ConwayLife.com

Posted: **March 28th, 2023, 11:45 am**

x = 392, y = 373, rule = B3/S23
24bo$22bobo$12b2o6b2o12b2o$11bo3bo4b2o12b2o$2o8bo5bo3b2o$2o8bo3bob2o4b
obo$10bo5bo7bo$11bo3bo$12b2o100$143b2o$143b2o8$161b2o$160bo2bo$123b3o
34bobo$161bo$171b2o$171b2o3$128b2o158b2o$128b2o157bobo$104bo182b2o$103b
obo79b2o$103bobo20bo58b2o$104bo20bobo37bo$125bobo36bobo$126bo38b2o8b2o
$76b2o97b2o$76b2o4b2o7bo9b2o$61b2o19b2o6bobo8b2o10b2o$61b2o28bo21b2o55b
o126b2o$75b2o93bo10b2o3b2o8b2o62b2o35b2o$74bo2bo92bo9bo2bo2bobo7b2o61b
o2bo$75b2o104b2o4bo12bo59bobo$166b3o3b3o24bobo59bo$136b2o61bobo$135bo
2bo17bo13bo24b2o3bo44bo$136b2o17bobo12bo24b2o47bobo20b2o$156b2o12bo73b
obo20b2o24b2o$245bo47b2o$159bo$67bo49bo40bobo73bo$67bo48bobo29b2o8b2o
74bo7bo$67bo37b3o8bobo25b2o2b2o84bo6bobo$117bo3b3o20b2o66bo28bo2bo$63b
3o3b3o140bo29b2o$60bo151bo$59bobo5bo40b2o$59bobo5bo39bo2bo$60bo6bo40b
2o17bo$126bobo142b2o12bo4bo$126b2o98b2o42bobo12bo4bo$115b3o108b2o43bo
13bo4bo$110b2o154b2o$50b2o58b2o21bo131bo2bo$49bo2bo80bo123b2o6bobo$50b
2o81bo70b2o42b2o7b2o7bo11b2o$65b2o102bo33bo2bo40bo2bo26bo2bo$65b2o102b
o33bobo32b3o7b2o28b2o$82bo86bo14b2o18bo$42b3o36bobo19b3o78b2o32b2o$82b
o82b3o3b3o44b2o$144b2o$57bo82b2o2b2o23bo$56bobo60b2o13bo5b2o27bo28bo70b
2o$56bobo31b2o26bo2bo12bo34bo28bo15b2o53b2o$57bo32b2o27b2o13bo63bo15b
2o$183b2o$55bo8bo107b2o8bobo$54bobo6bobo106b2o8b2o25b2o87b2o$51bo3b2o
6bobo143b2o53b2o31bo2bo$50bobo11bo12b2o58b2o26b3o96b2o32b2o$50b2o25b2o
57bo2bo$136bobo121b2o$137bo66bo55b2o33b2o$203bobo60b2o7bo19b2o$119b3o
81bobo59bo2bo5bobo$137b2o65bo52b2o7bobo5bo2bo3b2o$104b2o31b2o118b2o8b
o7b2o4b2o$81b2o21b2o46b2o$81b2o68bo2bo$100b2o50b2o119b2o$92bo7b2o170b
o2bo$91bobo179bobo$91bobo173b2o5bo$45b3o28b2o14bo103b2o69b2o$71b2o3b2o
118b2o$71b2o$108b3o2$56bo$56bo201b3o$56bo117b3o30b3o$83bo137b2o33bo$46b
2o4b3o3b3o22bo12b2o99bo7bo5bo8bo2bo32bo25bo$46b2o35bo11bo2bo98bo7bo5b
o9b2o33bo25bo$56bo39b2o99bo7bo5bo70bo$56bo22bo5b3o170b3o$56bo22bo127b
3o$79bo83bo125b2o$103b2o3b2o53bo124bo2bo$81b3o19b2o3b2o53bo48b2o75bob
o$128b2o49b3o30b2o76bo$127bo2bo95b2o$103b2o23b2o73b2o21b2o$103b2o97bo
bo$49bo152b2o76b3o$49bo$49bo3$173b2o78b2o$172bo2bo77b2o$173b2o56b3o$271b
2o$271b2o3$221bo$221bo$221bo50b2o$272b2o2$201b3o$252b2o17b2o$252b2o17b
2o$231b2o$230bo2bo$231b2o18b2o$251b2o5$239b2o$239b2o3b2o$244b2o$278b2o
$277bobo$277b2o4$252b3o4$208b2o$208b2o3$251b3o$221bo$221bo$221bo4$239b
o$238bobo$233bo4bobo$233bo5bo$208b3o22bo$243b2o$242bo2bo$243b2o2$235b
2o$235b2o3$209b3o2$234b2o$234b2o4$222bo$221bobo$206b2o14bo$206b2o4$218b
2o$218b2o2$233b2o$233b2o3$195bo6bo19b2o$195bo6bo18bobo$195bo6bo19bo2$
191b3o10b3o2$195bo6bo$195bo6bo$195bo6bo$221bo$221bo$221bo55$378b2o$376b
o3bo$367bo7bo5bo$367bobo4b2obo3bo8b2o$370b2o3bo5bo8b2o$356b2o12b2o4bo
3bo$356b2o12b2o6b2o$367bobo$367bo!

I like watching glider guns fight each other

Posted: **March 30th, 2023, 9:33 am**

Sokwe wrote: March 30th, 2023, 4:48 am ...

That being said, we do desperately need a queryable database of known oscillators and spaceships. It's become very difficult to check whether or not a given pattern is new.

This can be done with a Catagolue stdin symmetry, which should be named what_is_known_stdin.

I did try to write a script to scrape the forums for patterns, though it didn't go too far.

Posted: **March 31st, 2023, 5:59 am**

Citation needed wrote: March 28th, 2023, 12:21 am This just came out.

Could you translate the text?
Is tomorrow really your birthday ですか?

Posted: **April 5th, 2023, 2:30 am**

Elsewhere, I posted the following rule, where a single cell is a spaceship:

Code: Select all

@RULE 1C3SShip2
@TABLE
n_states:3
neighborhood:Moore
symmetries:none
#delay
2,0,0,0,0,0,1,0,0,1
1,0,0,0,0,0,1,0,0,0
2,0,0,0,0,0,2,0,0,1
1,0,0,0,0,0,2,0,0,0
0,2,1,2,2,0,0,0,1,2
#leftward expansion
0,0,0,1,0,0,0,0,0,2
0,0,0,0,0,1,2,0,0,2
0,0,0,2,1,2,0,0,0,1
2,0,0,0,2,1,2,0,0,0
2,1,0,1,2,0,0,0,0,1
1,0,0,0,1,1,0,0,0,0
1,1,0,1,2,0,0,0,0,2
0,0,1,1,0,0,0,0,0,2
0,0,0,1,1,0,0,0,0,1
2,1,0,2,0,0,0,0,0,1
2,0,0,0,0,1,2,0,0,0
1,1,0,2,0,0,0,0,0,2
1,0,0,0,2,1,0,0,0,0
#downward expansion
0,1,0,0,0,0,0,0,0,2
0,0,0,0,0,0,2,1,0,2
0,2,0,0,0,0,0,2,1,1
2,0,0,0,0,0,2,1,2,0
2,1,2,1,0,0,0,0,2,1
2,0,0,0,0,1,2,1,0,0
1,0,0,0,0,0,0,1,1,0
2,1,0,1,0,0,0,0,1,1
1,1,0,1,0,0,0,0,2,2
0,1,1,0,0,0,0,0,0,2
0,1,0,0,0,0,0,0,1,1
2,2,0,1,0,0,0,0,0,1
1,2,0,1,0,0,0,0,0,2
1,0,0,0,0,0,0,1,2,0
0,0,0,0,0,2,1,0,0,2
2,0,0,0,0,2,1,0,0,0
#downward stop
0,1,0,0,0,0,2,1,0,1
1,0,0,0,0,0,2,1,0,2
2,0,0,0,0,0,2,1,0,0
0,2,0,0,0,1,1,2,2,2
2,1,0,2,0,2,0,0,1,1
2,0,0,0,0,0,2,2,1,0
0,2,0,0,0,1,2,2,2,2
2,0,0,0,0,1,1,2,1,0
2,1,0,2,1,1,0,0,0,1
1,2,2,1,0,0,0,0,0,2
1,2,0,0,0,0,0,1,2,2
2,1,0,2,1,2,0,0,0,1
2,0,0,0,0,1,2,2,1,0
1,2,0,0,0,0,0,2,2,0
2,2,1,1,0,0,0,0,0,0
1,1,0,0,0,0,0,2,2,0
0,0,0,2,2,1,2,1,1,1
1,0,0,0,2,1,2,1,1,2
2,1,2,1,0,0,0,0,0,0
1,2,0,2,0,0,0,2,1,0
0,0,0,0,0,2,1,1,0,2
1,1,0,2,1,2,0,0,1,0
2,0,0,0,2,1,2,1,1,0
2,0,1,0,0,0,0,1,2,0
#downward counting
0,1,0,0,0,0,1,1,0,2
1,1,0,0,0,0,2,1,1,0
0,0,2,0,0,0,1,2,2,1
0,0,0,0,0,1,1,1,1,1
0,0,2,0,0,0,2,1,1,1
0,2,0,0,0,1,2,2,1,1
0,0,2,0,0,0,2,2,2,1
1,1,0,1,0,1,0,0,1,2
1,1,0,0,0,0,2,2,2,0
1,1,0,0,0,0,1,2,2,0
1,0,0,0,0,0,2,2,1,0
1,0,0,0,0,0,1,2,1,0
1,1,0,0,0,0,1,1,1,0
0,0,2,0,0,0,1,1,1,1
0,0,0,0,0,0,2,0,2,1
1,0,0,0,0,2,0,0,1,0
2,0,0,0,0,0,1,1,0,0
1,1,2,0,0,1,0,0,1,2
0,2,0,0,0,0,1,2,1,2
2,0,0,0,0,0,1,2,1,0
2,1,0,2,0,1,0,0,2,1
1,2,2,0,0,1,0,0,0,2
1,1,2,0,0,2,0,0,1,2
0,2,0,0,0,0,2,2,1,2
0,2,0,0,0,0,1,2,2,2
2,1,0,2,0,1,0,0,0,1
1,2,2,0,0,2,0,0,0,2
0,2,0,0,0,0,2,2,2,2
2,1,0,2,0,2,0,0,0,1
0,2,0,0,0,0,0,2,2,2

