Noam Elkies suggests the possibility of a p9 traffic light pusher and Dean Hickerson constructs a working example, noting that this allows the construction of oscillators of every period greater than 100 that is a multiple of 18.
20 Oct. 1994:
- Noam Elkies finds a p42 traffic light pusher by replacing the caterer in the 124P21 pusher with unix. Dean Hickerson notes that this gives traffic jams of all periods greater than 100 that are a multiple of 42. According to Hickerson, this does not give any new oscillator periods, but does give new gun periods (using the reflector reaction to support David Buckingham's 2g -> 3g reaction), the lowest being p462.
21 Nov. 1994:
- Noam Elkies finds a supports for a p6 domino sparking wick and asks whether it can be used to construct a p6 traffic light push

22 Nov. 1994:

Dean Hickerson uses a modified form of the p6 domino sparking wick to create a p6 traffic light push and gives an example of its use in a p36 traffic jam:

Code: Select all

x = 60, y = 48, rule = B3/S23
b2o36b2o$b2o36bobo$b2o37b3o$bo39b2o$obo36bobo$bobob3o26b2o2bobo$2bob4o
26bobo2bo$3bo31b4o$23bo6b2o4b2o$9bo2bob2obo2bobo2bo2bo4bo$6b2obo2bo4bo
2bo4bo2bo4bo$9bo2bob2obo2bobo2bo2bo4bo$30b2o3bo2bo$2b2o34bo$4bob2o16bo
9bo4bo$o2bo2b2o11b3o3bo3bo4b2o2bobo$obo15b5obo4bo9bob2o$bo18bo8bo$19b
2o$b2o16b2o4b3o3b3o5bo2bo$b2o36b2o$29bo$29bo$29bo$30bo$30bo$30bo$19b2o
36b2o$17bo2bo5b3o3b3o4b2o16b2o$39b2o$30bo8bo18bo$17b2obo9bo4bob5o15bob
o$19bobo2b2o4bo3bo3b3o11b2o2bo2bo$20bo4bo9bo16b2obo$21bo34b2o$21bo2bo
3b2o$26bo4bo2bo2bobo2bob2obo2bo$26bo4bo2bo4bo2bo4bo2bob2o$26bo4bo2bo2b
obo2bob2obo2bo$22b2o4b2o6bo$21b4o31bo$20bo2bobo26b4obo$19bobo2b2o26b3o
bobo$18bobo36bobo$17b2o39bo$17b3o37b2o$18bobo36b2o$19b2o36b2o!

This would allow traffic jams of all periods greater than 100 that are a multiple of 6 to be constructed using the following corner which requires extra traffic lights:

Code: Select all

x = 72, y = 68, rule = B3/S23
39b3o2$37bo5bo$37bo5bo$37bo5bo2$39b3o3$38b3o2$36bo5bo$36bo5bo$36bo5bo
2$38b3o2$4b2o9b2o$2o2b2o11bob2o$2o2bob2o5bo2bo2b2o$5b3o5bobo24bo10b3o
10bo$14bo25bo23bo$40bo8bo5bo8bo$5b2o7b2o33bo5bo$5b2o2b3o2b2o20b3o3b3o
4bo5bo4b3o3b3o$19bo10b3o$9b3o7bo20bo10b3o10bo$10bo8bo8bo5bo5bo23bo$10b
o17bo5bo5bo23bo$9b3o3b3o3b3o4bo5bo2$9b3o7bo10b3o$9b3o7bo24bo$10b2o7bo
24bo$9b2o3b3o27bo$14b2o$15b2o23b3o3b3o$9b2o4bo$10b2o6b2o24bo$9b3o3b2ob
o25bo$9b3o4bo27bo$16bo$9b3o$10bo$10bo$9b3o32b3o2$5b2o2b3o2b2o18b2o6bo
5bo19b2o$5b2o7b2o18b2o6bo5bo5b2o12bo2bo$42bo5bo4bo$6bo49bo$5bobo5b3o
17b3o8b3o5bo3bo11bob2o$2o2bo2bo5b2obo2b2o12b2obo2b2o8b4o3bo6b2o2bobo$
2obo11b2o2b2o14b2o2b2o13bo8bo4bo$4b2o9b2o18b2o30bo$64bo2bo$40bobo2bo
12bo2bo$40b3o2b6o2b6o2b3o$42bo2bo4bo2bo4bo2bobo$36bo2bo$36bo30b2o$35bo
4bo22b2o2b2o$34bobo2b2o22b2o2bob2o$32b2obo32b3o3$32bo2bo32b2o$34b2o32b
2o!

However, the details of this construction do not appear to have been posted or acknowledged. On 13 Jun. 1996, Noam Elkies claimed that the construction of period 6n oscillators greater than p100 had already been achieved using this traffic light push, but on 6 Aug. 1999 Dean Hickerson did not seem to know about the extra traffic light-based turner when trying to build a traffic jam oscillator with p7 components. Noam Elkies posted the p7 extra traffic light-based corner later that day. It is not clear to me whether Elkies knew about this technique in 1994, or if he realized it was necessary for the p6 traffic jam corner.

13 Jun. 1996:
- Noam Elkies finds a simplified p6 push:
  Code: Select all
```
x = 32, y = 24, rule = B3/S23
b2o25b2o$b2o25bo2bo2$bo$obo25bob2o$o2bo2b2o15b2o2bobo$4bob2o15bo4bo$2b
2o23bo$24bo2bo2$10bobo$9bo2bo6bobo$10bobo6bo2bo$19bobo2$4bo2bo$4bo23b
2o$3bo4bo15b2obo$2bobo2b2o15b2o2bo2bo$2obo25bobo$30bo2$o2bo25b2o$2b2o
25b2o!
```
  This allows a standard traffic jam corner (without extra traffic lights) to be built, and unambiguously showed that oscillators of all periods greater than 100 that are a multiple of 6 could be built.

Re: First Known Oscillators for Each Period

Posted: July 13th, 2021, 7:24 am

by Sokwe

On August 23, 1992, Dean Hickerson wrote:

Due mostly to the work of Buckingham and Wainwright, we now have
nontrivial examples (i.e. not just lcms of smaller period oscillators
acting almost independently) of oscillators of periods 1-16, 18, 26,
28, 29, 30, 32, 36, 40, 44, 46, 47, 52, 54, 55, 56, 60, 72, 100, 108,
128, 75+120n, 135+120n, 66+24n, 246+24n, 50+40n, 230+40n, 136+8n,
150+5n, and all multiples of 30, 44, 46, 94, and 100. We also have
an argument, based on construction universality, which implies that
all sufficiently large periods are possible. (No doubt you figured
that out for yourself long ago.)

The multiples of 30, 44, 46, 94, and 100 and the 75+120n and 135+120n
are based on gliders shuttling back and forth between either
oscillators (of periods 15, 30, 46, and 100) or output streams of
glider guns (of periods 30, 44, 46, 94, and 900+200n). The 66+24n,
246+24n, 50+40n, and 230+40n use a device discovered by Wainwright,
which reflects a symmetric pair of parallel gliders; it consists of
a still life ("eater3") and 2 spark producing oscillators, of periods
5 or 6. (Any larger nonmultiple of 4 would also work, but 5 and 6 are
the only ones we know with the right sparks.) Periods 136+8n and
150+5n use a mechanism developed by Buckingham, in which a B heptomino
is forced to turn a 90 degree corner. The turn can take either 64, 65,
or 73 generations; by combining them we can build a closed loop whose
length is any large multiple of 5 or 8; we put several copies of the B
in the track to reduce the period to one of those mentioned. For
example, I built a p155 oscillator in which 20 Bs travel around a track
of length 3100 (= 20*64 + 28*65) generations. For the multiples of 8,
the 73 gen turn can emit a glider, so we also get glider guns of those
periods.

This is probably a good starting point for determining the first known oscillators of each period. Note that Hickerson describes LCM oscillators as "trivial", but we would now consider them to be nontrivial.

The period 136+8n series mentioned above was completed by Dave Buckingham sometime in 1991 and is mentioned in this article.

The p150+5n series was completed by Dean Hickerson on April 20, 1992. The key discoveries that made this series possible were the toaster and middleweight volcano which were found earlier that month. Here is the p155 oscillator:

Code: Select all

#N p155 oscillator
#C 20 B heptominos travel around a track of length 3100 gens,
#C consisting of 20 64 gen turns and 28 65 gen turns.  The turns
#C use the p5 oscillators "toaster" and "middleweight volcano" to
#C replace the p8 "Kok's galaxy" and "blocker" used in David
#C Buckingham's turns.  4 of the toasters are 2-slicers rather than
#C the usual 4-slicers, to avoid destroying nearby eaters.
#O Dean Hickerson,  4/20/92
x = 305, y = 197
149bo2bo$95b4o$37bo2b2o2b2o2bo24bo17bo2bo4bo2bo24bo17bo2bo4bo2bo24bo
17bo2b6o2bo24bo$37b4ob2ob4o22b3o17b4o4b4o22b3o17b4ob2ob4o22b3o17b4ob2o
b4o22b3o$70bo53bo24bo2bo25bo25b2o26bo$39b3o2b3o23b2o21b3o2b3o23b2o21b
3o2b3o23b2o21b3o2b3o23b2o$38bo2bo2bo2bo27b2o15bo2bo2bo2bo27b2o15bo8bo
27b2o15bo2bo2bo2bo27b2o$38b2o6b2o27bo16b4o2b4o27bo16b2obo2bob2o27bo16b
3o4b3o27bo$41bo2bo28bobo19bo2bo28bobo51bobo19bo2bo28bobo$38b4o2b4o25b
2o17b4o2b4o25b2o17b4o2b4o11b2o3b3o6b2o17b4o2b4o25b2o$37bo10bo29bo2b2o
8bo10bo10bo18bo2b2o8bo3bo2bo3bo9bo7b2o10bo2b2o8bo4b2o4bo29bo2b2o$38b3o
b2ob3o29bobo2bo9b3o4b3o9bo19bobo2bo9b3ob2ob3o29bobo2bo9b3ob2ob3o29bobo
2bo$40b2o2b2o4b2o25bobobo12bo4bo4b2o5b2o18bobobo12bo4bo4b2o6b2o7bo9bob
obo12b6o4b2o25bobobo$50b2o24b2obob2o12b4o5b2o14bo9b2obob2o21b2o8b2o5bo
8b2obob2o21b2o24b2obob2o$76bo2bo3bo31b3o3b2o6bo3bo3bo11bo2bo14b2obo3bo
7bo3b2o3bo46bo2bo3bo$34b2o41bo2b3obo3b2o27bo4bo6bo4bobobo3b2o22bo4b3o
11b2o2b2obo3b2o40b3o2b2obo$35bo40bo2b2o3bo4bo25b2o2bo2bo6bo3b2o3bo4bo
23b2o12bo3bobo2bobo4bo40b4o4bo$35bobo10b2o27bo2b4o5bobo29bo7bo4bob2o5b
obo39b2o2b3o5bobo10b2o26b3o2b3o$36b2o9bo2bo25bo2bo10b2o28bo8bo3bo10b2o
36bo3b2o10b2o9bo2bo25bo2bo$47bo2bo25b2obob5o12b2o30b2obob5o44b2obob5o
15bo2b2o24b2obob5o$46b2ob2o26bobo2bo2bo12b2o6bo24bobo2bo2bo45bobo2bo2b
o14bo2b2o26bobo2bo2bo$39b2o6b2o28bo2bo12b2o11bobo22bo2bo50bo2bo12b2o5b
4o27bo2bo$39b2o37b2o13b2o11b2o24b2o52b2o13b2o37b2o2$56b2o52b2o52b2o52b
2o$56b2o52b2o40bo11b2o52b2o$151bo$151bo23b3o$175bo$19b2o26b2o25b2o25b
2o73bo32b2o25b2o$15b2o2bo14b2o11b2o25b2o25b2o45bo60b2o25b2o$14bo2bobo
14b2o111b3o30b2o$10b2obob3ob2o126b3o27b3obo$10bob2obobobo157bo2b2o$21b
o61b2o41b2ob2o6b2o8b4o27b3o10b2o52b2o14bo$11b4obob3obo60b2o42bobo7b2o
7b5o28bo11b2o52b2o12b3o$10bo3b2ob2o3bo105bo17b2obo108bo$11b3ob3ob3o12b
obo29b2o37b2o13b2o37b2o35bo16b2o13b2o28b2o6bo6b2o$6bo6bo5bo14b2o20bo9b
2o15bo20bo2bo12b2o36bo2bo34bobo13bo2bo12b2o14b2ob2o16bobob2o2bo$6b3o
20b2o4bo13bo5bobo13b2o9b6o16bobo2bo2bo12b2o31bobo2bo2bo29b2o14bobo2bo
2bo12b2o9bo4b2o14bobobobobo$9bo4bo3bo10b2o17bobob2o2bobo12b2o8bo2b2ob
2o14b2obob5o12b2o30b2obob5o44b2obob5o12b2o7b2o20b2obobobob2o$2b2o4b2o
6bo31bobobob2o2bo4b2o15b2obo3b2o14bo2bo10b2o37bo2b2o10b2o38bo2bo10b2o
15b2obo4bo12bo3b5o3bo$3bo35b2o6b2obo4bobo4bobo16bob4o16b3o2b3o5bobo28b
o7b3o3b2obo5bobo39bo2b4o5bobo15b2obo2b2o13bo11bo$3bobo33b2o6bo2b2ob2o
2b2o3bo21b2o17b4o4bo4bo28b3o7b3o2b2obobo4bo21b2o17bo2b2o3bo4bo20bo2bo
14bo11bo$4b2o42bo5bobo4b2o40b3o2b2obo3b2o27b2o9b3o3b2o2bo3b2o20b2o19bo
2b3obo3b2o38bo3b5o3bo$48bo5bobo46bo2bo3bo12b2o19b2o10bo2b2o3bo26bo19bo
2bo3bo45b2obobobob2o$47bo2b2ob2o2b2o18b2o24b2obob2o12b4o5b2o14bo3b2o4b
2obob2o21b2o24b2obob2o12b4o31bobobobobo$37b2o8b2obo4bobo9b6o4b2o25bobo
bo12bob2obo4b2o5b5o3bo4b2o5bobobo12b2o2b2o4b2o25bobobo12bo4bo30bobob2o
2bo$37b2o9bobobob2o2bo6b3ob2ob3o29bobo2bo9b3o4b3o9b4o4bo11bobo2bo9b3ob
2ob3o29bobo2bo9b3o4b3o29bo6b2o$48bobob2o2bobo5bo4b2o4bo29bo2b2o8bo3bo
2bo3bo11b2o16bo2b2o8bo10bo29bo2b2o8bo10bo$41b2o6bo5bobo7b4o2b4o25b2o
17b4o2b4o14b2o3b2o4b2o17b4o2b4o25b2o17b4o2b4o26b2o$41bo14bo11bo2bo28bo
bo20b2o23b2o4bobo19bo2bo28bobo19bo2bo29b2o$14b3o25b3o20b3o4b3o27bo16b
2ob4ob2o27bo16b2o6b2o27bo16b4o2b4o$14bo2bo26bo20bo2bo2bo2bo27b2o15bo3b
2o3bo27b2o15bo2bo2bo2bo27b2o15bo2bo2bo2bo$13bo2b2o48b3o2b3o23b2o21b3o
2b3o23b2o21b3o2b3o23b2o21b3o2b3o$13b2o54b2o26bo24bo2bo25bo53bo$39b2o
23b4ob2ob4o22b3o17b4o4b4o22b3o17b4ob2ob4o22b3o17b4o4b4o13b2o$17bo6b2o
14bo2b2o19bo2b6o2bo24bo17bo2bob2obo2bo24bo17bo2b2o2b2o2bo24bo17bo2bo4b
o2bo13b2o11b2o$18b2o4b2o14bobo2bo76b4o104b4o30b2o$17b2o20b2o2bo2bob2o
73b2o$40bobobob2obo$38bo3b3o$37bob3obob4o224b2o14bo$12b2o23bo3bo3bo3bo
223b2o12b3o$12b2o24b3o5b3o237bo$40bob3obo6bo202b2o11b2o15b2o6bo6b2o$2b
2o6bo18b2o10b5o5b3o202b2o11bobo21bobob2o2bo$3bo2b2obobo17b2o11b3o5bo
210b2o6bo23bobobobobo$3bobobobobo38b2o4b2o203b2o29b2obobobob2o$2b2obo
3bob2o6b2o35bo196b2o28bo7bo3b5o3bo$o3b2obob2o3bo4b2o33bobo195bobo29bo
6bo11bo$3bo7bo42b2o196bo25b2o2bo2bo5bo11bo$3bo7bo239b2o27bo4bo5bo3b5o
3bo$o3b2obob2o3bo263b3o3b2o6b2obobobob2o$2b2obo3bob2o8b2o235b4o21bo9bo
bobobobo$3bobobobobo9b2o234bo4bo11b2o17bobob2o2bo$3bo2b2obobo243b3o4b
3o9bo19bo6b2o$2b2o6bo6b2o235bo10bo10bo$18bo236b4o2b4o26b2o$15b3o240bo
2bo29b2o$15bo239b4o2b4o$255bo2bo2bo2bo$256bob4obo$19b2o233bob2o4b2obo$
15b2o2bo14b2o217bobo3b2o3bobo12b2o8b2o$14bo2bobo14b2o3b3o212bo2b2o2b2o
2bo13b2o$10b2obobobob2o17bo3bo212b2obo2bob2o$10bob2o5bo$15b3o3bo21bo$
11b4obob3obo15b5o217bo$10bo11bo16bo6b2o212b3o$11b3o5b3o24b2o215bo$6bo
6bo5bo227b2o6bo6b2o$6b3o5b5o10b2o18bo6b2o190bo2b2obobo$9bo19b2o17bobob
2o2bo191bobobobobo9b2o$2b2o4b2o38bobobobobo190b2obo3bob2o8b2o$3bo35b2o
6b2obo3bob2o188bo2b2obob2o2bo$3bobo33b2o5bo2b2obob2o2bo186b3o3b3o3b3o$
4b2o39b3o3b3o3b3o185b3o3b3o3b3o39b2o$45b3o3b3o3b3o186bo2b2obob2o2bo5b
2o33bobo$46bo2b2obob2o2bo188b2obo3bob2o6b2o35bo$37b2o8b2obo3bob2o190bo
bobobobo38b2o4b2o$37b2o9bobobobobo191bo2b2obobo17b2o19bo$48bobob2o2bo
190b2o6bo18b2o10b5o5b3o$41b2o6bo6b2o227bo5bo6bo$41bo215b2o24b3o5b3o$
42b3o212b2o6bo16bo11bo$44bo217b5o15bob3obob4o$261bo21bo3b3o$285bo5b2ob
o$40b2obo2bob2o212bo3bo17b2obobobob2o$24b2o13bo2b2o2b2o2bo212b3o3b2o
14bobo2bo$14b2o8b2o12bobo3b2o3bobo217b2o14bo2b2o$39bob2o4b2obo233b2o$
41bob4obo$40bo2bo2bo2bo$40b4o2b4o239bo$12b2o29bo2bo240b3o$12b2o26b4o2b
4o236bo$28bo10bo10bo235b2o6bo6b2o$2b2o6bo19bo9b3o4b3o243bobob2o2bo$3bo
2b2obobo17b2o11bo4bo234b2o9bobobobobo$3bobobobobo9bo21b4o235b2o8b2obo
3bob2o$2b2obobobob2o6b2o3b3o263bo3b2obob2o3bo$bo3b5o3bo5bo4bo27b2o239b
o7bo$bo11bo5bo2bo2b2o25bo196b2o42bo7bo$bo11bo6bo29bobo195bobo33b2o4bo
3b2obob2o3bo$bo3b5o3bo7bo28b2o196bo35b2o6b2obo3bob2o$2b2obobobob2o29b
2o203b2o4b2o38bobobobobo$3bobobobobo23bo6b2o210bo5b3o11b2o17bobob2o2bo
$3bo2b2obobo21bobo11b2o202b3o5b5o10b2o18bo6b2o$2b2o6bo6b2o15b2o11b2o
202bo6bob3obo$18bo237b3o5b3o24b2o$15b3o12b2o223bo3bo3bo3bo23b2o$15bo
14b2o224b4obob3obo$260b3o3bo$255bob2obobobo$180b2o73b2obo2bo2b2o20b2o$
39b2o30b4o104b4o76bo2bobo14b2o4b2o$39b2o11b2o13bo2bo4bo2bo17bo24bo2b2o
2b2o2bo17bo24bo2bob2obo2bo17bo24bo2b6o2bo19b2o2bo14b2o6bo$52b2o13b4o4b
4o17b3o22b4ob2ob4o17b3o22b4o4b4o17b3o22b4ob2ob4o23b2o$99bo53bo25bo2bo
24bo26b2o54b2o$69b3o2b3o21b2o23b3o2b3o21b2o23b3o2b3o21b2o23b3o2b3o48b
2o2bo$68bo2bo2bo2bo15b2o27bo2bo2bo2bo15b2o27bo3b2o3bo15b2o27bo2bo2bo2b
o20bo26bo2bo$68b4o2b4o16bo27b2o6b2o16bo27b2ob4ob2o16bo27b3o4b3o20b3o
25b3o$40b2o29bo2bo19bobo28bo2bo19bobo4b2o23b2o20bobo28bo2bo11bo14bo$
40b2o26b4o2b4o17b2o25b4o2b4o17b2o4b2o3b2o14b4o2b4o17b2o25b4o2b4o7bobo
5bo6b2o$67bo10bo8b2o2bo29bo10bo8b2o2bo16b2o11bo3bo2bo3bo8b2o2bo29bo4b
2o4bo5bobo2b2obobo$30b2o6bo29b3o4b3o9bo2bobo29b3ob2ob3o9bo2bobo11bo4b
4o9b3o4b3o9bo2bobo29b3ob2ob3o6bo2b2obobobo9b2o$31bo2b2obobo30bo4bo12bo
bobo25b2o4b2o2b2o12bobobo5b2o4bo3b5o5b2o4bob2obo12bobobo25b2o4b6o9bobo
4bob2o8b2o$31bobobobobo31b4o12b2obob2o24b2o21b2obob2o4b2o3bo14b2o5b4o
12b2obob2o24b2o18b2o2b2ob2o2bo$30b2obobobob2o45bo3bo2bo19bo26bo3b2o2bo
10b2o19b2o12bo3bo2bo46bobo5bo$29bo3b5o3bo38b2o3bob3o2bo19b2o20b2o3bo2b
2o3b3o9b2o27b2o3bob2o2b3o40b2o4bobo5bo42b2o$29bo11bo14bo2bo20bo4bo3b2o
2bo17b2o21bo4bobob2o2b3o7b3o28bo4bo4b4o17b2o21bo3b2o2b2ob2o2bo6b2o33bo
bo$29bo11bo13b2o2bob2o15bobo5b4o2bo39bobo5bob2o3b3o7bo28bobo5b3o2b3o
16b4obo16bobo4bobo4bob2o6b2o35bo$29bo3b5o3bo12bo4bob2o15b2o10bo2bo38b
2o10b2o2bo37b2o10bo2bo14b2o3bob2o15b2o4bo2b2obobobo31bo6b2o4b2o$30b2ob
obobob2o20b2o7b2o12b5obob2o44b5obob2o30b2o12b5obob2o14b2ob2o2bo8b2o12b
obo2b2obobo17b2o10bo3bo4bo$31bobobobobo14b2o4bo9b2o12bo2bo2bobo14b2o
29bo2bo2bobo31b2o12bo2bo2bobo16b6o9b2o13bobo5bo13bo4b2o20b3o$31bo2b2ob
obo16b2ob2o14b2o12bo2bo13bobo34bo2bo36b2o12bo2bo20bo15b2o9bo20b2o14bo
5bo6bo$30b2o6bo6b2o28b2o13b2o16bo35b2o37b2o13b2o37b2o29bobo12b3ob3ob3o
$46bo108bob2o17bo105bo3b2ob2o3bo$43b3o12b2o52b2o11bo28b5o7b2o7bobo42b
2o60bob3obob4o$43bo14b2o52b2o10b3o27b4o8b2o6b2ob2o41b2o61bo$123b2o2bo
157bobobob2obo$123bob3o27b3o126b2ob3obob2o$123b2o30b3o111b2o14bobo2bo$
67b2o25b2o60bo45b2o25b2o25b2o11b2o14bo2b2o$67b2o25b2o32bo73b2o25b2o25b
2o26b2o$129bo$127b3o23bo$153bo$85b2o52b2o11bo40b2o52b2o$85b2o52b2o52b
2o52b2o2$63b2o37b2o13b2o52b2o24b2o11b2o13b2o37b2o$62bo2bo27b4o5b2o12bo
2bo50bo2bo22bobo11b2o12bo2bo28b2o6b2o$57bo2bo2bobo26b2o2bo14bo2bo2bobo
45bo2bo2bobo24bo6b2o12bo2bo2bobo26b2ob2o$57b5obob2o24b2o2bo15b5obob2o
44b5obob2o30b2o12b5obob2o25bo2bo$63bo2bo25bo2bo9b2o10b2o3bo36b2o10bo3b
o8bo28b2o10bo2bo25bo2bo9b2o$59b3o2b3o26b2o10bobo5b3o2b2o39bobo5b2obo4b
o7bo29bobo5b4o2bo27b2o10bobo$58bo4b4o40bo4bobo2bobo3bo12b2o23bo4bo3b2o
3bo6bo2bo2b2o25bo4bo3b2o2bo40bo$58bob2o2b3o40b2o3bob2o2b2o11b3o4bo22b
2o3bobobo4bo6bo4bo27b2o3bob3o2bo41b2o$59bo3bo2bo46bo3b2o3bo7bo3bob2o
14bo2bo11bo3bo3bo6b2o3b3o31bo3bo2bo$60b2obob2o24b2o21b2obob2o8bo5b2o8b
2o21b2obob2o9bo14b2o5b4o12b2obob2o24b2o$61bobobo25b2o4b6o12bobobo9bo7b
2o6b2o4bo4bo12bobobo18b2o5b2o4bo4bo12bobobo25b2o4b2o2b2o$60bo2bobo29b
3ob2ob3o9bo2bobo29b3ob2ob3o9bo2bobo19bo9b3o4b3o9bo2bobo29b3ob2ob3o$60b
2o2bo29bo4b2o4bo8b2o2bo10b2o7bo9bo3bo2bo3bo8b2o2bo18bo10bo10bo8b2o2bo
29bo10bo$68b2o25b4o2b4o17b2o6b3o3b2o11b4o2b4o17b2o25b4o2b4o17b2o25b4o
2b4o$67bobo28bo2bo19bobo51bobo28bo2bo19bobo28bo2bo$67bo27b3o4b3o16bo
27b2obo2bob2o16bo27b4o2b4o16bo27b2o6b2o$66b2o27bo2bo2bo2bo15b2o27bo8bo
15b2o27bo2bo2bo2bo15b2o27bo2bo2bo2bo$71b2o23b3o2b3o21b2o23b3o2b3o21b2o
23b3o2b3o21b2o23b3o2b3o$72bo26b2o25bo25bo2bo24bo53bo$69b3o22b4ob2ob4o
17b3o22b4ob2ob4o17b3o22b4o4b4o17b3o22b4ob2ob4o$69bo24bo2b6o2bo17bo24bo
2bo4bo2bo17bo24bo2bo4bo2bo17bo24bo2b2o2b2o2bo$206b4o$152bo2bo!