2,0,0,0,0,0,0,1,1,1
2,0,1,2,0,0,0,0,0,0
2,1,0,0,0,0,0,2,0,1
2,1,1,1,0,0,0,0,2,0
1,1,0,0,0,0,0,2,1,0
1,0,0,0,0,0,0,2,0,2
0,0,2,0,0,0,1,1,2,1
1,1,0,0,1,2,0,2,0,2
#upward signal
0,0,1,1,2,2,0,0,0,2
0,0,1,1,1,2,0,0,0,2
0,0,2,1,1,2,0,0,0,2
0,0,2,2,1,2,0,0,0,2
0,0,2,2,2,2,0,0,0,2
0,0,2,1,2,2,0,0,0,2
0,0,1,2,1,2,0,0,0,2
0,0,1,2,2,2,0,0,0,2
2,0,1,1,1,0,0,0,0,0
2,0,1,1,2,0,0,0,0,0
2,0,1,2,1,0,0,0,0,0
2,0,1,2,2,0,0,0,0,0
2,0,2,1,1,0,0,0,0,0
2,2,2,1,2,0,0,0,0,0
2,0,2,2,1,0,0,0,0,0
2,0,2,2,2,0,0,0,0,0
2,1,0,0,0,1,0,2,0,1
2,2,0,0,0,1,0,2,0,1
0,1,1,2,1,2,0,0,2,1
0,1,1,1,2,2,0,0,1,1
1,1,1,2,2,0,0,0,2,2
0,2,1,2,0,0,0,0,1,2
2,1,0,2,0,2,2,0,1,1
2,1,0,2,0,1,0,2,0,1
2,1,1,0,1,1,0,1,1,1
1,1,2,0,0,2,0,1,1,2
1,1,0,0,0,2,0,1,1,2
1,0,1,2,1,0,1,0,0,2
2,2,2,0,0,1,0,0,2,1
1,0,0,1,2,1,0,1,0,2
2,0,0,1,1,2,0,1,0,1
1,1,1,2,2,0,0,0,1,2
2,1,0,0,0,2,0,1,1,1
2,2,1,1,2,0,0,0,1,0
1,0,0,2,2,0,0,1,0,2
1,0,0,2,2,0,0,2,0,2
2,0,0,1,0,2,0,1,0,1

1,1,2,0,0,2,0,2,1,2
2,1,1,1,2,0,0,0,2,0
2,1,0,2,0,1,2,0,1,1
1,1,1,2,1,0,0,0,2,0

2,2,2,0,0,1,0,2,0,1
0,0,1,0,0,2,1,1,1,2
2,2,0,0,0,0,1,1,1,0
2,0,1,0,0,2,1,1,1,0
2,1,0,2,0,1,2,0,0,1
2,2,1,0,0,0,0,0,0,0
#leftward stop
0,0,0,0,0,2,2,0,0,2
2,0,0,0,0,2,2,0,0,0
0,0,0,0,0,0,2,2,0,2
0,0,0,2,2,2,2,0,0,2
2,0,0,0,2,2,2,0,0,0
2,2,0,2,0,0,0,2,0,1
2,0,0,0,1,2,2,0,0,0
2,2,0,1,0,0,0,2,0,1
0,0,0,2,2,2,1,1,0,2
0,0,0,2,2,2,2,1,0,2
1,0,0,2,2,1,0,0,0,2
2,0,0,0,1,2,1,1,0,0
2,2,0,1,0,0,0,1,1,1
1,0,0,2,1,2,0,0,0,0
2,0,2,0,1,1,2,1,0,1
1,0,1,0,1,1,2,0,0,0
2,1,1,0,0,0,0,0,2,0
1,0,0,1,1,2,0,0,0,0
1,0,0,0,1,1,1,0,0,0
2,0,0,1,2,0,0,1,1,1
2,0,0,2,0,2,0,1,1,1
0,0,0,0,1,1,2,1,0,1
1,0,0,1,1,2,0,0,0,0
1,0,0,0,1,1,2,0,0,0
2,0,1,1,0,0,0,0,0,1
2,2,1,0,0,0,0,0,1,0
2,0,0,1,0,2,0,1,1,1
#leftward counting
0,2,1,2,0,0,0,0,2,2
2,2,1,0,0,0,0,0,2,0
0,2,2,2,0,0,0,0,1,2
0,2,2,2,0,0,0,0,2,2
2,0,0,1,0,2,0,2,0,1
2,1,1,2,2,0,0,0,2,0
2,1,1,0,0,0,0,0,1,0
0,2,2,2,0,0,0,0,0,2
2,0,0,2,2,0,0,0,0,0
2,0,1,0,0,0,0,0,0,0
1,0,0,1,0,0,2,0,0,2
#extra length
2,0,2,1,2,0,0,1,1,1
2,1,0,0,1,1,0,0,1,1
2,1,0,0,1,1,0,2,1,1
1,2,0,1,0,0,0,0,2,2
2,0,0,0,0,0,1,1,2,0
1,1,0,0,0,0,0,0,0,0
2,0,1,0,2,0,0,0,0,0
0,1,0,0,0,2,0,2,0,1
2,0,0,1,2,0,0,2,1,1
2,1,1,2,1,0,0,0,2,0
#downward signal
0,2,1,1,0,0,0,0,0,2
2,1,1,0,1,1,0,2,1,1
0,2,1,1,1,0,0,0,2,2
2,2,1,2,2,0,0,0,0,0
2,1,1,1,1,2,0,2,2,0
2,0,1,1,1,2,0,2,0,0
#reverse counter
0,2,1,1,2,0,0,0,2,2
0,0,0,0,0,0,2,0,1,2
1,1,0,0,0,2,0,2,2,0
2,0,0,0,0,1,2,1,1,0
2,0,1,1,2,2,0,2,0,1
1,0,1,1,2,2,2,0,0,0
2,1,1,2,0,0,0,2,0,0

1,2,2,0,1,2,0,0,0,2
0,2,0,0,0,1,2,1,2,1

#ending
2,2,0,2,0,0,0,0,0,0
2,0,0,0,2,0,0,0,0,0

#2,0,0,0,0,0,0,0,0,0

2,0,0,0,0,0,0,0,0,1
0,0,0,2,0,0,1,1,1,2
2,0,0,2,0,0,1,1,1,0
2,0,1,0,0,0,0,2,0,0
1,1,0,2,0,1,0,0,1,0
0,2,2,0,0,1,2,1,1,1
1,0,0,0,0,0,0,1,0,0
0,0,0,0,1,0,0,0,1,2
2,0,2,2,0,0,0,0,0,0
1,0,0,0,1,0,2,0,0,0
1,0,0,0,0,0,2,0,1,0
#diagonal mode
#0,0,0,1,0,2,0,0,0,2
#2,0,1,0,0,0,0,2,0,0

I didn't want to make the other post too long, so I split the detailed math into this post.

The basic outline of the ship is that a binary counter pointing down ("the first counter") counts, and when it reaches the end of the tape it turns that into a c/2 wickstretcher. When the counter reaches the wickstretcher, it transforms it back into a stationary tip. When it activates the wickstretcher head, it also sends a signal upwards, and when it sends enough signals it will advance a long leftward counter ("the second counter") by 1. The second counter will gradually shrink, and once it disappears it sends a signal down the first counter, which caps off the end so the first counter shrinks rather than grows. Once it shrinks all the way, it collapses into a single cell.

Every 27 generations, the first counter flips the cell with ones on either side:

Code: Select all

x = 84, y = 10, rule = 1C3SShip2
10.B2A$12.B$12.A$6.A5.A7.A$5.2A5.A7.2A$4.3A5.A7.4A$3.4A5.A7.8A$2.5A5.
A7.16A$.6A5.A7.32A$7A5.B7.64A!
@RULE 1C3SShip2
@TABLE
n_states:3
neighborhood:Moore
symmetries:none
#delay
0,0,0,0,0,0,1,2,0,1
1,1,1,0,0,2,0,0,1,2
2,0,0,0,0,0,1,0,0,1
1,0,0,0,0,0,1,0,0,0
2,0,0,0,0,0,2,0,0,1
1,0,0,0,0,0,2,0,0,0
#leftward expansion
0,0,0,1,0,0,0,0,0,2
0,0,0,0,0,1,2,0,0,2
0,0,0,2,1,2,0,0,0,1
2,0,0,0,2,1,2,0,0,0
2,1,0,1,2,0,0,0,0,1
1,0,0,0,1,1,0,0,0,0
1,1,0,1,2,0,0,0,0,2
0,0,1,1,0,0,0,0,0,2
0,0,0,1,1,0,0,0,0,1
2,1,0,2,0,0,0,0,0,1
2,0,0,0,0,1,2,0,0,0
1,1,0,2,0,0,0,0,0,2
1,0,0,0,2,1,0,0,0,0
#downward expansion
0,1,0,0,0,0,0,0,0,2
0,0,0,0,0,0,2,1,0,2
0,2,0,0,0,0,0,2,1,1
2,0,0,0,0,0,2,1,2,0
2,1,2,1,0,0,0,0,2,1
2,0,0,0,0,1,2,1,0,0
1,0,0,0,0,0,0,1,1,0
2,1,0,1,0,0,0,0,1,1
1,1,0,1,0,0,0,0,2,2
0,1,1,0,0,0,0,0,0,2
0,1,0,0,0,0,0,0,1,1
2,2,0,1,0,0,0,0,0,1
1,2,0,1,0,0,0,0,0,2
1,0,0,0,0,0,0,1,2,0
0,0,0,0,0,2,1,0,0,2
2,0,0,0,0,2,1,0,0,0
#downward stop
0,1,0,0,0,0,2,1,0,1
1,0,0,0,0,0,2,1,0,2
2,0,0,0,0,0,2,1,0,0
0,2,0,0,0,1,1,2,2,2
2,1,0,2,0,2,0,0,1,1
2,0,0,0,0,0,2,2,1,0
0,2,0,0,0,1,2,2,2,2
2,0,0,0,0,1,1,2,1,0
2,1,0,2,1,1,0,0,0,1
1,2,2,1,0,0,0,0,0,2
1,2,0,0,0,0,0,1,2,2
2,1,0,2,1,2,0,0,0,1
2,0,1,0,0,1,2,2,1,0
1,2,0,0,0,0,0,2,2,0
2,2,1,1,0,0,0,0,0,0
1,1,0,0,0,0,0,2,2,0
0,0,0,2,2,1,2,1,1,1
1,0,0,0,2,1,2,1,1,2
2,1,2,1,0,0,0,0,0,0
1,2,0,2,0,0,0,2,1,0
0,0,0,0,0,2,1,1,0,2
1,1,0,2,1,2,0,0,1,0
2,0,0,0,2,1,2,1,1,0
2,0,1,0,0,0,0,1,2,0
#downward counting
0,1,0,0,0,0,1,1,0,2
1,1,0,0,0,0,2,1,1,0
0,0,2,0,0,0,1,2,2,1
0,0,0,0,0,1,1,1,1,1
0,0,2,0,0,0,2,1,1,1
0,2,0,0,0,1,2,2,1,1
0,0,2,0,0,0,2,2,2,1
1,1,0,1,0,1,0,0,1,2
1,1,0,0,0,0,2,2,2,0
1,1,0,0,0,0,1,2,2,0
1,0,0,0,0,0,2,2,1,0
1,0,0,0,0,0,1,2,1,0
1,1,0,0,0,0,1,1,1,0
0,0,2,0,0,0,1,1,1,1
0,0,0,0,0,0,2,0,2,1
1,0,0,0,0,2,0,0,1,0
2,0,0,0,0,0,1,1,0,0
1,1,2,0,0,1,0,0,1,2
0,2,0,0,0,0,1,2,1,2
2,0,0,0,0,0,1,2,1,0
2,1,0,2,0,1,0,0,2,1
1,2,2,0,0,1,0,0,0,2
1,1,2,0,0,2,0,0,1,2
0,2,0,0,0,0,2,2,1,2
0,2,0,0,0,0,1,2,2,2
2,1,0,2,0,1,0,0,0,1
1,2,2,0,0,2,0,0,0,2
0,2,0,0,0,0,2,2,2,2
2,1,0,2,0,2,0,0,0,1
0,2,0,0,0,0,0,2,2,2

2,0,0,0,0,0,0,1,1,1
2,0,1,2,0,0,0,0,0,0
2,1,0,0,0,0,0,2,0,1
2,1,1,1,0,0,0,0,2,0
1,1,0,0,0,0,0,2,1,0
1,0,0,0,0,0,0,2,0,2
0,0,2,0,0,0,1,1,2,1
1,1,0,0,1,2,0,2,0,2
#upward signal
0,0,1,1,2,2,0,0,0,2
0,0,1,1,1,2,0,0,0,2
0,0,2,1,1,2,0,0,0,2
0,0,2,2,1,2,0,0,0,2
0,0,2,2,2,2,0,0,0,2
0,0,2,1,2,2,0,0,0,2
0,0,1,2,1,2,0,0,0,2
0,0,1,2,2,2,0,0,0,2
2,0,1,1,1,0,0,0,0,0
2,0,1,1,2,0,0,0,0,0
2,0,1,2,1,0,0,0,0,0
2,0,1,2,2,0,0,0,0,0
2,0,2,1,1,0,0,0,0,0
2,2,2,1,2,0,0,0,0,0
2,0,2,2,1,0,0,0,0,0
2,0,2,2,2,0,0,0,0,0
2,1,0,0,0,1,0,2,0,1
2,2,0,0,0,1,0,2,0,1
0,1,1,2,1,2,0,0,2,1
0,1,1,1,2,2,0,0,1,1
1,1,1,2,2,0,0,0,2,2
0,2,1,2,0,0,0,0,1,2
2,1,0,2,0,2,2,0,1,1
2,1,0,2,0,1,0,2,0,1
2,1,1,0,1,1,0,1,1,1
1,1,2,0,0,2,0,1,1,2
1,1,0,0,0,2,0,1,1,2
1,0,1,2,1,0,1,0,0,2
2,2,2,0,0,1,0,0,2,1
1,0,0,1,2,1,0,1,0,2
2,0,0,1,1,2,0,1,0,1
1,1,1,2,2,0,0,0,1,2
2,1,0,0,0,2,0,1,1,1
2,2,1,1,2,0,0,0,1,0
1,0,0,2,2,0,0,1,0,2
1,0,0,2,2,0,0,2,0,2
2,0,0,1,0,2,0,1,0,1

1,1,2,0,0,2,0,2,1,2
2,1,1,1,2,0,0,0,2,0
2,1,0,2,0,1,2,0,1,1
1,1,1,2,1,0,0,0,2,0

2,2,2,0,0,1,0,2,0,1
0,0,1,0,0,2,1,1,1,2
2,2,0,0,0,0,1,1,1,0
2,0,1,0,0,2,1,1,1,0
2,1,0,2,0,1,2,0,0,1
2,2,1,0,0,0,0,0,0,0
#leftward stop
0,0,0,0,0,2,2,0,0,2
2,0,0,0,0,2,2,0,0,0
0,0,0,0,0,0,2,2,0,2
0,0,0,2,2,2,2,0,0,2
2,0,0,0,2,2,2,0,0,0
2,2,0,2,0,0,0,2,0,1
2,0,0,0,1,2,2,0,0,0
2,2,0,1,0,0,0,2,0,1
0,0,0,2,2,2,1,1,0,2
0,0,0,2,2,2,2,1,0,2
1,0,0,2,2,1,0,0,0,2
2,0,0,0,1,2,1,1,0,0
2,2,0,1,0,0,0,1,1,1
1,0,0,2,1,2,0,0,0,0
2,0,2,0,1,1,2,1,0,1
1,0,1,0,1,1,2,0,0,0
2,1,1,0,0,0,0,0,2,0
1,0,0,1,1,2,0,0,0,0
1,0,0,0,1,1,1,0,0,0
2,0,0,1,2,0,0,1,1,1
2,0,0,2,0,2,0,1,1,1
0,0,0,0,1,1,2,1,0,1
1,0,0,1,1,2,0,0,0,0
1,0,0,0,1,1,2,0,0,0
2,0,1,1,0,0,0,0,0,1
2,2,1,0,0,0,0,0,1,0
2,0,0,1,0,2,0,1,1,1
#leftward counting
0,2,1,2,0,0,0,0,2,2
2,2,1,0,0,0,0,0,2,0
0,2,2,2,0,0,0,0,1,2
0,2,2,2,0,0,0,0,2,2
2,0,0,1,0,2,0,2,0,1
2,1,1,2,2,0,0,0,2,0
2,1,1,0,0,0,0,0,1,0
0,2,2,2,0,0,0,0,0,2
2,0,0,2,2,0,0,0,0,0
2,0,1,0,0,0,0,0,0,0
1,0,0,1,0,0,2,0,0,2
#extra length
2,0,2,1,2,0,0,1,1,1
2,1,0,0,1,1,0,0,1,1
2,0,0,0,0,0,1,1,2,0
1,1,0,0,0,0,0,0,0,0
2,0,1,0,2,0,0,0,0,0
0,1,0,0,0,2,0,2,0,1
#downward signal
0,2,1,1,0,0,0,0,0,2
2,1,1,0,1,1,0,2,1,1
0,2,1,1,1,0,0,0,2,2
2,2,1,2,2,0,0,0,0,0
2,1,1,1,1,2,0,2,2,0
2,0,1,1,1,2,0,2,0,0
#reverse counter
0,2,1,1,2,0,0,0,2,2
0,0,0,0,0,0,2,0,1,2
1,1,0,0,0,2,0,2,2,0
2,0,0,0,0,1,2,1,1,0
2,0,1,1,2,2,0,2,0,1
1,0,1,1,2,2,2,0,0,0
2,1,1,2,0,0,0,2,0,0

1,2,2,0,1,2,0,0,0,2
0,2,0,0,0,1,2,1,2,1

#ending
2,2,0,2,0,0,0,0,0,0
2,0,0,0,2,0,0,0,0,0

#2,0,0,0,0,0,0,0,0,0

2,0,0,0,0,0,0,0,0,1
0,0,0,2,0,0,1,1,1,2
2,0,0,2,0,0,1,1,1,0
2,0,1,0,0,0,0,2,0,0
1,1,0,2,0,1,0,0,1,0
0,2,2,0,0,1,2,1,1,1
1,0,0,0,0,0,0,1,0,0
0,0,0,0,1,0,0,0,1,2
2,0,2,2,0,0,0,0,0,0
1,0,0,0,1,0,2,0,0,0
1,0,0,0,0,0,2,0,1,0

We will measure the length of the counter from that cell, so this example has length 7. A length-n counter takes 2^(n-1)-7+n generations to turn the tip of the counter into a c/2 wickstretcher; a signal then takes n-2 generations to reach the counter. It erases any state-2 cells on the tape and may change the phase of the counter, delaying it by 54*floor(n/27)+f(n mod 27) generations. Values of f for each n mod 27 are shown here:

Code: Select all

The table corresponds to this army of counters:

Code: Select all

x = 572, y = 231, rule = 1C3SShip2
B3A15.B3A6.B3A6.B3A6.B3A6.B3A6.B3A6.B3A6.B3A6.B3A6.B3A6.B3A6.B3A6.B3A
6.B3A6.B3A6.B3A6.B3A6.B3A6.B3A6.B3A6.B3A6.B3A6.B3A6.B3A6.B3A6.B3A6.B
3A6.AB9.B3A6.B3A6.B3A6.B3A6.B3A6.B3A6.B3A6.B3A6.B3A6.B3A6.B3A6.B3A6.B
3A6.B3A6.B3A6.B3A6.B3A6.B3A6.B3A6.B3A6.B3A6.B3A6.B3A6.B3A6.B3A6.B3A6.
B3A6.AB$3.B18.B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B
9.B9.B9.B9.B9.B9.B9.B9.B20.B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.
B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B$3.B18.B9.B9.B9.B9.B9.B9.B9.B9.B
9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B20.B9.B9.B9.B9.
B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B$
3.B18.B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.
B9.B9.B9.B9.B9.B20.B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B
9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B$3.A18.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A
9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A20.B9.B9.B9.B9.B9.B9.
B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B9.B$3.A18.A
9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A
9.A9.A9.A20.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.
A9.A9.A9.A9.A9.A9.A9.A$3.A18.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A
9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A20.A9.A9.A9.A9.A9.A9.A9.A9.A9.
A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A$2.BA17.BA9.A9.A
9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A
9.A19.BA9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A
9.A9.A9.A9.A9.A9.A$3.A18.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A
9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A20.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.
A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A$3.A18.A8.BA9.A9.A9.
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20.A8.BA9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A
9.A9.A9.A9.A9.A$3.A18.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A
9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A20.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.
A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A$3.A18.A9.A8.BA9.A9.A9.
A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A20.A
9.A8.BA9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.
A9.A9.A9.A$3.A18.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A
9.A9.A9.A9.A9.A9.A9.A9.A9.A20.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.
A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A$3.A18.A9.A9.A8.BA9.A9.A9.A9.
A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A20.A9.A9.A
8.BA9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.
A9.A$3.A18.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A
9.A9.A9.A9.A9.A9.A9.A20.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.
A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A$3.A18.A9.A9.A9.A8.BA9.A9.A9.A9.A9.
A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A20.A9.A9.A9.A8.BA
9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A$3.
A18.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A
9.A9.A9.A9.A9.A20.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.
A9.A9.A9.A9.A9.A9.A9.A9.A9.A$3.A18.A9.A9.A9.A9.A8.BA9.A9.A9.A9.A9.A9.
A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A20.A9.A9.A9.A9.A8.BA9.A
9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A$3.A18.A
9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A
9.A9.A9.A20.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.
A9.A9.A9.A9.A9.A9.A9.A$3.A18.A9.A9.A9.A9.A9.A8.BA9.A9.A9.A9.A9.A9.A9.
A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A20.A9.A9.A9.A9.A9.A8.BA9.A9.A
9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A$3.A18.A9.A9.A
9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A
9.A20.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.
A9.A9.A9.A9.A9.A$3.A18.A9.A9.A9.A9.A9.A9.A8.BA9.A9.A9.A9.A9.A9.A9.A9.
A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A20.A9.A9.A9.A9.A9.A9.A8.BA9.A9.A9.A
9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A$3.A18.A9.A9.A9.A9.A
9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A20.
A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.A9.
A9.A9.A9.A$3.A18.A9.A9.A9.A9.A9.A9.A9.A8.BA9.A9.A9.A9.A9.A9.A9.A9.A9.
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@RULE 1C3SShip2
@TABLE
n_states:3
neighborhood:Moore
symmetries:none
#delay
2,0,0,0,0,0,1,0,0,1
1,0,0,0,0,0,1,0,0,0
2,0,0,0,0,0,2,0,0,1
1,0,0,0,0,0,2,0,0,0
0,2,1,2,2,0,0,0,1,2
#leftward expansion
0,0,0,1,0,0,0,0,0,2
0,0,0,0,0,1,2,0,0,2
0,0,0,2,1,2,0,0,0,1
2,0,0,0,2,1,2,0,0,0
2,1,0,1,2,0,0,0,0,1
1,0,0,0,1,1,0,0,0,0
1,1,0,1,2,0,0,0,0,2
0,0,1,1,0,0,0,0,0,2
0,0,0,1,1,0,0,0,0,1
2,1,0,2,0,0,0,0,0,1
2,0,0,0,0,1,2,0,0,0
1,1,0,2,0,0,0,0,0,2
1,0,0,0,2,1,0,0,0,0
#downward expansion
0,1,0,0,0,0,0,0,0,2
0,0,0,0,0,0,2,1,0,2
0,2,0,0,0,0,0,2,1,1
2,0,0,0,0,0,2,1,2,0
2,1,2,1,0,0,0,0,2,1
2,0,0,0,0,1,2,1,0,0
1,0,0,0,0,0,0,1,1,0
2,1,0,1,0,0,0,0,1,1
1,1,0,1,0,0,0,0,2,2
0,1,1,0,0,0,0,0,0,2
0,1,0,0,0,0,0,0,1,1
2,2,0,1,0,0,0,0,0,1
1,2,0,1,0,0,0,0,0,2
1,0,0,0,0,0,0,1,2,0
0,0,0,0,0,2,1,0,0,2
2,0,0,0,0,2,1,0,0,0
#downward stop
0,1,0,0,0,0,2,1,0,1
1,0,0,0,0,0,2,1,0,2
2,0,0,0,0,0,2,1,0,0
0,2,0,0,0,1,1,2,2,2
2,1,0,2,0,2,0,0,1,1
2,0,0,0,0,0,2,2,1,0
0,2,0,0,0,1,2,2,2,2
2,0,0,0,0,1,1,2,1,0
2,1,0,2,1,1,0,0,0,1
1,2,2,1,0,0,0,0,0,2
1,2,0,0,0,0,0,1,2,2
2,1,0,2,1,2,0,0,0,1
2,0,0,0,0,1,2,2,1,0
1,2,0,0,0,0,0,2,2,0
2,2,1,1,0,0,0,0,0,0
1,1,0,0,0,0,0,2,2,0
0,0,0,2,2,1,2,1,1,1
1,0,0,0,2,1,2,1,1,2
2,1,2,1,0,0,0,0,0,0
1,2,0,2,0,0,0,2,1,0
0,0,0,0,0,2,1,1,0,2
1,1,0,2,1,2,0,0,1,0
2,0,0,0,2,1,2,1,1,0
2,0,1,0,0,0,0,1,2,0
#downward counting
0,1,0,0,0,0,1,1,0,2
1,1,0,0,0,0,2,1,1,0
0,0,2,0,0,0,1,2,2,1
0,0,0,0,0,1,1,1,1,1
0,0,2,0,0,0,2,1,1,1
0,2,0,0,0,1,2,2,1,1
0,0,2,0,0,0,2,2,2,1
1,1,0,1,0,1,0,0,1,2
1,1,0,0,0,0,2,2,2,0
1,1,0,0,0,0,1,2,2,0
1,0,0,0,0,0,2,2,1,0
1,0,0,0,0,0,1,2,1,0
1,1,0,0,0,0,1,1,1,0
0,0,2,0,0,0,1,1,1,1
0,0,0,0,0,0,2,0,2,1
1,0,0,0,0,2,0,0,1,0
2,0,0,0,0,0,1,1,0,0
1,1,2,0,0,1,0,0,1,2
0,2,0,0,0,0,1,2,1,2
2,0,0,0,0,0,1,2,1,0
2,1,0,2,0,1,0,0,2,1
1,2,2,0,0,1,0,0,0,2
1,1,2,0,0,2,0,0,1,2
0,2,0,0,0,0,2,2,1,2
0,2,0,0,0,0,1,2,2,2
2,1,0,2,0,1,0,0,0,1
1,2,2,0,0,2,0,0,0,2
0,2,0,0,0,0,2,2,2,2
2,1,0,2,0,2,0,0,0,1
0,2,0,0,0,0,0,2,2,2

2,0,0,0,0,0,0,1,1,1
2,0,1,2,0,0,0,0,0,0
2,1,0,0,0,0,0,2,0,1
2,1,1,1,0,0,0,0,2,0
1,1,0,0,0,0,0,2,1,0
1,0,0,0,0,0,0,2,0,2
0,0,2,0,0,0,1,1,2,1
1,1,0,0,1,2,0,2,0,2
#upward signal
0,0,1,1,2,2,0,0,0,2
0,0,1,1,1,2,0,0,0,2
0,0,2,1,1,2,0,0,0,2
0,0,2,2,1,2,0,0,0,2
0,0,2,2,2,2,0,0,0,2
0,0,2,1,2,2,0,0,0,2
0,0,1,2,1,2,0,0,0,2
0,0,1,2,2,2,0,0,0,2
2,0,1,1,1,0,0,0,0,0
2,0,1,1,2,0,0,0,0,0
2,0,1,2,1,0,0,0,0,0
2,0,1,2,2,0,0,0,0,0
2,0,2,1,1,0,0,0,0,0
2,2,2,1,2,0,0,0,0,0
2,0,2,2,1,0,0,0,0,0
2,0,2,2,2,0,0,0,0,0
2,1,0,0,0,1,0,2,0,1
2,2,0,0,0,1,0,2,0,1
0,1,1,2,1,2,0,0,2,1
0,1,1,1,2,2,0,0,1,1
1,1,1,2,2,0,0,0,2,2
0,2,1,2,0,0,0,0,1,2
2,1,0,2,0,2,2,0,1,1
2,1,0,2,0,1,0,2,0,1
2,1,1,0,1,1,0,1,1,1
1,1,2,0,0,2,0,1,1,2
1,1,0,0,0,2,0,1,1,2
1,0,1,2,1,0,1,0,0,2
2,2,2,0,0,1,0,0,2,1
1,0,0,1,2,1,0,1,0,2
2,0,0,1,1,2,0,1,0,1
1,1,1,2,2,0,0,0,1,2
2,1,0,0,0,2,0,1,1,1
2,2,1,1,2,0,0,0,1,0
1,0,0,2,2,0,0,1,0,2
1,0,0,2,2,0,0,2,0,2
2,0,0,1,0,2,0,1,0,1

1,1,2,0,0,2,0,2,1,2
2,1,1,1,2,0,0,0,2,0
2,1,0,2,0,1,2,0,1,1
1,1,1,2,1,0,0,0,2,0

2,2,2,0,0,1,0,2,0,1
0,0,1,0,0,2,1,1,1,2
2,2,0,0,0,0,1,1,1,0
2,0,1,0,0,2,1,1,1,0
2,1,0,2,0,1,2,0,0,1
2,2,1,0,0,0,0,0,0,0
#leftward stop
0,0,0,0,0,2,2,0,0,2
2,0,0,0,0,2,2,0,0,0
0,0,0,0,0,0,2,2,0,2
0,0,0,2,2,2,2,0,0,2
2,0,0,0,2,2,2,0,0,0
2,2,0,2,0,0,0,2,0,1
2,0,0,0,1,2,2,0,0,0
2,2,0,1,0,0,0,2,0,1
0,0,0,2,2,2,1,1,0,2
0,0,0,2,2,2,2,1,0,2
1,0,0,2,2,1,0,0,0,2
2,0,0,0,1,2,1,1,0,0
2,2,0,1,0,0,0,1,1,1
1,0,0,2,1,2,0,0,0,0
2,0,2,0,1,1,2,1,0,1
1,0,1,0,1,1,2,0,0,0
2,1,1,0,0,0,0,0,2,0
1,0,0,1,1,2,0,0,0,0
1,0,0,0,1,1,1,0,0,0
2,0,0,1,2,0,0,1,1,1
2,0,0,2,0,2,0,1,1,1
0,0,0,0,1,1,2,1,0,1
1,0,0,1,1,2,0,0,0,0
1,0,0,0,1,1,2,0,0,0
2,0,1,1,0,0,0,0,0,1
2,2,1,0,0,0,0,0,1,0
2,0,0,1,0,2,0,1,1,1
#leftward counting
0,2,1,2,0,0,0,0,2,2
2,2,1,0,0,0,0,0,2,0
0,2,2,2,0,0,0,0,1,2
0,2,2,2,0,0,0,0,2,2
2,0,0,1,0,2,0,2,0,1
2,1,1,2,2,0,0,0,2,0
2,1,1,0,0,0,0,0,1,0
0,2,2,2,0,0,0,0,0,2
2,0,0,2,2,0,0,0,0,0
2,0,1,0,0,0,0,0,0,0
1,0,0,1,0,0,2,0,0,2
#extra length
2,0,2,1,2,0,0,1,1,1
2,1,0,0,1,1,0,0,1,1
2,1,0,0,1,1,0,2,1,1
1,2,0,1,0,0,0,0,2,2
2,0,0,0,0,0,1,1,2,0
1,1,0,0,0,0,0,0,0,0
2,0,1,0,2,0,0,0,0,0
0,1,0,0,0,2,0,2,0,1
2,0,0,1,2,0,0,2,1,1
2,1,1,2,1,0,0,0,2,0
#downward signal
0,2,1,1,0,0,0,0,0,2
2,1,1,0,1,1,0,2,1,1
0,2,1,1,1,0,0,0,2,2
2,2,1,2,2,0,0,0,0,0
2,1,1,1,1,2,0,2,2,0
2,0,1,1,1,2,0,2,0,0
#reverse counter
0,2,1,1,2,0,0,0,2,2
0,0,0,0,0,0,2,0,1,2
1,1,0,0,0,2,0,2,2,0
2,0,0,0,0,1,2,1,1,0
2,0,1,1,2,2,0,2,0,1
1,0,1,1,2,2,2,0,0,0
2,1,1,2,0,0,0,2,0,0