Edit: the following is a (possibly incomplete) list of periods above 60 for which nontrivial oscillators were known prior to July 1996:

66, 72, 75, 87, 105, 203, 329
80 + 4n
120 + 5n
84 + 6n
80 + 10n
92 + 46n
94 + 94n

where n is a nonnegative integer.

The following is discovery information for the first known nontrivial oscillator of certain periods. Some series include periods that were found earlier (e.g., p90 was known before the discovery of the p66 + 24n series).

66 + 24n: Robert Wainwright, Sep 1984 (see p42 glider shuttle)
72: Robert Wainwright, Jul 1990 (Two blockers hassling R-pentomino)
75 + 120n: Robert Wainwright, Sep 1984 (6 bits)
80: Dean Hickerson, 28 Oct 1994 (LCM: Achim's other p16 on middleweight volcano)
84: No later than 31 Jul 1994 (LCM: caterer on p28 pre-pulsar shuttle variant supported by molds that Bill Gosper attributes to Dean Hickerson)
87: Bill Gosper, 24 Sep 1994 (LCM: p29 pentadecathlon hassler on caterer)
88 + 44n: David Buckingham, 2 Apr 1992 (glider loop or period-doubled p44 gun)
90 + 30n: Bill Gosper, 1970-1971 (glider loop or period-tripled p30 gun)
92 + 46n: Bill Gosper, 1971 (glider loop or period-doubled p46 gun)
94n: Dean Hickerson, 25 Jun 1990 (capped P94S and related glider loops)
96: Noam Elkies, 28 Jan 1995 (p96 Hans Leo hassler)
100n: Bill Gosper, no earlier than 1973 and no later than 1987 (Centinal and resulting glider loops using centinals as reflectors)
100 + 4n and 100 + 10n: Bill Gosper, 17 Oct 1994 (traffic jam oscillators)
102 + 18n: Dean Hickerson, 19 Oct 1994 (traffic jam oscillators)
102 + 6n: Noam Elkies, no earlier than 22 Nov 1994 and no later than 13 Jun 1996 (traffic jam oscillators)
105: (LCM: pentadecathlon on 44P7.2)
124: Dean Hickerson, 31 Jul 1994 (variant of p124 Lumps of Muck Hassler)
125: Noam Elkies, 11 Jan 1996 (glider loop using p25 reflector)
128 and 256: David Buckingham, 1991 (spark-assisted Herschel track: see period-256 glider gun)
135 + 120n: Bill Gosper, 1989 (glider shuttle with rephasers)
136 + 8n: David Buckingham, 1991 (spark-assisted Herschel tracks)
144 + 72n: David Buckingham, 1990 (capped gunstar)
150 + 5n: Dean Hickerson, 20 Apr 1992 (spark-assisted Herschel tracks)
203: (LCM: 44P7.2 on p29 pre-pulsar shuttle variant with blinkers)
329: (LCM: 44P7.2 on p47 pre-pulsar shuttle)
856n: David Buckingham, 1991 (capped period-856 glider gun and related glider loops)

The following is the timeline of oscillator period discoveries using Buckingham's stable Herschel conduits:

5 Jul 1996: All periods 153 and above (using R64, L112, and F117) and all periods 64 and above that are not multiples of 3 or 13 (using just L112 and F117)
7 Jul 1996: All periods 107 and above (using L112, F117, and R190)
3 Aug 1996: All periods 61 and above (using L112, F117, and Fx77)

Re: First Known Oscillators for Each Period

Posted: June 2nd, 2022, 10:08 am

by Sokwe

This is my best attempt to determine the first known nontrivial oscillator of each period in Life. For periods below 61, see the oscillator page on the wiki.

The following is a list of periods 60 and above discovered before 5 Jul 1996 (i.e., before Buckingham found any extensible stable Herschel tracks) in roughly chronological order (n is any nonnegative integer):

240+240n: no later than 6 Dec 1970 (Conway's proof of universality, claimed in a message to Gardner on 6 Dec 1970 [see Genius at Play], used p240 glider logic, as noted by V. Everett Boyer in Lifeline Volume 11)
60 + 120n: no later than Feb 1971 (see p60 glider shuttle, mentioned in Martin Gardner's Feb 1971 column)
92 + 46n: Bill Gosper, 1971 no later than September (glider loops mentioned on page 14 of Lifeline Volume 3)

60 + 30n: no later than Sep 1973 (glider loops mentioned on page 11 of Lifeline Volume 11 in a segment written by V. Everett Boyer; I've copied the glider reflector below)

Code: Select all

x = 45, y = 20, rule = B3/S23
25b2o$23bo2bo$10bobo9bo7b5o$10bo3bo7bo6bo5bo$14bo7bo7b2o3bo$2o8bo4bo7b
o2bo7bo$2o12bo10b2o$10bo3bo16b2o$10bobo8bobo5bo3bo$22b2o4bo5bo$22bo4b
2obo3bo8b2o$28bo5bo8b2o$29bo3bo$19bo11b2o$19b2o$18bobo2$26bobo$27b2o$
27bo!

216: possible to build as early as 1976 (LCM: p54 shuttle on figure eight)
105: no earlier than 19 Jun 1977 and no later than 11 May 1992 (LCM: 44P7.2 on pentadecathlon; not clear when the spark interaction was first recognized; Dean Hickerson noted its existence in an email on 11 May 1992)
108: no earlier than Jun 1980 and no later than 11 May 1992 (LCM: p54 shuttle on middleweight emulator; Dean Hickerson noted its existence in an email on 11 May 1992). p108 toad hasslers were also possible as early as June 1984 (using the p54 shuttle) as noted by David Buckingham in an email on 12 May 1992.
232: possible to build as early as 2 Aug 1980 (LCM: figure eight on p29 pre-pulsar shuttle)
329: no earlier than 5 Dec 1982 and no later than 18 May 1992 (LCM: 44P7.2 on p47 pre-pulsar shuttle; Dean Hickerson noted its existence in an email on 18 May 1992)
376: possible to build as early as 5 Dec 1982 (LCM: figure eight on p47 pre-pulsar shuttle; Bill Gosper noted its existence in an email on 18 May 1992, but by then oscillators of this period were possible using the p94 gun)
66 + 24n: Robert Wainwright, Sep 1984 (see p42 glider shuttle)
75 + 120n: Robert Wainwright, Sep 1984 (6 bits)
100+100n: Bill Gosper, no later than Sep 1987 (centinal; an email from Bill Gosper on 20 Sep 2007 claims that the first p1100 gun, which uses centinals, was constructed "ca. 1984"; the Sep 1987 date comes from Dean Hickerson's stamp collection)

165 + 120n: Robert Wainwright, no later than 1989:

Code: Select all

x = 75, y = 64, rule = B3/S23
17bo$16bobo$15bo3bo$15bo3bo$15bo3bo$15bo3bo$15bo3bo$15bo3bo$16bobo$17b
o7$2b2o6b2o$o4bo2bo4bo$o4bo2bo4bo$o4bo2bo4bo$2b2o6b2o$32bo2b2o4b2o2bo$
31bo3b3o2b3o3bo$32bo2b2o4b2o2bo7$38b2o$36bobobo$34bobobo$35b2o7$29bo2b
2o4b2o2bo$28bo3b3o2b3o3bo$29bo2b2o4b2o2bo$63b2o6b2o$61bo4bo2bo4bo$61bo
4bo2bo4bo$61bo4bo2bo4bo$63b2o6b2o7$57bo$56bobo$55bo3bo$55bo3bo$55bo3bo
$55bo3bo$55bo3bo$55bo3bo$56bobo$57bo!