1,2,2,0,1,2,0,0,0,2
0,2,0,0,0,1,2,1,2,1

#ending
2,2,0,2,0,0,0,0,0,0
2,0,0,0,2,0,0,0,0,0

#2,0,0,0,0,0,0,0,0,0

2,0,0,0,0,0,0,0,0,1
0,0,0,2,0,0,1,1,1,2
2,0,0,2,0,0,1,1,1,0
2,0,1,0,0,0,0,2,0,0
1,1,0,2,0,1,0,0,1,0
0,2,2,0,0,1,2,1,1,1
1,0,0,0,0,0,0,1,0,0
0,0,0,0,1,0,0,0,1,2
2,0,2,2,0,0,0,0,0,0
1,0,0,0,1,0,2,0,0,0
1,0,0,0,0,0,2,0,1,0
#diagonal mode
#0,0,0,1,0,2,0,0,0,2
#2,0,1,0,0,0,0,2,0,0

Each signal is delayed 2 generations behind the last, because if the tape is 1 cell longer, it takes 1 more generation to reach the end and 1 more to go back. There are two timings that advance the second counter, marked with a hashtag in the table above and a domino in this pattern. Those two and one more change the phase differently depending on the first bit of the second counter.

Also, the delays you get from this pattern are 54 more than they should be, since I wanted 0 to be first, which means these start with length 27 rather than 0.

So if a counter is n cells long, a wickstretcher is activated in 27*2^(n-1)-7+n generations, and after a total of 81*2^(n-2)+54*floor(n/27)+f(n mod 27)+n-12 generations another signal appears on cell n-1 (27*2^(n-1)+27*2^(n-2)+(n-1)-11+54*floor(n/27)+f(n mod 27)). If a downward signal appears on that cell k generations after the wickstretcher is activated, it will extend the counter k cells:

Code: Select all

x = 64, y = 20, rule = 1C3SShip2
16.3A.3A.3A11.3A20.3A$10.A5.A.A.A5.A13.A22.A$9.3A4.3A.3A.3A8.A2.3A16.
A3.3A$10.A5.A.A.A.A3.A7.3A.A17.3A4.A$16.B2A.3A.3A8.A2.3A16.A3.3A5$18.
B44.B$10.B2A6.A4.B2A17.B2AB12.B2A$12.B3.B4A5.BA18.B15.2B$12.A6.B6.A
19.A15.A$12.A5.B7.A19.A14.BA$12.A13.A18.BA15.A$12.A13.A19.A15.A$12.A
12.BA19.A15.A$4AB7.A13.B19.2B14.2B$12.B13.BA18.B15.B$46.BA14.2A!
@RULE 1C3SShip2
@TABLE
n_states:3
neighborhood:Moore
symmetries:none
#delay
2,0,0,0,0,0,1,0,0,1
1,0,0,0,0,0,1,0,0,0
2,0,0,0,0,0,2,0,0,1
1,0,0,0,0,0,2,0,0,0
0,2,1,2,2,0,0,0,1,2
#leftward expansion
0,0,0,1,0,0,0,0,0,2
0,0,0,0,0,1,2,0,0,2
0,0,0,2,1,2,0,0,0,1
2,0,0,0,2,1,2,0,0,0
2,1,0,1,2,0,0,0,0,1
1,0,0,0,1,1,0,0,0,0
1,1,0,1,2,0,0,0,0,2
0,0,1,1,0,0,0,0,0,2
0,0,0,1,1,0,0,0,0,1
2,1,0,2,0,0,0,0,0,1
2,0,0,0,0,1,2,0,0,0
1,1,0,2,0,0,0,0,0,2
1,0,0,0,2,1,0,0,0,0
#downward expansion
0,1,0,0,0,0,0,0,0,2
0,0,0,0,0,0,2,1,0,2
0,2,0,0,0,0,0,2,1,1
2,0,0,0,0,0,2,1,2,0
2,1,2,1,0,0,0,0,2,1
2,0,0,0,0,1,2,1,0,0
1,0,0,0,0,0,0,1,1,0
2,1,0,1,0,0,0,0,1,1
1,1,0,1,0,0,0,0,2,2
0,1,1,0,0,0,0,0,0,2
0,1,0,0,0,0,0,0,1,1
2,2,0,1,0,0,0,0,0,1
1,2,0,1,0,0,0,0,0,2
1,0,0,0,0,0,0,1,2,0
0,0,0,0,0,2,1,0,0,2
2,0,0,0,0,2,1,0,0,0
#downward stop
0,1,0,0,0,0,2,1,0,1
1,0,0,0,0,0,2,1,0,2
2,0,0,0,0,0,2,1,0,0
0,2,0,0,0,1,1,2,2,2
2,1,0,2,0,2,0,0,1,1
2,0,0,0,0,0,2,2,1,0
0,2,0,0,0,1,2,2,2,2
2,0,0,0,0,1,1,2,1,0
2,1,0,2,1,1,0,0,0,1
1,2,2,1,0,0,0,0,0,2
1,2,0,0,0,0,0,1,2,2
2,1,0,2,1,2,0,0,0,1
2,0,0,0,0,1,2,2,1,0
1,2,0,0,0,0,0,2,2,0
2,2,1,1,0,0,0,0,0,0
1,1,0,0,0,0,0,2,2,0
0,0,0,2,2,1,2,1,1,1
1,0,0,0,2,1,2,1,1,2
2,1,2,1,0,0,0,0,0,0
1,2,0,2,0,0,0,2,1,0
0,0,0,0,0,2,1,1,0,2
1,1,0,2,1,2,0,0,1,0
2,0,0,0,2,1,2,1,1,0
2,0,1,0,0,0,0,1,2,0
#downward counting
0,1,0,0,0,0,1,1,0,2
1,1,0,0,0,0,2,1,1,0
0,0,2,0,0,0,1,2,2,1
0,0,0,0,0,1,1,1,1,1
0,0,2,0,0,0,2,1,1,1
0,2,0,0,0,1,2,2,1,1
0,0,2,0,0,0,2,2,2,1
1,1,0,1,0,1,0,0,1,2
1,1,0,0,0,0,2,2,2,0
1,1,0,0,0,0,1,2,2,0
1,0,0,0,0,0,2,2,1,0
1,0,0,0,0,0,1,2,1,0
1,1,0,0,0,0,1,1,1,0
0,0,2,0,0,0,1,1,1,1
0,0,0,0,0,0,2,0,2,1
1,0,0,0,0,2,0,0,1,0
2,0,0,0,0,0,1,1,0,0
1,1,2,0,0,1,0,0,1,2
0,2,0,0,0,0,1,2,1,2
2,0,0,0,0,0,1,2,1,0
2,1,0,2,0,1,0,0,2,1
1,2,2,0,0,1,0,0,0,2
1,1,2,0,0,2,0,0,1,2
0,2,0,0,0,0,2,2,1,2
0,2,0,0,0,0,1,2,2,2
2,1,0,2,0,1,0,0,0,1
1,2,2,0,0,2,0,0,0,2
0,2,0,0,0,0,2,2,2,2
2,1,0,2,0,2,0,0,0,1
0,2,0,0,0,0,0,2,2,2

2,0,0,0,0,0,0,1,1,1
2,0,1,2,0,0,0,0,0,0
2,1,0,0,0,0,0,2,0,1
2,1,1,1,0,0,0,0,2,0
1,1,0,0,0,0,0,2,1,0
1,0,0,0,0,0,0,2,0,2
0,0,2,0,0,0,1,1,2,1
1,1,0,0,1,2,0,2,0,2
#upward signal
0,0,1,1,2,2,0,0,0,2
0,0,1,1,1,2,0,0,0,2
0,0,2,1,1,2,0,0,0,2
0,0,2,2,1,2,0,0,0,2
0,0,2,2,2,2,0,0,0,2
0,0,2,1,2,2,0,0,0,2
0,0,1,2,1,2,0,0,0,2
0,0,1,2,2,2,0,0,0,2
2,0,1,1,1,0,0,0,0,0
2,0,1,1,2,0,0,0,0,0
2,0,1,2,1,0,0,0,0,0
2,0,1,2,2,0,0,0,0,0
2,0,2,1,1,0,0,0,0,0
2,2,2,1,2,0,0,0,0,0
2,0,2,2,1,0,0,0,0,0
2,0,2,2,2,0,0,0,0,0
2,1,0,0,0,1,0,2,0,1
2,2,0,0,0,1,0,2,0,1
0,1,1,2,1,2,0,0,2,1
0,1,1,1,2,2,0,0,1,1
1,1,1,2,2,0,0,0,2,2
0,2,1,2,0,0,0,0,1,2
2,1,0,2,0,2,2,0,1,1
2,1,0,2,0,1,0,2,0,1
2,1,1,0,1,1,0,1,1,1
1,1,2,0,0,2,0,1,1,2
1,1,0,0,0,2,0,1,1,2
1,0,1,2,1,0,1,0,0,2
2,2,2,0,0,1,0,0,2,1
1,0,0,1,2,1,0,1,0,2
2,0,0,1,1,2,0,1,0,1
1,1,1,2,2,0,0,0,1,2
2,1,0,0,0,2,0,1,1,1
2,2,1,1,2,0,0,0,1,0
1,0,0,2,2,0,0,1,0,2
1,0,0,2,2,0,0,2,0,2
2,0,0,1,0,2,0,1,0,1