135 + 120n: Bill Gosper, 1989 (106P135)
145: possible to build as early as 3 Sep 1989 (LCM: fumarole on p29 pre-pulsar shuttle). First acknowledged (only implicitly) on 26 Sep 1994 after the discovery of the p29 pentadecathlon hassler.

270 + 24n: Dean Hickerson, Nov 1989 ("pinball"; reorienting the unices allows this to work at p246 as well, but this wasn't noticed until Apr 1992):

Code: Select all

x = 68, y = 54, rule = B3/S23
22b2o20b2o$9bo11b4o18b4o11bo$8bobo9bo2bobo16bobo2bo9bobo$9bo9bobo2b2o
16b2o2bobo9bo$18bobo26bobo$7b5o5b2o30b2o5b5o$6bo4bo5b3o28b3o5bo4bo$5bo
2bo9bobo26bobo9bo2bo$2bo2bob2o10b2o26b2o10b2obo2bo$bobobo5bo44bo5bobob
o$2bo2bo4bobo42bobo4bo2bo$5b2o2bo2bo42bo2bo2b2o$10b2o44b2o5$5b2o54b2o$
4b4o52b4o$3bo2bobo24b2o24bobo2bo$2bobo2b2o24b2o24b2o2bobo$bobo60bobo$
2o64b2o$3o62b3o$bobo27bo4bo27bobo$2b2o28bo2bo28b2o$30b3o2b3o3$9b2o46b
2o$9b2o15bo6b2o6bo15b2o$24bobo6b2o6bobo$9bo15b2o14b2o15bo$8bobo46bobo$
8bo2bo2b2o36b2o2bo2bo$12bob2o36b2obo$10b2o44b2o5$33b2o$17b2o14b2o14b2o
$12b2o2bo2bo28bo2bo2b2o$9bo2bo4bobo28bobo4bo2bo$8bobobo5bo30bo5bobobo$
9bo2bob2o10b2o12b2o10b2obo2bo$12bo2bo10b2o12b2o10bo2bo$13bo4bo30bo4bo$
14b5o7bo14bo7b5o$25bobo12bobo$16bo8bo2bo2b2o2b2o2bo2bo8bo$15bobo11bob
2o2b2obo11bobo$16bo10b2o10b2o10bo!

94 + 94n: Dean Hickerson, 25 Jun 1990 (capped P94S and resulting glider loops)
72: Robert Wainwright, Jul 1990 (Two blockers hassling R-pentomino)
144 + 72n: David Buckingham, 1990 no earlier than Jul (capped gunstar)
856 + 856n: David Buckingham, 1991 no later than Oct (period-856 glider gun and resulting glider loops; this was found before the p136 + 8n series):

128 and 256: David Buckingham, 1991 no later than Oct (spark-assisted Herschel tracks):

Code: Select all

x = 153, y = 63, rule = B3/S23
38bo89bo$37bobo87bobo$36bo3bo85bo3bo$37bo3bo85bo3bo$38bo3bo85bo3bo$17b
ob2ob2o15bo3bo63bob2ob2o15bo3bo$16b2ob2o2b2o15bobo63b2ob2o2b2o15bobo$
16bo24bo64bo24bo$23b2o88b2o$16b2o5b2o81b2o5b2o$16b2o88b2o$24bo89bo$16b
2o2b2ob2o81b2o2b2ob2o$17b2ob2obo83b2ob2obo3$50bob2ob2o83bob2ob2o$49b2o
b2o2b2o81b2ob2o2b2o$13b2o34bo53b2o34bo$5bo6b3o10bob2o27b2o37bo6b3o10bo
b2o27b2o$4bobo6b2o10bo3bobo17b2o5b2o36bobo6b2o10bo3bobo17b2o5b2o$3bo3b
o6bo7b2o7bo17b2o42bo3bo6bo7b2o7bo17b2o$2bo3bo8b2o6bo5bobo25bo34bo3bo8b
2o6bo5bobo25bo$bo3bo10bo5bob2obo21b2o2b2ob2o33bo3bo10bo5bob2obo21b2o2b
2ob2o$o3bo45b2ob2obo33bo3bo45b2ob2obo$bobo87bobo$2bo89bo4$13b2o88b2o$
13b2o33b2o53b2o$48b2o4$60bo89bo$59bobo87bobo$6bob2ob2o45bo3bo33bob2ob
2o45bo3bo$5b2ob2o2b2o21bob2obo5bo10bo3bo33b2ob2o2b2o43bo3bo$5bo25bobo
5bo6b2o8bo3bo34bo50bo3bo$12b2o17bo7b2o7bo6bo3bo42b2o41bo3bo$5b2o5b2o
17bobo3bo10b2o6bobo36b2o5b2o42bobo$5b2o27b2obo10b3o6bo37b2o50bo$13bo
34b2o53bo$5b2o2b2ob2o81b2o2b2ob2o$6b2ob2obo83b2ob2obo3$39bob2ob2o83bob
2ob2o$38b2ob2o2b2o81b2ob2o2b2o$38bo89bo$45b2o88b2o$38b2o5b2o81b2o5b2o$
38b2o88b2o$21bo24bo64bo24bo$20bobo15b2o2b2ob2o63bobo15b2o2b2ob2o$19bo
3bo15b2ob2obo63bo3bo15b2ob2obo$20bo3bo85bo3bo$21bo3bo85bo3bo$22bo3bo
85bo3bo$23bobo87bobo$24bo89bo!

136, 150 +3n, 152 + 4n: David Buckingham, 1991 no later than Oct (spark-assisted Herschel tracks; Buckingham seems to claim, possibly incorrectly, that 150 + 5n is achievable at this time)
The p150 + 3n and p152 + 4n oscillators can be built using the following tracks:

Code: Select all

x = 105, y = 78, rule = B3/S23
12b2o3b2o63b2o3b2o$12b2o4bo63b2o4bo$18b3o67b3o8$33bo62b3o$23b3obo3b3o
62b3o$26bobo3bobo59b2o2b3o$27b3o3bob3o56b2o$27bo66b3o$5bo69bo20bo$5bob
o67bobo18bo$5b3o67b3o$7bo69bo2$19b2o68b2o$19bo69bo$20b3o67b3o$22bo69bo
27$23bo69bo$21b3o67b3o$20bo69bo$20b2o68b2o$25b2o68b2o$25bo69bo$23bobo
67bobo$23b2o68b2o2$103b2o$2o68b2o30bobo$2o24bo43b2o28b3o$25b2o72bo3bo$
95b5o2b2o$23b3o2bo65b3ob2o$5bo19bobobo45bo19b5o2b2o$5bobo18bo2bo45bobo
21bo3bo$5b3o19b2o46b3o22b3o$7bo69bo24bobo$103b2o6$17b3o67b3o$17bo69bo$
16b2o68b2o!

Here is the p136:

Code: Select all

#C 12-barrelled p136 glider gun
#C
#C A 12-barrelled, period 136 glider gun, using 29 B-heptominoes moving
#C around a p3944 track consisting of 16 of David Buckingham's 64 gen
#C turns and 40 of his 73 gen turns.  This is the smallest possible
#C period that can be obtained using Buckingham's turns.  Any larger
#C multiple of 8 can also be obtained as a gun period.
x = 277, y = 309, rule = B3/S23
75bo61bo$75b3o59b3o$78bo61bo$77b2o29bo30b2o$72b2o33b3o24b2o$73bo32bob
3o24bo$73bobo29bo3bo25bobo$74b2o28bo3bo27b2o26bo3bo$103b3obo55bo3b2o2b
2o$104b3o56bo7bo$97b2o6bo53b2o3b4o$97bo61bo2$72b2o61bo$72bo61b2o2$135b
o$73b2o59bobo$71bobo59bo2bo$71bo60bo2bo$71bo13b2o59b2o$71bo2bo10bo49bo
10bo41b2o$58b4o10b2o60b2o51bo2bo$53b2o7bo79bo44bo$53bo3b2o3bo17bo60b4o
42bo$57bo3bo16b2ob2o58b4o28b3o11bob2o$78b3ob2o27b3o58bo16bo$79b5o26bo
3bo57bo2bo$80b3o26bo31b4o28b2o$81bo60b3o28b2o13b2o$109bo3b2o28bo28bo2b
o12bo$110b3o62bo$172b2o$103b2o$102bobo11b2o$101b3o12bo$101b2o$104b2o$
103b3o$165b2o32b2o$40b2o153b2obo2bob2o$39bo2bo60b2o59bo3bo15b2o9bo4bo
2bo$39bo63bo59bo4bo15bo14bo$39bo122bobobo31bo$39bob2o85b2o31bobobo$41b
o17b2o13bo53bo6b3o21bo4bo$59bo13bobo58bo24bo3bo$72bo3bo57bo3bo$40b2o
31bo3bo27b2o27bo2bobo21b2o$40bo33bo3bo25bobo29bobo2bo$75bo3bo24bo32bo
3bo$76bobo24b2o36bo$42b2o33bo30b2o28b3o$42bo7bo58bo110b2o$46bo3bo55b3o
112bo$47bo2bo55bo$47b2ob2o150b2o14bo2bo$48bobo150bobo15bo2bo$49bo151bo
18bobo$201bobo17bo$204bo$202bobo15b2o$204bo15bo$138bo66bo$136b3o$104b
2o29bo$135b2o$102bo3bo33b2o$102bo4bo32bo$104bobobo29bobo$105bobobo28b
2o$106bo4bo120b4o$34b2o46bo24bo3bo115b2o7bo$33bobo44bob2o31b2o80bo18b
2o9bo3b2o3bo$33bo45bo28b2o5bo79bob2o17bo14bo3bo$32b2o4b2o8bo33bo111bo$
39bo9bo9b2o17b2obo58b2o55bo$36b3o6bo4bo2b2o4bo19bo60b2o51b2obo$36bo8b
2obo2bobo79bo6b2o52bo$49b2o82bo6bo$125b2o5b3o4bobo$125bo7b2o4bob2o$71b
o58b2o$68bo2bo57bo2bo$70b3o67b2o92bo$70b3o60b2o5bo92b3o16b2o$69bo2bo
58bo2bo97b2o2bo15bo$69bobo59b3o99b2obo$56bo12b3o158b2ob2o$55b2o174bo5b
o14bo$231bo4bo14b2obo$55bo176bo2bo18bo$54bobo176bo20bo$54bo2bo43bo149b
o2bo$55bo2bo41b3o149b2o$100bo2bo$55bo46b2o5b2o$55b2o45bo6bo$95b2o2b2o$
95bo3b4o$100bo2bo6b2o$101bo6bobo$108bo$108bo66b3o77b4o$108bo2bo66bo50b
o24bo7b2o8bo$109b2o63bo3bo49bobo23bo3b2o2bo7b3o$173bobo2bo48bo3bo23bo
2bo10bo$78bo5b2o53bo26b2o3bo2bobo49bo3bo38b2o4b2o$77bo6bo54b2o12b2o11b
o4bo3bo49bo3bo45bo$73bo2bo4bo56b2obo11bo17bo52bo3bo44bobo$72b2obo2bob
2o55bo2b3o29b3o50bobo45b2o$76b2o29b2o27bobobo85bo$107bobo25bobobo22b2o
bo$109bo23b3o2bo23bo2bo$109b2o23bob2o25b3o$104b2o29b2o125b3o$104bo31bo
125bo2bo$105b3o153bo3bo$107bo158bo$262b3ob2o$266bo$261bo3b2o$265bo4$
75bo$75b3o$78bo29bo$77b2o29b2o155b2o$72b2o33b2obo154bo$73bo32bo2b3o83b
o$73bobo29bobobo84b3o$74b2o28bobobo84b2obo43b2o$102b3o2bo132b3o$103bob
2o101bo16bo8b2o2bo2bobo24bo$97b2o5b2o90bob2o7bobo15b3o6bo3b2o2b2o23b3o
$88b2o7bo7bo90bo9bo3bo17bo9b2o26b3obo$86b2obo109bo5bo3bo11b2o4b2o38bo
3bo$73bo12bo108bo3bo4bo3bo13bo45bo3bo$72b2o12bobo82bo13b2o8bo2bo4bo3bo
14bobo44bob3o$87b2o81b3o12bo9b3o6bobo16b2o45b3o$73bo95bob3o31bo65bo$
72bobo93bo3bo$71bo2bo92bo3bo$70bo2bo92b3obo63bo$167b3o63b3o$59bo13bo
94bo33b2o28bo2b2o$58bo13b2o128bo28b2o$54bo2bo4bo167b2ob3o$53b2obo2bob
2o167b2o2bo$57b2o174b3o$231b2o$231b2o7$231b2o$140bo90bo2$138b3obo32b3o
$137bob2o33bo2bo79bo$103b2o32b2obo36bo80bo$40b2o15bo61b2o14bob3o33bo
54b3o23bo4bo2b2o8bo$41bo14b2o44bo3bo14b2o39b3o8bo2bo33b2o19bo22b2obo2b
obo7b3o$55b2o44bo4bo9bo5bo14bo24b3o8b3o34bobo14bo3bo26b2o9bo$38bo2bo
14bo2bo40bobobo17bo39b3o7b2o38bo13bobo2bo37b2o4b2o$39bo2bo14b2o40bobob
o9b3obo47b3o5b2obo29b2o4b2o10bo2bobo45bo$40bobo30b3o21bo4bo10bo2bobo
46b3o6b3o8b2o9bo9bo17bo3bo44bobo$41bo30bo24bo3bo11b2obobob2o43b3o7bo9b
o5b3ob2o2b2o6b3o14bo48b2o$72bo3bo114b4o4bo9bo15b3o$40b2o30bo2bobo21b2o
14b3o77b2o$40bo33bobo2bo$75bo3bo182b3o$79bo181bo2bo$76b3o182b2o2b2o$
261bo5bo$26b4o232b3o$21b2o7bo235b2o$21bo3b2o3bo231b3o2bo$25bo3bo233bo
2bo$265b2o$41b2o$41bo5$135b2o93b2o33b2o$135bo129bo$228bo3bo$25b2o3bo
197bo4bo$25b2o2b2o103b3o93bobobo32b2o$24b2o6bo101b2o11bo83bobobo30bo2b
o$25bo7bo103b2o8bo84bo4bo28bo$8b2o15b2ob2ob2o103b3o6bo87bo3bo28bo$7bo
2bo14b2o3bo104bobo6b3o3bo115bob2o$7bo127b2o6bo3bob2o83b2o32bo$7bo136b
5o$7bob2o134b3o12b2o$9bo32bo110b2o5bo70bo35b2o$41bobo109bo14bo61bobo
34bo$40bo3bo122b2obo62bo$8b2o31bo3bo91b2o32bo56b3o2bo$8bo33bo3bo89bobo
29bo58b2o3b2o$43bo3bo88bo32bob2o55b2ob2o$44bobo88b2o34bo57b2ob2o$10b2o
33bo94b2o88bo2bo$10bo130bo88bo2bo$138b3o91b2o$138bo3$234b2o$234bo2$
251b4o$246b2o7bo$106bo139bo3b2o3bo$104b3o143bo3bo$20b2o50b2o29bo$20bo
82b2o$25b2ob2o40bo3bo33b2o89bo$25bo4b2o38bo4bo32bo89b2obo$23b2o47bobob
o29bobo93bo32b2o$23b2obo4bo41bobobo28b2o91bo36bo$23b2obo2b2o43bo4bo
120bob2o$2b2o22bo2bo20bo24bo3bo122bo30bo2bo$bobo44bob2o31b2o149bo2bo$b
o45bo28b2o5bo151bobo$2o4b2o8bo33bo150b2o33bo$7bo9bo28b2obo58b2o93bo$4b
3o6bo4bo2b2o24bo60b2o89bo3bo31b2o$4bo8b2obo2bobo65bo20b2o92b2o31bo$17b
2o68bobo18bo83b3o3bo2bo2b3o$90b2o15bobo81b2o3bo4b3o2bo$89bo17bob2o79b
2o2bobo2bo6bo$191bo5bo2b2o2b2o$192b2o2bo5b2o$108b2o86bo$108bo3$24bo$
23b2o$45b2o29b2o29b2o93b2o$23bo21bo30bo30bo94bo$22bobo195bo$22bo2bo
193bo$23bo2bo188bo2bo4bo$214b2obo2bob2o$23bo53b2o139b2o$23b2o52bo$167b
o$166bobo$59bo18b2o39bobo43bo3bo$57b3o16bobo42bo44bo3bo32b2o$57bobo16b
o38bo3bobo45bo3bo31bo$57bo18bo38bob2o24b3o22bo3bo$76bo2bo66bo22bobo$
77b2o63bo3bo23bo32bo$141bobo2bo55b2obo$46bo5b2o53bo31bo2bobo60bo$45bo
6bo54b2o30bo3bo61bo$41bo2bo4bo56b2obo29bo29b2o5bo25bo2bo$40b2obo2bob2o
55bo2b3o29b3o26bo6b3o24b2o$44b2o29b2o27bobobo66bo3bo$75bobo25bobobo64b
3o4bo$77bo23b3o2bo65b3obob2o$77b2o23bob2o66b2o3bo$72b2o29b2o$72bo31bo$
73b3o$75bo2$117b2o$118bo$139b2o29b2o$115bo2bo20bo30bo$116bo2bo$117bobo
63bo3bo$118bo63bo3b2o2b2o$182bo7bo$117b2o52b2o10b4o$117bo52bo2bo$173bo
$141bobo2b2o25bo$140bo3bob3o22bobo$141bo6b2o20b2o$142b5obo$138b2o4b4o$
138bo6bo25b2o$171bo2$146b2o$138b2o6bo$134b2obo2bob2o$134bo4bo2bo$138bo
30b2o$137bo31bobo$171bo$171b2o$166b2o$166bo$167b3o$169bo!

90 + 40n: Dean Hickerson, 19 Mar 1992 (see p50 glider shuttle; the original oscillator used an early version of toaster; the following, taken from an email from Dean Hickerson on 16 Sep 1992, might be that early toaster)
Code: Select all
```
x = 25, y = 12, rule = B3/S23
4b2o11b2o$3bo2bo10bobo3b2o$3bobo2b2o9b3o2bo$2b2ob3o2bo4b4o3b2o$o3bo3bo
bo4bo4bo$3bobob2o3bo3b5ob2o$3bobo3b8o2b3o2bo$o3bob3o8b2o4b2o$2b2obo2bo
2b2ob3o2bo$3bobobo3b2obo3b2o$3bo2bo$4b2o!
```

230 + 40n: Dean Hickerson, 19 Mar 1992 (as in the p50 + 40n case, the original oscillator used an early version of toaster):

Code: Select all

x = 68, y = 58, rule = B3/S23
26b2o12b2o$18b2o2b2o2bo14bo2b2o2b2o$18bo2bo2bobo14bobo2bo2bo$19b2ob3ob
2o12b2ob3ob2o$20bobobobo14bobobobo$13bo4bo9bo10bo9bo4bo$12bobo2bob3obo
b3obo8bob3obob3obo2bobo$13bo3bo3b2ob2o3bo8bo3b2ob2o3bo3bo$18b3ob3ob3o
10b3ob3ob3o$11b5o4bo5bo14bo5bo4b5o$10bo4bo36bo4bo$9bo2bo8bo3bo16bo3bo
8bo2bo$6bo2bob2o10bo20bo10b2obo2bo$5bobobo5bo36bo5bobobo$6bo2bo4bobo
34bobo4bo2bo$9b2o2bo2bo34bo2bo2b2o$14b2o36b2o$6b2o52b2o$b2o2bo2bo50bo
2bo2b2o$bobo2bobo24b2o24bobo2bobo$3b2obob2o23b2o23b2obob2o$2bo3b2o3bo
44bo3b2o3bo$bob2o2b2o50b2o2b2obo$bobo2bobo3bo42bo3bobo2bobo$2b3o2b2o
50b2o2b3o$6b2o3bo18bobo2bobo18bo3b2o$5obob2o21b2o2b2o21b2obob5o$o2bo2b
obo22bo4bo22bobo2bo2bo$5b2obo2bo44bo2bob2o$6bobobobo42bobobobo$4bo3bob
obo12bo7b2o7bo12bobobo3bo$4b5obob2o12b2o5b2o5b2o12b2obob5o$10b2o3bo9b
2o14b2o9bo3b2o$6b3o2b2o42b2o2b3o$5bobo2bobo3bo34bo3bobo2bobo$5bob2o2b
2o42b2o2b2obo$6bo3b2o3bo36bo3b2o3bo$7b2obob2o40b2obob2o$5bobo2bobo42bo
bo2bobo$5b2o2bo2bo42bo2bo2b2o$10b2o44b2o$18b2o13b2o13b2o$13b2o2bo2bo
12b2o12bo2bo2b2o$10bo2bo4bobo26bobo4bo2bo$9bobobo5bo28bo5bobobo$10bo2b
ob2o10bo12bo10b2obo2bo$13bo2bo8bo3bo3b2o3bo3bo8bo2bo$14bo4bo13b2o13bo
4bo$15b5o4bo5bo6bo5bo4b5o$22b3ob3ob8ob3ob3o$17bo3bo3b2ob2o8b2ob2o3bo3b
o$16bobo2bob3obob4o2b4obob3obo2bobo$17bo4bo9bo2bo9bo4bo$24bobobobo6bob
obobo$23b2ob3ob2o4b2ob3ob2o$24bobo2bo2bo2bo2bo2bobo$24bo2b2o2b2o2b2o2b
2o2bo$23b2o18b2o!

246: Dean Hickerson, Apr 1992 (this is actually part of the p270 + 24n series from Nov 1989, but the p246 form wasn't noticed until Apr 1992):

Code: Select all

x = 60, y = 51, rule = B3/S23
10bo11bo14bo11bo$9bobo9bob4o6b4obo9bobo$10bo9bobob3o6b3obobo9bo$19bobo
16bobo$8b5o7bo18bo7b5o$7bo4bo7b2o16b2o7bo4bo$6bo2bo10b2o16b2o10bo2bo$
3bo2bob2o10b2o16b2o10b2obo2bo$2bobobo5bo34bo5bobobo$3bo2bo4bobo32bobo
4bo2bo$6b2o2bo2bo32bo2bo2b2o$11b2o34b2o2$29b2o$29b2o$5b2o46b2o$5b2o46b
2o$5b2o46b2o$6bo20bo4bo20bo$5bobo20bo2bo20bobo$3obobo19b3o2b3o19bobob
3o$4obo48bob4o$4bo50bo2$22bo6b2o6bo$20bobo6b2o6bobo$bo2bo16b2o14b2o16b
o2bo$4bo50bo$o4bo48bo4bo$2o2bobo46bobo2b2o$5bob2o42b2obo3$5bo2bo42bo2b
o$5b2o46b2o$29b2o$29b2o2$11b2o34b2o$6b2o2bo2bo32bo2bo2b2o$3bo2bo4bobo
32bobo4bo2bo$2bobobo5bo34bo5bobobo$3bo2bob2o10b2o16b2o10b2obo2bo$6bo2b
o8bo2bo16bo2bo8bo2bo$7bo4bo34bo4bo$8b5o34b5o$18b2obo16bob2o$10bo9bobo
2b2o6b2o2bobo9bo$9bobo9bo4bo6bo4bo9bobo$10bo11bo14bo11bo$22bo2bo8bo2bo
!

88 + 44n: David Buckingham, 2 Apr 1992 (period-44 glider gun and resulting glider loops; the original p44 gun is shown below)

Code: Select all

x = 68, y = 60, rule = B3/S23
41b2o6b2o$41b2o6b2o3$41b3o4b3o$43bo4bo$41b2o6b2o$25b2o38b2o$24bobo38bo
bo$24bobob2o3b2o22b2o3b2obobo$25bobobo3b2o22b2o3bobobo$27bo36bo$25bo2b
o34bo2bo$28bo34bo$24bo3bo5bo7b2o4b2o7bo5bo3bo$24bo3bo3b2ob2o5b3o2b3o5b
2ob2o3bo3bo$8b2o10b2o6bo5bo7b2o4b2o7bo5bo$7bo2bo8bo2bo2bo2bo34bo2bo$7b
3o2b6o2b3o4bo36bo$10b2o6b2o5bobobo32bobobo$9bo10bo3bobob2o32b2obobo$9b
2obo4bob2o3bobo38bobo$14b2o9b2o38b2o2$40b3o6b3o$9b2o28bo3b2o2b2o3bo$9b
2o14b2o12bo12bo$25b2o12b2o10b2o$41bo2bo2bo2bo$41b3o4b3o3$15bo$2o12b3o$
2o11bo3bo39b2o$13b2ob2o10bo28bobo$29bo29bo$27b3o29b2o$41b2o$41bo$13b2o
b2o24b3o7b2o$2o11bo3bo26bo7b2o$2o12b3o$15bo12b2o$28bobo$30bo$30b2o7bo$
40bo$38b3o$9b2o$9b2o3$14b2o$9b2obo4bob2o$9bo10bo$10b2o6b2o28b2o$7b3o2b
6o2b3o25bobo$7bo2bo8bo2bo27bo$8b2o10b2o28b2o!

150 + 5n: Dean Hickerson, 20 Apr 1992 (spark-assisted Herschel tracks; the p155 oscillator is shown below; Buckingham seems to claim, possibly incorrectly, that p150 + 5n was achievable in 1991 at the same time as the p136)