1,1,2,0,0,2,0,2,1,2
2,1,1,1,2,0,0,0,2,0
2,1,0,2,0,1,2,0,1,1
1,1,1,2,1,0,0,0,2,0

2,2,2,0,0,1,0,2,0,1
0,0,1,0,0,2,1,1,1,2
2,2,0,0,0,0,1,1,1,0
2,0,1,0,0,2,1,1,1,0
2,1,0,2,0,1,2,0,0,1
2,2,1,0,0,0,0,0,0,0
#leftward stop
0,0,0,0,0,2,2,0,0,2
2,0,0,0,0,2,2,0,0,0
0,0,0,0,0,0,2,2,0,2
0,0,0,2,2,2,2,0,0,2
2,0,0,0,2,2,2,0,0,0
2,2,0,2,0,0,0,2,0,1
2,0,0,0,1,2,2,0,0,0
2,2,0,1,0,0,0,2,0,1
0,0,0,2,2,2,1,1,0,2
0,0,0,2,2,2,2,1,0,2
1,0,0,2,2,1,0,0,0,2
2,0,0,0,1,2,1,1,0,0
2,2,0,1,0,0,0,1,1,1
1,0,0,2,1,2,0,0,0,0
2,0,2,0,1,1,2,1,0,1
1,0,1,0,1,1,2,0,0,0
2,1,1,0,0,0,0,0,2,0
1,0,0,1,1,2,0,0,0,0
1,0,0,0,1,1,1,0,0,0
2,0,0,1,2,0,0,1,1,1
2,0,0,2,0,2,0,1,1,1
0,0,0,0,1,1,2,1,0,1
1,0,0,1,1,2,0,0,0,0
1,0,0,0,1,1,2,0,0,0
2,0,1,1,0,0,0,0,0,1
2,2,1,0,0,0,0,0,1,0
2,0,0,1,0,2,0,1,1,1
#leftward counting
0,2,1,2,0,0,0,0,2,2
2,2,1,0,0,0,0,0,2,0
0,2,2,2,0,0,0,0,1,2
0,2,2,2,0,0,0,0,2,2
2,0,0,1,0,2,0,2,0,1
2,1,1,2,2,0,0,0,2,0
2,1,1,0,0,0,0,0,1,0
0,2,2,2,0,0,0,0,0,2
2,0,0,2,2,0,0,0,0,0
2,0,1,0,0,0,0,0,0,0
1,0,0,1,0,0,2,0,0,2
#extra length
2,0,2,1,2,0,0,1,1,1
2,1,0,0,1,1,0,0,1,1
2,1,0,0,1,1,0,2,1,1
1,2,0,1,0,0,0,0,2,2
2,0,0,0,0,0,1,1,2,0
1,1,0,0,0,0,0,0,0,0
2,0,1,0,2,0,0,0,0,0
0,1,0,0,0,2,0,2,0,1
2,0,0,1,2,0,0,2,1,1
2,1,1,2,1,0,0,0,2,0
#downward signal
0,2,1,1,0,0,0,0,0,2
2,1,1,0,1,1,0,2,1,1
0,2,1,1,1,0,0,0,2,2
2,2,1,2,2,0,0,0,0,0
2,1,1,1,1,2,0,2,2,0
2,0,1,1,1,2,0,2,0,0
#reverse counter
0,2,1,1,2,0,0,0,2,2
0,0,0,0,0,0,2,0,1,2
1,1,0,0,0,2,0,2,2,0
2,0,0,0,0,1,2,1,1,0
2,0,1,1,2,2,0,2,0,1
1,0,1,1,2,2,2,0,0,0
2,1,1,2,0,0,0,2,0,0

1,2,2,0,1,2,0,0,0,2
0,2,0,0,0,1,2,1,2,1

#ending
2,2,0,2,0,0,0,0,0,0
2,0,0,0,2,0,0,0,0,0

#2,0,0,0,0,0,0,0,0,0

2,0,0,0,0,0,0,0,0,1
0,0,0,2,0,0,1,1,1,2
2,0,0,2,0,0,1,1,1,0
2,0,1,0,0,0,0,2,0,0
1,1,0,2,0,1,0,0,1,0
0,2,2,0,0,1,2,1,1,1
1,0,0,0,0,0,0,1,0,0
0,0,0,0,1,0,0,0,1,2
2,0,2,2,0,0,0,0,0,0
1,0,0,0,1,0,2,0,0,0
1,0,0,0,0,0,2,0,1,0
#diagonal mode
#0,0,0,1,0,2,0,0,0,2
#2,0,1,0,0,0,0,2,0,0

Therefore, one cycle extends the counter by 27*2^(n-2)+54*floor(n/27)+f(n mod 27)-5, so it now has a length of n-5+27*2^(n-2)+54*floor(n/27)+f(n mod 27), which mod 27 is n-5+f(n mod 27). This table shows what happens to each mod:

Code: Select all

The counter starts with length 7 mod 27, and it proceeds in the sequence 7-2-24-19-0-22-17-13-8-3-25-6-14-9-4-26-13#-8-3-25-6-14-9-4-26-21-16-11-19-16#, at which point a signal enters the second counter and eventually stops the wickstretcher. Note that the 19s and 26es have different results because the first bit is different. Then, it enters the cycle 16#-11-19-0-22-17-13-8-3-25-6-14-9-4-26-13#-8-3-25-6-14-9-4-26-21-16-11-19-16#. When the second counter only has the sequence 22, it goes to 2, causing the cycle to end with 16#-11-19-16#. At this point, a downward signal is sent out, and the first counter begins to shrink.
Now if the first counter has length n, it takes 81*2^(n-2)+54*floor(n/27)+f(n mod 27) to begin counting on a counter of length n-5+27*2^(n-2)+54*floor(n/27)+f(n mod 27).
If we define a1,a2,... as in this table, the 16# will be triggered when the first counter reaches a length of a29:

Code: Select all

7-2: a1=7
2-24: a2=27*2^(a1-2)+a1-5   =   27*2^(a1-2)+2   =   866
24-19: a3=27*2^(a2-2)+2*(a2-a1+5)+a2-5   =   27(2^(a2-2)+3*2^(a1-2)-1)+24   =   27(2^864)+2589, which has 261 digits
19-0: a4=27*2^(a3-2)+2*(a3-27+10-a1)+a3-5   =   27*(2^(a3-2)+3*2^(a2-2)+9*2^(a1-2)-3)+19; the number of digits a4 has has 260 digits
0-22: a5=27*2^(a4-2)+2*(a4-27+15-a1)+a4-5+40   =   27*(2^(a4-2)+3*2^(a3-2)+9*2^(a2-2)+27*2^(a1-2)-7); the number of digits the number of digits has has 260 digits
...
19-16#: a29 is a very big number—you have to take the number of digits 25 times to get a number that you could fit all the digits of inside the observable universe.

The observable universe is about 4.65*10^10 light years across. A meter is around 6.19*10^34 Planck lengths, and a light year is about 9.46*10^15 meters, so the radius of the observable universe is around 1.78*10^60 Planck lengths, and its volume is 2.37*10^181 Planck volumes, which only has 182 digits. Therefore, (log_10)^24(a29) is much too big for our universe, and (log_10)^25(a29) is the smallest that fits, with 246 digits.

Now, it takes about 27*2^(a29-1)+2*a29 generations to count through a tape of length a29 and send a signal back to the top of the counter, and because this is much bigger than any of the other intervals, we will ignore them as irrelevant.
When the first 16# occurs after k generations, the second counter becomes complete with a length of k+7:

Code: Select all

x = 89, y = 71, rule = 1C3SShip2
10.9BA24.9BA$10.B3A.3AB25.B3A.A.AB$10.B2.A3.AB25.BA3.A.AB$10.B3A3.AB
25.B3A.3AB$10.BA5.AB25.B2.A3.AB$10.B3A3.AB25.B3A3.AB$10.9B25.9B5$14.B
33.B$15.A6.A13.B12.A4.A26.B$4.A7.B4A5.11B3A10.B4A3.A23B3A$15.B19.2B
12.B30.2B$14.B20.A12.B31.A$35.A44.B$35.A44.A$35.A44.A$35.A44.A$35.A
44.A$35.A44.A$35.B44.B3$28.B$28.A40.B$26.B.A.B38.A$27.B2A37.B.A.B$28.
A39.B2A$69.A6$B32.B$A32.A$B32.B4$22.A13.B$22.12B2A$35.2B$34.BA6.AB$
35.A$35.A$35.A$35.A$35.A$35.A$35.B2$18.B59.B$18.A59.A$18.B59.B4$54.A
26.B$54.A24B2A$80.2B$79.BA6.AB$80.A$80.A$80.A$80.A$80.A$80.A$80.B!
@RULE 1C3SShip2
@TABLE
n_states:3
neighborhood:Moore
symmetries:none
#delay
2,0,0,0,0,0,1,0,0,1
1,0,0,0,0,0,1,0,0,0
2,0,0,0,0,0,2,0,0,1
1,0,0,0,0,0,2,0,0,0
0,2,1,2,2,0,0,0,1,2
#leftward expansion
0,0,0,1,0,0,0,0,0,2
0,0,0,0,0,1,2,0,0,2
0,0,0,2,1,2,0,0,0,1
2,0,0,0,2,1,2,0,0,0
2,1,0,1,2,0,0,0,0,1
1,0,0,0,1,1,0,0,0,0
1,1,0,1,2,0,0,0,0,2
0,0,1,1,0,0,0,0,0,2
0,0,0,1,1,0,0,0,0,1
2,1,0,2,0,0,0,0,0,1
2,0,0,0,0,1,2,0,0,0
1,1,0,2,0,0,0,0,0,2
1,0,0,0,2,1,0,0,0,0
#downward expansion
0,1,0,0,0,0,0,0,0,2
0,0,0,0,0,0,2,1,0,2
0,2,0,0,0,0,0,2,1,1
2,0,0,0,0,0,2,1,2,0
2,1,2,1,0,0,0,0,2,1
2,0,0,0,0,1,2,1,0,0
1,0,0,0,0,0,0,1,1,0
2,1,0,1,0,0,0,0,1,1
1,1,0,1,0,0,0,0,2,2
0,1,1,0,0,0,0,0,0,2
0,1,0,0,0,0,0,0,1,1
2,2,0,1,0,0,0,0,0,1
1,2,0,1,0,0,0,0,0,2
1,0,0,0,0,0,0,1,2,0
0,0,0,0,0,2,1,0,0,2
2,0,0,0,0,2,1,0,0,0
#downward stop
0,1,0,0,0,0,2,1,0,1
1,0,0,0,0,0,2,1,0,2
2,0,0,0,0,0,2,1,0,0
0,2,0,0,0,1,1,2,2,2
2,1,0,2,0,2,0,0,1,1
2,0,0,0,0,0,2,2,1,0
0,2,0,0,0,1,2,2,2,2
2,0,0,0,0,1,1,2,1,0
2,1,0,2,1,1,0,0,0,1
1,2,2,1,0,0,0,0,0,2
1,2,0,0,0,0,0,1,2,2
2,1,0,2,1,2,0,0,0,1
2,0,0,0,0,1,2,2,1,0
1,2,0,0,0,0,0,2,2,0
2,2,1,1,0,0,0,0,0,0
1,1,0,0,0,0,0,2,2,0
0,0,0,2,2,1,2,1,1,1
1,0,0,0,2,1,2,1,1,2
2,1,2,1,0,0,0,0,0,0
1,2,0,2,0,0,0,2,1,0
0,0,0,0,0,2,1,1,0,2
1,1,0,2,1,2,0,0,1,0
2,0,0,0,2,1,2,1,1,0
2,0,1,0,0,0,0,1,2,0
#downward counting
0,1,0,0,0,0,1,1,0,2
1,1,0,0,0,0,2,1,1,0
0,0,2,0,0,0,1,2,2,1
0,0,0,0,0,1,1,1,1,1
0,0,2,0,0,0,2,1,1,1
0,2,0,0,0,1,2,2,1,1
0,0,2,0,0,0,2,2,2,1
1,1,0,1,0,1,0,0,1,2
1,1,0,0,0,0,2,2,2,0
1,1,0,0,0,0,1,2,2,0
1,0,0,0,0,0,2,2,1,0
1,0,0,0,0,0,1,2,1,0
1,1,0,0,0,0,1,1,1,0
0,0,2,0,0,0,1,1,1,1
0,0,0,0,0,0,2,0,2,1
1,0,0,0,0,2,0,0,1,0
2,0,0,0,0,0,1,1,0,0
1,1,2,0,0,1,0,0,1,2
0,2,0,0,0,0,1,2,1,2
2,0,0,0,0,0,1,2,1,0
2,1,0,2,0,1,0,0,2,1
1,2,2,0,0,1,0,0,0,2
1,1,2,0,0,2,0,0,1,2
0,2,0,0,0,0,2,2,1,2
0,2,0,0,0,0,1,2,2,2
2,1,0,2,0,1,0,0,0,1
1,2,2,0,0,2,0,0,0,2
0,2,0,0,0,0,2,2,2,2
2,1,0,2,0,2,0,0,0,1
0,2,0,0,0,0,0,2,2,2