Code: Select all

#N p155 oscillator
#C 20 B heptominos travel around a track of length 3100 gens,
#C consisting of 20 64 gen turns and 28 65 gen turns.  The turns
#C use the p5 oscillators "toaster" and "middleweight volcano" to
#C replace the p8 "Kok's galaxy" and "blocker" used in David
#C Buckingham's turns.  4 of the toasters are 2-slicers rather than
#C the usual 4-slicers, to avoid destroying nearby eaters.
#O Dean Hickerson,  4/20/92
x = 305, y = 197
149bo2bo$95b4o$37bo2b2o2b2o2bo24bo17bo2bo4bo2bo24bo17bo2bo4bo2bo24bo
17bo2b6o2bo24bo$37b4ob2ob4o22b3o17b4o4b4o22b3o17b4ob2ob4o22b3o17b4ob2o
b4o22b3o$70bo53bo24bo2bo25bo25b2o26bo$39b3o2b3o23b2o21b3o2b3o23b2o21b
3o2b3o23b2o21b3o2b3o23b2o$38bo2bo2bo2bo27b2o15bo2bo2bo2bo27b2o15bo8bo
27b2o15bo2bo2bo2bo27b2o$38b2o6b2o27bo16b4o2b4o27bo16b2obo2bob2o27bo16b
3o4b3o27bo$41bo2bo28bobo19bo2bo28bobo51bobo19bo2bo28bobo$38b4o2b4o25b
2o17b4o2b4o25b2o17b4o2b4o11b2o3b3o6b2o17b4o2b4o25b2o$37bo10bo29bo2b2o
8bo10bo10bo18bo2b2o8bo3bo2bo3bo9bo7b2o10bo2b2o8bo4b2o4bo29bo2b2o$38b3o
b2ob3o29bobo2bo9b3o4b3o9bo19bobo2bo9b3ob2ob3o29bobo2bo9b3ob2ob3o29bobo
2bo$40b2o2b2o4b2o25bobobo12bo4bo4b2o5b2o18bobobo12bo4bo4b2o6b2o7bo9bob
obo12b6o4b2o25bobobo$50b2o24b2obob2o12b4o5b2o14bo9b2obob2o21b2o8b2o5bo
8b2obob2o21b2o24b2obob2o$76bo2bo3bo31b3o3b2o6bo3bo3bo11bo2bo14b2obo3bo
7bo3b2o3bo46bo2bo3bo$34b2o41bo2b3obo3b2o27bo4bo6bo4bobobo3b2o22bo4b3o
11b2o2b2obo3b2o40b3o2b2obo$35bo40bo2b2o3bo4bo25b2o2bo2bo6bo3b2o3bo4bo
23b2o12bo3bobo2bobo4bo40b4o4bo$35bobo10b2o27bo2b4o5bobo29bo7bo4bob2o5b
obo39b2o2b3o5bobo10b2o26b3o2b3o$36b2o9bo2bo25bo2bo10b2o28bo8bo3bo10b2o
36bo3b2o10b2o9bo2bo25bo2bo$47bo2bo25b2obob5o12b2o30b2obob5o44b2obob5o
15bo2b2o24b2obob5o$46b2ob2o26bobo2bo2bo12b2o6bo24bobo2bo2bo45bobo2bo2b
o14bo2b2o26bobo2bo2bo$39b2o6b2o28bo2bo12b2o11bobo22bo2bo50bo2bo12b2o5b
4o27bo2bo$39b2o37b2o13b2o11b2o24b2o52b2o13b2o37b2o2$56b2o52b2o52b2o52b
2o$56b2o52b2o40bo11b2o52b2o$151bo$151bo23b3o$175bo$19b2o26b2o25b2o25b
2o73bo32b2o25b2o$15b2o2bo14b2o11b2o25b2o25b2o45bo60b2o25b2o$14bo2bobo
14b2o111b3o30b2o$10b2obob3ob2o126b3o27b3obo$10bob2obobobo157bo2b2o$21b
o61b2o41b2ob2o6b2o8b4o27b3o10b2o52b2o14bo$11b4obob3obo60b2o42bobo7b2o
7b5o28bo11b2o52b2o12b3o$10bo3b2ob2o3bo105bo17b2obo108bo$11b3ob3ob3o12b
obo29b2o37b2o13b2o37b2o35bo16b2o13b2o28b2o6bo6b2o$6bo6bo5bo14b2o20bo9b
2o15bo20bo2bo12b2o36bo2bo34bobo13bo2bo12b2o14b2ob2o16bobob2o2bo$6b3o
20b2o4bo13bo5bobo13b2o9b6o16bobo2bo2bo12b2o31bobo2bo2bo29b2o14bobo2bo
2bo12b2o9bo4b2o14bobobobobo$9bo4bo3bo10b2o17bobob2o2bobo12b2o8bo2b2ob
2o14b2obob5o12b2o30b2obob5o44b2obob5o12b2o7b2o20b2obobobob2o$2b2o4b2o
6bo31bobobob2o2bo4b2o15b2obo3b2o14bo2bo10b2o37bo2b2o10b2o38bo2bo10b2o
15b2obo4bo12bo3b5o3bo$3bo35b2o6b2obo4bobo4bobo16bob4o16b3o2b3o5bobo28b
o7b3o3b2obo5bobo39bo2b4o5bobo15b2obo2b2o13bo11bo$3bobo33b2o6bo2b2ob2o
2b2o3bo21b2o17b4o4bo4bo28b3o7b3o2b2obobo4bo21b2o17bo2b2o3bo4bo20bo2bo
14bo11bo$4b2o42bo5bobo4b2o40b3o2b2obo3b2o27b2o9b3o3b2o2bo3b2o20b2o19bo
2b3obo3b2o38bo3b5o3bo$48bo5bobo46bo2bo3bo12b2o19b2o10bo2b2o3bo26bo19bo
2bo3bo45b2obobobob2o$47bo2b2ob2o2b2o18b2o24b2obob2o12b4o5b2o14bo3b2o4b
2obob2o21b2o24b2obob2o12b4o31bobobobobo$37b2o8b2obo4bobo9b6o4b2o25bobo
bo12bob2obo4b2o5b5o3bo4b2o5bobobo12b2o2b2o4b2o25bobobo12bo4bo30bobob2o
2bo$37b2o9bobobob2o2bo6b3ob2ob3o29bobo2bo9b3o4b3o9b4o4bo11bobo2bo9b3ob
2ob3o29bobo2bo9b3o4b3o29bo6b2o$48bobob2o2bobo5bo4b2o4bo29bo2b2o8bo3bo
2bo3bo11b2o16bo2b2o8bo10bo29bo2b2o8bo10bo$41b2o6bo5bobo7b4o2b4o25b2o
17b4o2b4o14b2o3b2o4b2o17b4o2b4o25b2o17b4o2b4o26b2o$41bo14bo11bo2bo28bo
bo20b2o23b2o4bobo19bo2bo28bobo19bo2bo29b2o$14b3o25b3o20b3o4b3o27bo16b
2ob4ob2o27bo16b2o6b2o27bo16b4o2b4o$14bo2bo26bo20bo2bo2bo2bo27b2o15bo3b
2o3bo27b2o15bo2bo2bo2bo27b2o15bo2bo2bo2bo$13bo2b2o48b3o2b3o23b2o21b3o
2b3o23b2o21b3o2b3o23b2o21b3o2b3o$13b2o54b2o26bo24bo2bo25bo53bo$39b2o
23b4ob2ob4o22b3o17b4o4b4o22b3o17b4ob2ob4o22b3o17b4o4b4o13b2o$17bo6b2o
14bo2b2o19bo2b6o2bo24bo17bo2bob2obo2bo24bo17bo2b2o2b2o2bo24bo17bo2bo4b
o2bo13b2o11b2o$18b2o4b2o14bobo2bo76b4o104b4o30b2o$17b2o20b2o2bo2bob2o
73b2o$40bobobob2obo$38bo3b3o$37bob3obob4o224b2o14bo$12b2o23bo3bo3bo3bo
223b2o12b3o$12b2o24b3o5b3o237bo$40bob3obo6bo202b2o11b2o15b2o6bo6b2o$2b
2o6bo18b2o10b5o5b3o202b2o11bobo21bobob2o2bo$3bo2b2obobo17b2o11b3o5bo
210b2o6bo23bobobobobo$3bobobobobo38b2o4b2o203b2o29b2obobobob2o$2b2obo
3bob2o6b2o35bo196b2o28bo7bo3b5o3bo$o3b2obob2o3bo4b2o33bobo195bobo29bo
6bo11bo$3bo7bo42b2o196bo25b2o2bo2bo5bo11bo$3bo7bo239b2o27bo4bo5bo3b5o
3bo$o3b2obob2o3bo263b3o3b2o6b2obobobob2o$2b2obo3bob2o8b2o235b4o21bo9bo
bobobobo$3bobobobobo9b2o234bo4bo11b2o17bobob2o2bo$3bo2b2obobo243b3o4b
3o9bo19bo6b2o$2b2o6bo6b2o235bo10bo10bo$18bo236b4o2b4o26b2o$15b3o240bo
2bo29b2o$15bo239b4o2b4o$255bo2bo2bo2bo$256bob4obo$19b2o233bob2o4b2obo$
15b2o2bo14b2o217bobo3b2o3bobo12b2o8b2o$14bo2bobo14b2o3b3o212bo2b2o2b2o
2bo13b2o$10b2obobobob2o17bo3bo212b2obo2bob2o$10bob2o5bo$15b3o3bo21bo$
11b4obob3obo15b5o217bo$10bo11bo16bo6b2o212b3o$11b3o5b3o24b2o215bo$6bo
6bo5bo227b2o6bo6b2o$6b3o5b5o10b2o18bo6b2o190bo2b2obobo$9bo19b2o17bobob
2o2bo191bobobobobo9b2o$2b2o4b2o38bobobobobo190b2obo3bob2o8b2o$3bo35b2o
6b2obo3bob2o188bo2b2obob2o2bo$3bobo33b2o5bo2b2obob2o2bo186b3o3b3o3b3o$
4b2o39b3o3b3o3b3o185b3o3b3o3b3o39b2o$45b3o3b3o3b3o186bo2b2obob2o2bo5b
2o33bobo$46bo2b2obob2o2bo188b2obo3bob2o6b2o35bo$37b2o8b2obo3bob2o190bo
bobobobo38b2o4b2o$37b2o9bobobobobo191bo2b2obobo17b2o19bo$48bobob2o2bo
190b2o6bo18b2o10b5o5b3o$41b2o6bo6b2o227bo5bo6bo$41bo215b2o24b3o5b3o$
42b3o212b2o6bo16bo11bo$44bo217b5o15bob3obob4o$261bo21bo3b3o$285bo5b2ob
o$40b2obo2bob2o212bo3bo17b2obobobob2o$24b2o13bo2b2o2b2o2bo212b3o3b2o
14bobo2bo$14b2o8b2o12bobo3b2o3bobo217b2o14bo2b2o$39bob2o4b2obo233b2o$
41bob4obo$40bo2bo2bo2bo$40b4o2b4o239bo$12b2o29bo2bo240b3o$12b2o26b4o2b
4o236bo$28bo10bo10bo235b2o6bo6b2o$2b2o6bo19bo9b3o4b3o243bobob2o2bo$3bo
2b2obobo17b2o11bo4bo234b2o9bobobobobo$3bobobobobo9bo21b4o235b2o8b2obo
3bob2o$2b2obobobob2o6b2o3b3o263bo3b2obob2o3bo$bo3b5o3bo5bo4bo27b2o239b
o7bo$bo11bo5bo2bo2b2o25bo196b2o42bo7bo$bo11bo6bo29bobo195bobo33b2o4bo
3b2obob2o3bo$bo3b5o3bo7bo28b2o196bo35b2o6b2obo3bob2o$2b2obobobob2o29b
2o203b2o4b2o38bobobobobo$3bobobobobo23bo6b2o210bo5b3o11b2o17bobob2o2bo
$3bo2b2obobo21bobo11b2o202b3o5b5o10b2o18bo6b2o$2b2o6bo6b2o15b2o11b2o
202bo6bob3obo$18bo237b3o5b3o24b2o$15b3o12b2o223bo3bo3bo3bo23b2o$15bo
14b2o224b4obob3obo$260b3o3bo$255bob2obobobo$180b2o73b2obo2bo2b2o20b2o$
39b2o30b4o104b4o76bo2bobo14b2o4b2o$39b2o11b2o13bo2bo4bo2bo17bo24bo2b2o
2b2o2bo17bo24bo2bob2obo2bo17bo24bo2b6o2bo19b2o2bo14b2o6bo$52b2o13b4o4b
4o17b3o22b4ob2ob4o17b3o22b4o4b4o17b3o22b4ob2ob4o23b2o$99bo53bo25bo2bo
24bo26b2o54b2o$69b3o2b3o21b2o23b3o2b3o21b2o23b3o2b3o21b2o23b3o2b3o48b
2o2bo$68bo2bo2bo2bo15b2o27bo2bo2bo2bo15b2o27bo3b2o3bo15b2o27bo2bo2bo2b
o20bo26bo2bo$68b4o2b4o16bo27b2o6b2o16bo27b2ob4ob2o16bo27b3o4b3o20b3o
25b3o$40b2o29bo2bo19bobo28bo2bo19bobo4b2o23b2o20bobo28bo2bo11bo14bo$
40b2o26b4o2b4o17b2o25b4o2b4o17b2o4b2o3b2o14b4o2b4o17b2o25b4o2b4o7bobo
5bo6b2o$67bo10bo8b2o2bo29bo10bo8b2o2bo16b2o11bo3bo2bo3bo8b2o2bo29bo4b
2o4bo5bobo2b2obobo$30b2o6bo29b3o4b3o9bo2bobo29b3ob2ob3o9bo2bobo11bo4b
4o9b3o4b3o9bo2bobo29b3ob2ob3o6bo2b2obobobo9b2o$31bo2b2obobo30bo4bo12bo
bobo25b2o4b2o2b2o12bobobo5b2o4bo3b5o5b2o4bob2obo12bobobo25b2o4b6o9bobo
4bob2o8b2o$31bobobobobo31b4o12b2obob2o24b2o21b2obob2o4b2o3bo14b2o5b4o
12b2obob2o24b2o18b2o2b2ob2o2bo$30b2obobobob2o45bo3bo2bo19bo26bo3b2o2bo
10b2o19b2o12bo3bo2bo46bobo5bo$29bo3b5o3bo38b2o3bob3o2bo19b2o20b2o3bo2b
2o3b3o9b2o27b2o3bob2o2b3o40b2o4bobo5bo42b2o$29bo11bo14bo2bo20bo4bo3b2o
2bo17b2o21bo4bobob2o2b3o7b3o28bo4bo4b4o17b2o21bo3b2o2b2ob2o2bo6b2o33bo
bo$29bo11bo13b2o2bob2o15bobo5b4o2bo39bobo5bob2o3b3o7bo28bobo5b3o2b3o
16b4obo16bobo4bobo4bob2o6b2o35bo$29bo3b5o3bo12bo4bob2o15b2o10bo2bo38b
2o10b2o2bo37b2o10bo2bo14b2o3bob2o15b2o4bo2b2obobobo31bo6b2o4b2o$30b2ob
obobob2o20b2o7b2o12b5obob2o44b5obob2o30b2o12b5obob2o14b2ob2o2bo8b2o12b
obo2b2obobo17b2o10bo3bo4bo$31bobobobobo14b2o4bo9b2o12bo2bo2bobo14b2o
29bo2bo2bobo31b2o12bo2bo2bobo16b6o9b2o13bobo5bo13bo4b2o20b3o$31bo2b2ob
obo16b2ob2o14b2o12bo2bo13bobo34bo2bo36b2o12bo2bo20bo15b2o9bo20b2o14bo
5bo6bo$30b2o6bo6b2o28b2o13b2o16bo35b2o37b2o13b2o37b2o29bobo12b3ob3ob3o
$46bo108bob2o17bo105bo3b2ob2o3bo$43b3o12b2o52b2o11bo28b5o7b2o7bobo42b
2o60bob3obob4o$43bo14b2o52b2o10b3o27b4o8b2o6b2ob2o41b2o61bo$123b2o2bo
157bobobob2obo$123bob3o27b3o126b2ob3obob2o$123b2o30b3o111b2o14bobo2bo$
67b2o25b2o60bo45b2o25b2o25b2o11b2o14bo2b2o$67b2o25b2o32bo73b2o25b2o25b
2o26b2o$129bo$127b3o23bo$153bo$85b2o52b2o11bo40b2o52b2o$85b2o52b2o52b
2o52b2o2$63b2o37b2o13b2o52b2o24b2o11b2o13b2o37b2o$62bo2bo27b4o5b2o12bo
2bo50bo2bo22bobo11b2o12bo2bo28b2o6b2o$57bo2bo2bobo26b2o2bo14bo2bo2bobo
45bo2bo2bobo24bo6b2o12bo2bo2bobo26b2ob2o$57b5obob2o24b2o2bo15b5obob2o
44b5obob2o30b2o12b5obob2o25bo2bo$63bo2bo25bo2bo9b2o10b2o3bo36b2o10bo3b
o8bo28b2o10bo2bo25bo2bo9b2o$59b3o2b3o26b2o10bobo5b3o2b2o39bobo5b2obo4b
o7bo29bobo5b4o2bo27b2o10bobo$58bo4b4o40bo4bobo2bobo3bo12b2o23bo4bo3b2o
3bo6bo2bo2b2o25bo4bo3b2o2bo40bo$58bob2o2b3o40b2o3bob2o2b2o11b3o4bo22b
2o3bobobo4bo6bo4bo27b2o3bob3o2bo41b2o$59bo3bo2bo46bo3b2o3bo7bo3bob2o
14bo2bo11bo3bo3bo6b2o3b3o31bo3bo2bo$60b2obob2o24b2o21b2obob2o8bo5b2o8b
2o21b2obob2o9bo14b2o5b4o12b2obob2o24b2o$61bobobo25b2o4b6o12bobobo9bo7b
2o6b2o4bo4bo12bobobo18b2o5b2o4bo4bo12bobobo25b2o4b2o2b2o$60bo2bobo29b
3ob2ob3o9bo2bobo29b3ob2ob3o9bo2bobo19bo9b3o4b3o9bo2bobo29b3ob2ob3o$60b
2o2bo29bo4b2o4bo8b2o2bo10b2o7bo9bo3bo2bo3bo8b2o2bo18bo10bo10bo8b2o2bo
29bo10bo$68b2o25b4o2b4o17b2o6b3o3b2o11b4o2b4o17b2o25b4o2b4o17b2o25b4o
2b4o$67bobo28bo2bo19bobo51bobo28bo2bo19bobo28bo2bo$67bo27b3o4b3o16bo
27b2obo2bob2o16bo27b4o2b4o16bo27b2o6b2o$66b2o27bo2bo2bo2bo15b2o27bo8bo
15b2o27bo2bo2bo2bo15b2o27bo2bo2bo2bo$71b2o23b3o2b3o21b2o23b3o2b3o21b2o
23b3o2b3o21b2o23b3o2b3o$72bo26b2o25bo25bo2bo24bo53bo$69b3o22b4ob2ob4o
17b3o22b4ob2ob4o17b3o22b4o4b4o17b3o22b4ob2ob4o$69bo24bo2b6o2bo17bo24bo
2bo4bo2bo17bo24bo2bo4bo2bo17bo24bo2b2o2b2o2bo$206b4o$152bo2bo!

84: possible 31 Jul 1994 or perhaps even earlier, but not explicitly constructed or even mentioned (LCM: caterer on p28 pre-pulsar shuttle variant supported by molds that Bill Gosper, in an email on 31 Jul 1994, attributes to Dean Hickerson Edit: in and email on 29 Apr 1992 Dean Hickerson attributes this p28 pre-pulsar shuttle variant to Robert Wainwright). The first acknowledged p84 is pi orbital found on 22 Aug 1995.
124: Dean Hickerson, 31 Jul 1994 (variant of p124 lumps of muck hassler)
203: possible to build as early as 5 Aug 1994 (LCM: 44P7.2 on a p29 pre-pulsar shuttle variant using blinkers by Bill Gosper on 5 Aug 1994)
87: Bill Gosper, as early as 24 Sep 1994 (LCM: p29 pentadecathlon hassler on caterer); implicitly acknowledged by Gosper on 26 Sep 1994.
100 + 4n and 100 + 10n: Bill Gosper, 17 Oct 1994 (traffic jam oscillators)
102 + 18n: Dean Hickerson, 19 Oct 1994 (traffic jam oscillators); p102 was the only new period in this series.
80: Dean Hickerson, 28 Oct 1994 (LCM: Achim's other p16 on middleweight volcano)
102 + 6n: Noam Elkies, no earlier than 22 Nov 1994 and no later than 13 Jun 1996 (traffic jam oscillators; see here for details); p126 was the only new period in this series.
96: Noam Elkies, 28 Jan 1995 (p96 Hans Leo hassler)

125: Noam Elkies, 11 Jan 1996:

Code: Select all

x = 159, y = 159, rule = B3/S23
96bo$95bobo16b2o$93b3obo9b2o3bo2bo$64bo27bo4bob2o7bo3b2o$45b2o16bobo
26bob2obo2bo7bob2o2b4ob2o$45bo2bo3b2o9bob3o23b2obobob2o6b2obobobo3bobo
bo$47b2o3bo7b2obo4bo29bo6bobobobo2b2obobobo$40b2ob4o2b2obo7bo2bob2obo
20bob2ob2ob2o13bobo2bobob2o$39bobobo3bobobob2o6b2obobob2o22b2o3b3ob2ob
ob3obo2b3o3bo$39bobobob2o2bobobobo6bo14bo9bo3bobo2b2obob2ob2o4bobo4bob
o$38b2obobo2bobo13b2ob2ob2obo4bobo4b2o2bo3bobo2bo3bobo4b2obob4ob2o$41b
o3b3o2bob3obob2ob3o3b2o6bo2bo3bo2bo6b2o5b4o8bo4bo$41bobo4bobo4b2ob2obo
b2o2bobo3bo2b2o4bobo4bob2ob2obo5bo4b2obob2obo$42b2ob4obob2o4bobo3bo2bo
bo3bo9bo12bob5o6bobobobo$44bo4bo8b4o5b2o22b2obob2o10bo2b2o$44bob2obob
2o4bo5bob2ob2obo20bob2o3b2o7b2o$45bobobobo6b5obo27bo4b2obo$48b2o2bo10b
2obob2o23b3obo$51b2o7b2o3b2obo26bobo$60bob2o4bo27bo$63bob3o17bo$63bobo
18b2o$64bo19bobo14$7bo$5b3o$4bo143bo$4b6o138b3o$10bo140bo$4b4ob2o41bo
93b6o$4bo6b2o39bobo90bo$b2obobobobo2bo38b2o91b2ob4o$bo2bob3obobo130b2o
6bo$3bobo2bobob2o128bo2bobobobob2o$2b2o3bob2o3bo128bobob3obo2bo$4b3o4b
4o127b2obobo2bobo$4bo3b3o130bo3b2obo3b2o$5b2o5b2obo125b4o4b3o$2b3o3bob
obob2o129b3o3bo$2bo2b2obobo129bob2o5b2o$5bo2bo106b3o22b2obobobo3b3o$6b
o2bo105bo29bobob2o2bo$8b2o106bo30bo2bo$12bo133bo2bo$8b4obo132b2o$8b2ob
obo129bo$3b2o5b2obob2o125bob4o$3bobo2b2obobobo126bobob2o$5b4o4bo2bo
122b2obob2o5b2o$b4o2b3o2bobob3o121bobobob2o2bobo$o4bo3b2o2b2o4bo119bo
2bo4b4o$b2obo2bo4bo2bob2o118b3obobo2b3o2b4o$2bob2obo4bob2obo118bo4b2o
2b2o3bo4bo$2bo5b4o5bo119b2obo2bo4bo2bob2o$3b3ob2o2b2ob3o121bob2obo4bob
2obo$5bobob2obobo123bo5b4o5bo$139b3ob2o2b2ob3o$7bo4bo128bobob2obobo2$
9b2o132bo4bo$22bo$11bo8b2o123b2o$10bobo8b2o$10bo2bo133bo$11b2o133bobo$
146bo2bo$147b2o2$10b2o$9bo2bo$10bobo133b2o$11bo133bo2bo$136b2o8bobo$
12b2o123b2o8bo$136bo$10bo4bo132b2o2$8bobob2obobo128bo4bo$6b3ob2o2b2ob
3o$5bo5b4o5bo123bobob2obobo$5bob2obo4bob2obo121b3ob2o2b2ob3o$4b2obo2bo
4bo2bob2o119bo5b4o5bo$3bo4bo3b2o2b2o4bo118bob2obo4bob2obo$4b4o2b3o2bob
ob3o118b2obo2bo4bo2bob2o$8b4o4bo2bo119bo4b2o2b2o3bo4bo$6bobo2b2obobobo
121b3obobo2b3o2b4o$6b2o5b2obob2o122bo2bo4b4o$11b2obobo126bobobob2o2bob
o$11b4obo125b2obob2o5b2o$15bo129bobob2o$11b2o132bob4o$9bo2bo133bo$8bo
2bo30bo106b2o$5bo2b2obobo29bo105bo2bo$5b3o3bobobob2o22b3o106bo2bo$8b2o
5b2obo129bobob2o2bo$7bo3b3o129b2obobobo3b3o$7b3o4b4o125bob2o5b2o$5b2o
3bob2o3bo130b3o3bo$6bobo2bobob2o127b4o4b3o$4bo2bob3obobo128bo3b2obo3b
2o$4b2obobobobo2bo128b2obobo2bobo$7bo6b2o130bobob3obo2bo$7b4ob2o91b2o
38bo2bobobobob2o$13bo90bobo39b2o6bo$7b6o93bo41b2ob4o$7bo140bo$8b3o138b
6o$10bo143bo$151b3o$151bo14$72bobo19bo$73b2o18bobo$73bo17b3obo$62bo27b
o4b2obo$61bobo26bob2o3b2o7b2o$61bob3o23b2obob2o10bo2b2o$58bob2o4bo27bo
b5o6bobobobo$49b2o7b2o3b2obo20bob2ob2obo5bo4b2obob2obo$46b2o2bo10b2obo
b2o22b2o5b4o8bo4bo$43bobobobo6b5obo12bo9bo3bobo2bo3bobo4b2obob4ob2o$
42bob2obob2o4bo5bob2ob2obo4bobo4b2o2bo3bobo2b2obob2ob2o4bobo4bobo$42bo
4bo8b4o5b2o6bo2bo3bo2bo6b2o3b3ob2obob3obo2b3o3bo$40b2ob4obob2o4bobo3bo
2bobo3bo2b2o4bobo4bob2ob2ob2o13bobo2bobob2o$39bobo4bobo4b2ob2obob2o2bo
bo3bo9bo14bo6bobobobo2b2obobobo$39bo3b3o2bob3obob2ob3o3b2o22b2obobob2o
6b2obobobo3bobobo$36b2obobo2bobo13b2ob2ob2obo20bob2obo2bo7bob2o2b4ob2o
$37bobobob2o2bobobobo6bo29bo4bob2o7bo3b2o$37bobobo3bobobob2o6b2obobob
2o23b3obo9b2o3bo2bo$38b2ob4o2b2obo7bo2bob2obo26bobo16b2o$45b2o3bo7b2ob
o4bo27bo$43bo2bo3b2o9bob3o$43b2o16bobo$62bo!

The following is what I believe to be a complete list of periods above 60 known before 5 Jul 1996:

66, 72, 75, 87, 105, 329
150 + 3n
80 + 4n
120 + 5n
84 + 6n
80 + 10n
92 + 46n
94 + 94n
A period-203 lcm oscillator also would have been possible, but it was never acknowledged.

Any period above 60 that is not on this list would then have been first achieved using stable Herschel tracks.

The following is a timeline of David Buckingham's discovery of all remaining periods above 60 using stable Herschel tracks:

5 Jul 1996: All periods 153 and above (using R64, L112, and F117) and all periods 64 and above that are not multiples of 3 or 13 (using just L112 and F117)
7 Jul 1996: All periods 107 and above (using L112, F117, and R190)
3 Aug 1996: All periods 61 and above (using L112, F117, and Fx77)

Please comment if you see any errors or inconsistencies.

Re: First Known Oscillators for Each Period

Posted: April 24th, 2025, 5:20 am

by WhiteHawk

Necropost, but noting that Centinal previously incorrectly stated that Pentadecathlon on Centinal was the smallest p300 oscillator even though the p60+120n glider shuttle is older and smaller by pop & bounding box.

Re: First Known Oscillators for Each Period

Posted: April 24th, 2025, 12:59 pm

by confocaloid

WhiteHawk wrote: April 24th, 2025, 5:20 am Necropost, but noting that Centinal previously incorrectly stated that Pentadecathlon on Centinal was the smallest p300 oscillator even though the p60+120n glider shuttle is older and smaller by pop & bounding box.

After the recent edit https://conwaylife.com/w/index.php?titl ... did=152122 the page now claims:

Centinal&diff=161467&oldid=152122 wrote: Pentadecathlon on centinal. Though the p60+120n glider shuttle is older, this oscillator was previously considered to be the smallest p300 oscillator.

- which sounds less than accurate.

Check the revision history of the page, and watch carefully to see what is going on:

(Revision as of 18:30, 12 April 2022) diff (added penta on cent to gallery)
The embedded viewer added in that edit had caption claiming "pentadecathlon on centinal // smallest known p200 oscillator by population". This is clearly wrong, as pentadecathlon on centinal is a p300 oscillator, not a p200 oscillator.
At the time when that edit was made, the preceding viewer (which was already present) had caption: "figure eight on centinal // smallest known p200 oscillator by population" where the second part matches exactly.
It looks plausible that User:Book could simply copy-and-paste the EmbedViewer markup, and accidentally copied the part claiming "smallest known p200 oscillator by population" even though it doesn't apply in this case.
(Revision as of 12:48, 18 May 2022) diff (no longer SKOP200)
This edit removed the preceding viewer (figureeightoncentinal), and at the same time "corrected" what would look like a typo by that time in the (pentadecathlononcentinal) viewer (p200 -> p300).
It looks like the thing to do would be simply to remove the (likely accidentally-copied) part "smallest known p200 oscillator by population", instead of interpreting it as a typo and correcting it to p300.
(Revision as of 19:04, 10 November 2023) diff (the p300 isn't current SKOP (User:Galoomba/Skopje indicates it's a 29 cell glider shuttle))
This edit replaced "smallest known" by "former smallest known", again interpreting the claim made in the wiki as if it were previously correct at some time in the past (while it looks like it never was).
(Latest revision as of 12:31, 17 April 2025) diff (the p60+120n glider shuttle is older, and since 60+120(2)=60+240=300, Pentadecathlon on centinal was never SKOP300)

This edit replaced the unsubstantiated claim "(former smallest known p300 oscillator by population)" by the new unsubstantiated claim "Though the p60+120n glider shuttle is older, this oscillator was previously considered to be the smallest p300 oscillator."

Hence a question: "... previously considered to be the smallest..." -- considered by whom and when?

I think the wiki currently contains enough errors or inaccuracies of various kinds, that it's always a good idea to double-check any claims, and it's always a good idea to go and check the revision history to see who and when added some claim, and otherwise attempt to verify the assertions (instead of just taking them on faith).