2,0,0,0,0,0,0,1,1,1
2,0,1,2,0,0,0,0,0,0
2,1,0,0,0,0,0,2,0,1
2,1,1,1,0,0,0,0,2,0
1,1,0,0,0,0,0,2,1,0
1,0,0,0,0,0,0,2,0,2
0,0,2,0,0,0,1,1,2,1
1,1,0,0,1,2,0,2,0,2
#upward signal
0,0,1,1,2,2,0,0,0,2
0,0,1,1,1,2,0,0,0,2
0,0,2,1,1,2,0,0,0,2
0,0,2,2,1,2,0,0,0,2
0,0,2,2,2,2,0,0,0,2
0,0,2,1,2,2,0,0,0,2
0,0,1,2,1,2,0,0,0,2
0,0,1,2,2,2,0,0,0,2
2,0,1,1,1,0,0,0,0,0
2,0,1,1,2,0,0,0,0,0
2,0,1,2,1,0,0,0,0,0
2,0,1,2,2,0,0,0,0,0
2,0,2,1,1,0,0,0,0,0
2,2,2,1,2,0,0,0,0,0
2,0,2,2,1,0,0,0,0,0
2,0,2,2,2,0,0,0,0,0
2,1,0,0,0,1,0,2,0,1
2,2,0,0,0,1,0,2,0,1
0,1,1,2,1,2,0,0,2,1
0,1,1,1,2,2,0,0,1,1
1,1,1,2,2,0,0,0,2,2
0,2,1,2,0,0,0,0,1,2
2,1,0,2,0,2,2,0,1,1
2,1,0,2,0,1,0,2,0,1
2,1,1,0,1,1,0,1,1,1
1,1,2,0,0,2,0,1,1,2
1,1,0,0,0,2,0,1,1,2
1,0,1,2,1,0,1,0,0,2
2,2,2,0,0,1,0,0,2,1
1,0,0,1,2,1,0,1,0,2
2,0,0,1,1,2,0,1,0,1
1,1,1,2,2,0,0,0,1,2
2,1,0,0,0,2,0,1,1,1
2,2,1,1,2,0,0,0,1,0
1,0,0,2,2,0,0,1,0,2
1,0,0,2,2,0,0,2,0,2
2,0,0,1,0,2,0,1,0,1

1,1,2,0,0,2,0,2,1,2
2,1,1,1,2,0,0,0,2,0
2,1,0,2,0,1,2,0,1,1
1,1,1,2,1,0,0,0,2,0

2,2,2,0,0,1,0,2,0,1
0,0,1,0,0,2,1,1,1,2
2,2,0,0,0,0,1,1,1,0
2,0,1,0,0,2,1,1,1,0
2,1,0,2,0,1,2,0,0,1
2,2,1,0,0,0,0,0,0,0
#leftward stop
0,0,0,0,0,2,2,0,0,2
2,0,0,0,0,2,2,0,0,0
0,0,0,0,0,0,2,2,0,2
0,0,0,2,2,2,2,0,0,2
2,0,0,0,2,2,2,0,0,0
2,2,0,2,0,0,0,2,0,1
2,0,0,0,1,2,2,0,0,0
2,2,0,1,0,0,0,2,0,1
0,0,0,2,2,2,1,1,0,2
0,0,0,2,2,2,2,1,0,2
1,0,0,2,2,1,0,0,0,2
2,0,0,0,1,2,1,1,0,0
2,2,0,1,0,0,0,1,1,1
1,0,0,2,1,2,0,0,0,0
2,0,2,0,1,1,2,1,0,1
1,0,1,0,1,1,2,0,0,0
2,1,1,0,0,0,0,0,2,0
1,0,0,1,1,2,0,0,0,0
1,0,0,0,1,1,1,0,0,0
2,0,0,1,2,0,0,1,1,1
2,0,0,2,0,2,0,1,1,1
0,0,0,0,1,1,2,1,0,1
1,0,0,1,1,2,0,0,0,0
1,0,0,0,1,1,2,0,0,0
2,0,1,1,0,0,0,0,0,1
2,2,1,0,0,0,0,0,1,0
2,0,0,1,0,2,0,1,1,1
#leftward counting
0,2,1,2,0,0,0,0,2,2
2,2,1,0,0,0,0,0,2,0
0,2,2,2,0,0,0,0,1,2
0,2,2,2,0,0,0,0,2,2
2,0,0,1,0,2,0,2,0,1
2,1,1,2,2,0,0,0,2,0
2,1,1,0,0,0,0,0,1,0
0,2,2,2,0,0,0,0,0,2
2,0,0,2,2,0,0,0,0,0
2,0,1,0,0,0,0,0,0,0
1,0,0,1,0,0,2,0,0,2
#extra length
2,0,2,1,2,0,0,1,1,1
2,1,0,0,1,1,0,0,1,1
2,1,0,0,1,1,0,2,1,1
1,2,0,1,0,0,0,0,2,2
2,0,0,0,0,0,1,1,2,0
1,1,0,0,0,0,0,0,0,0
2,0,1,0,2,0,0,0,0,0
0,1,0,0,0,2,0,2,0,1
2,0,0,1,2,0,0,2,1,1
2,1,1,2,1,0,0,0,2,0
#downward signal
0,2,1,1,0,0,0,0,0,2
2,1,1,0,1,1,0,2,1,1
0,2,1,1,1,0,0,0,2,2
2,2,1,2,2,0,0,0,0,0
2,1,1,1,1,2,0,2,2,0
2,0,1,1,1,2,0,2,0,0
#reverse counter
0,2,1,1,2,0,0,0,2,2
0,0,0,0,0,0,2,0,1,2
1,1,0,0,0,2,0,2,2,0
2,0,0,0,0,1,2,1,1,0
2,0,1,1,2,2,0,2,0,1
1,0,1,1,2,2,2,0,0,0
2,1,1,2,0,0,0,2,0,0

1,2,2,0,1,2,0,0,0,2
0,2,0,0,0,1,2,1,2,1

#ending
2,2,0,2,0,0,0,0,0,0
2,0,0,0,2,0,0,0,0,0

#2,0,0,0,0,0,0,0,0,0

2,0,0,0,0,0,0,0,0,1
0,0,0,2,0,0,1,1,1,2
2,0,0,2,0,0,1,1,1,0
2,0,1,0,0,0,0,2,0,0
1,1,0,2,0,1,0,0,1,0
0,2,2,0,0,1,2,1,1,1
1,0,0,0,0,0,0,1,0,0
0,0,0,0,1,0,0,0,1,2
2,0,2,2,0,0,0,0,0,0
1,0,0,0,1,0,2,0,0,0
1,0,0,0,0,0,2,0,1,0
#diagonal mode
#0,0,0,1,0,2,0,0,0,2
#2,0,1,0,0,0,0,2,0,0

So the starting length of the second counter is around 2^a29, which is between 10^^26 and 10^^27. It takes roughly 2^(2^a29)) hashtags (between 10^^27 and 10^^28) to clear, and a hashtag appears every 14 cycles on average, which takes 2^^(14*2^(2^(a29))) generations, which is more than 10^^(10^^27).
How big is this? If you took the number of digits it had, then took the number of digits that had, then repeated this over and over again, the number of times you would have to repeat this before getting a manageable number is so large that you would have to take its number of digits 27 times before it could fit inside the observable universe.

There are several ways to make this last even longer. Obviously, changing the collapse at the end would add a few more generations on, but there are better options. For example:

If we could make it start off with more state 1 cells or have a large number of them turn to state 1, it would last much longer. If the starting sequence is longer, the second counter could even be replaced with a unary countdown.
We could change the way the signal rephases the counter and/or use a different counter. This could make the sequence of residues longer. For a different rule, we might be able to use a different starting length. (7 has the longest sequence, and 34 or any 7+27n is probably out of reach)
We could modify the second counter to become a long array of downward counters, which would far surpass any of the other improvements.
We could find a different design entirely. It wouldn't surprise me if there were a way to make, say, Goodstein sequences with 3 states.

If you read all the way to the end, congratulations!

Posted: **April 5th, 2023, 5:24 pm**

Edit: the new p61 gun was found by mvr.

Before this gets lost, here's the p61 gun that I found in a Catagolue update log, along with the link to the log:

Code: Select all

#C https://gitlab.com/hatsya/open-source/catagolue/-/jobs/4069285462
x = 48, y = 44, rule = B3/S23
7bob2o$7b2obo2$5b5o4b2o$4bo4bo5bo$3bo2bo8bob2ob2obo$3bob2o9bobobob2o$
2obo5bo7bo$bobo4bobo$o2b2o2bo2bo14b2o9b2o$2o6b2o15bo10b2o$23bobo4b2o$
23b2o4bobo2b4o$29bobobo4bo$30bobobobobo$32bobob2o4b2o$31bobo8bo$32bo7b
obo$40b2o$16b2o$15b2obo11bo$14bo3bo10b3o$4b2o9b3o10bo3bo$4b2o10bo11bob
2o$29b2o2$14bo$13bobo$9b2obobo30bo$8bobobobobo29b2o$8bo4bobobo27b2o$9b
4o2bobo4b2o$15b2o4bobo$9b2o10bo15b2o$9b2o9b2o14bo2bo2b2o$36bobo4bo$29b
o7bo5bob2o$23b2obobobo9b2obobo$23bob2ob2obo8bo2bo2bo$31bo5bo4bo2b2o$
31b2o4b5o2$36bob2o$36b2obo!

The previous design which was shown on Catagolue before is this:

Code: Select all

x = 101, y = 88, rule = B3/S23
28b2o$27bobo$21b2o4bo$19bo2bo2b2ob4o$19b2obobobo4bo$22bobobob2o31b2o$
22bob4o32bobo$23b2obo27b2o4bo$26bobo23bo2bo2b2ob4o$26b3o7b2o14b2obobob
obo2bo$24b2obo8bo18bobobobo$9bo14b2o8bobo18bobob2o$9b3o11b4o7b2o20bo$
12bo9b2o2bo$11b2o8b2o46b2o$60b2o7bo$60b2o5bobo$3b2o62b2o$3bo$2obo20b2o
$o2b3o4b2o13bo15bo$b2o3bo3b2o10b3o16b3o$3b4o15bo21bo5bobo45bo$3bo15b2o
bo13b2o5b2o5b2o45bobo$4b3o12bobob2o11bobo12bo5b2o5b3o30bobo$7bo13bo2bo
11bo21bo5bo14b2o15b2ob2o$2b5o8bo5b2o32b3o7bo13b2o19bo$2bo13bo38bo35b2o
3b4o$4bo9b3o73bo5bo$3b2o74b2o3b3o4bo6b2o$53b2o23bob2o2b5o10bo$46b2o5bo
bo21b2o4bo14bo$46b2o7bo22b2o3b3o3b2o7b2o$55b2o26b2o2b2o2$42bo$41bobob
2o$41bobobobo$38b2obobobobo2bo23b2o$38bo2bo2b2ob4o24bo$40b2o4bo25b3o$
46bobo23bo6b2o$29bobo15b2o30b2o4bo8b2o$30b2o51b2ob2o6bo$30bo52b2ob2o7b
3o$47bobo28bo5bob3o8bo$47b2obo26bobo3b3o$50bo27bo$26b2o19b3ob2obo20b3o
$25bobo2b2o14bo2bobob2o20bo$24bo2bobobo14b2o$24b2obobo$27bob2o$24b2obo
$22bo2bobo$22b2o2bo4b2o7b2ob2o$30bo2bo6bo3bo$22b2o2bo4b2o7bo3bo$22bo2b
obo13bobo4b2o$24b2obo14bo5bobo35b2o$27bob2o19bo35b2o$24b2obobo14b2o4b
2o$24bo2bobobo12bo48bob2o$25bobo2b2o5b2o6b3o45b2obo$26b2o9b2o8bo4b2o$
53bo$53bobo28b3o$29bo24bobo11b2o14bo2bo$28bobo24bo3b2o8bo12bo3b2o$28bo
bo28b2o8bobo10b3o$27b2ob2o38b2o11bo7bo$27bo62bobo$28b4o10bo30b2o6bo9b
2o$32bo9b2o28bo2bo4b6o$30bobo10b2o12b3o13bobo3bo7bo$30b2o11bo13bo16bo
5bo6bo$38b3obo15bo3b4o14bo$27b2o9b3o24b2o14bobo$26bobo32bo2bob2o$26bo
34b2obobo$25b2o35bob2o$63b2o$38b2o$38bo20b2o$39b3o18bo7b2o$41bo15b3o9b
o10bo$57bo8b3o12bo$66bo12b3o!

Posted: **April 26th, 2023, 8:36 am**

does anyone else think this should be nominated for (i meant OCADOTY) OCADOTY2023?

pipsqueek wrote: April 12th, 2023, 5:57 pma (2,1)c/51 knightship

Code: Select all

x = 10, y = 10, rule = B3-j4z/S2-in3-a4i5e6e7
6b3o$6bobo$5bo2bo$6bob2o$3bo3b2o$2bo4bo$2o7bo$o2b3ob2o$obo$b2o!

two of them can make a p462 OMOS!

Code: Select all

x = 62, y = 40, rule = B3-j4z/S2-in3-a4i5e6e7
11$37b3o$37bobo$36bo2bo$37bob2o$7b3o24bo3b2o$7bobo23bo4bo$7bo2bo20b2o
7bo$6b2obo21bo2b3ob2o$7b2o3bo18bobo$8bo4bo18b2o$6bo7b2o$7b2ob3o2bo$13b
obo$13b2o!

and another p312 OMOS!

Code: Select all

x = 17, y = 17, rule = B3-j4z/S2-in3-a4i5e6e7
12b2o$11b4o$9b2o4bo$9bo3bobo$9bo2b2o2bo$10b2obo2bo$12b2o$13bo2bo$13bo
2bo$2b3o9b3o$2bo2bo$bo3bo$2o2bobo$2ob6o$bo7bo$2b2o5bo$4b2ob3o!

p1386 OMOS!!

Code: Select all

x = 19, y = 10, rule = B3-j4z/S2-in3-a4i5e6e7
14bo$13bob2o$2bo9b2o2b3o$b3o9b3o2bo$2obo11bo$bo2bo10b3o$o4b2o9bo$b3o2b
2o$3b4o$4bo!

Posted: **April 26th, 2023, 8:37 am**

Speaking of POTY, when is the 2022 one happening?

Posted: **May 3rd, 2023, 12:13 pm**

Glider syntheses could be measured by the bounding box of the continuous synthesis.

This 4-glider synthesis would be 38 x 25 = 950 cells (the next generation is the first generation where neighbourhoods of two gliders intersect),

Code: Select all

x = 38, y = 25, rule = B3/S23
12bo$2bo8bo$obo8b3o$b2o5bo$7b2o$7bobo17$36b2o$35b2o$37bo!

while this 5-glider synthesis would be only 20 x 18 = 360 cells.

Code: Select all

x = 20, y = 18, rule = B3/S23
4bo$2bobo$3b2o5$11bo$obo7bo$b2o7b3o$bo2$9b2o$9bobo$9bo$17b3o$17bo$18bo!

Even if every constructible pattern can be constructed with only 15 gliders, the bounding-box metric would automatically prefer a different synthesis with more gliders but smaller bounding box.

Posted: **May 5th, 2023, 8:30 am**

pcallahan wrote: April 22nd, 2023, 3:58 pm Google Bard has a reputation for being a lot worse than C-----T, and it is certainly less expressive. I have found in some cases it's better at identifying song lyrics. It also gave me better answers about Conway's Game of Life infinite growth patterns (admittedly with errors). I have not compared it to C-----T 4 but should do so in the interest of fairness.

Here is a disclaimer. ColorfulGalaxy has an extremely doubtful attitude towards the robot.

Posted: **May 18th, 2023, 6:00 am**

hotdogPi wrote: April 26th, 2023, 8:37 am

Please help: conwaylife.com/forums/viewtopic.php?f=12&t=5852&p=161651#p161651

Posted: **May 21st, 2023, 11:13 pm**

Wonder if pretending some recently found CA was discovered a few decades ago would be comparable to pretending Conway's Life was just discovered. Remember that p328 RROMOS in 3/234/2eins3zwei4drei, discovered in 1973 by a reader of Rulegolfing Quarterly?

Posted: **June 4th, 2023, 6:00 am**

Oh, no, I may need another surgery. My eyes are getting worse.

Posted: **June 11th, 2023, 3:36 pm**

I guess I can put raoofha into the same category as Koiti Kimura, hiro-saki (and possibly ntdsc). Their understanding of some theories seems to be of alternative types, which I am not sure are suitable for conwaylife.com forums.

Posted: **June 25th, 2023, 4:33 am**

Today I learned that there is a chapter of the Rust Webassembly book dedicated to implementing the Game of Life.

Posted: **June 27th, 2023, 8:44 am**

just finished counting all of the conduits in the U-turner gallery. here are the results:

stable conduits:

4 U to Glider
4 U to B-heptomino
2 U to R-pentomino
2 U to Pi-heptomino
1 U to Herschel
2 U to Century
1 U to LoM
1 U to U
1 H to U

periodic conduits:

5 U to U
33 U to Glider
14 U to B-heptomino
11 U to R-pentomino
13 U to Pi-heptomino
8 U to Herschel
5 U to Century
2 U to Dove
5 U to Wing
2 U to I-heptomino
1 U to Octomino II
1 U to LoM
1 U to Two-glider octomino
3 U to Blonk-tie
1 U to E-heptomino
1 R-pentomino to U
2 Herschel to U

19 stable conduits and 108 periodic conduits, for a total of 127 conduits that input a U-turner and/or output it (110 of which were discovered by me).

Posted: **July 2nd, 2023, 1:51 am**

Could you help clean up ColorfulGalaxy's Neography Wiki?

Posted: **July 3rd, 2023, 12:01 am**

Citation needed wrote: July 2nd, 2023, 1:51 am Could you help clean up ColorfulGalaxy's Neography Wiki?

There was a lot of spam on the Hangulized English page, from seemingly random IP addresses.

Posted: **July 7th, 2023, 8:26 pm**

i don't know why, but there is something oddly entertaining in watching the r/SMG4 subreddit having a mini panic attack over whether or not Tari is gonna die on Saturday

Posted: **July 18th, 2023, 9:54 am**

Good news: my post count of Other Cellular Automata (570) has just overtaken that of Sandbox (569)*, and my post count in Thread for basic questions (96) has just surpassed that in Random posts (95)**.

*Before this post of course
**The old thread has been locked since 2021

I keep trying to improve quality of my posts, often comparing community reaction and the efforts in composing them.

---

Today's experiments in Glimmering Garden see an inadvertent catalyst formation...

Code: Select all

x = 25, y = 25, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7c
2o11bo$obo9bobo$bo11bo2$16bo$15bobo2bo$16bo2bobo$20bo2$22bo$21bobo$18b
o3bo$17b2o2b2o$18bo3bobo$21bob2o$22bo2$20bo$16bo2bobo$15bobo2bo$16bo2$
bo11bo$obo9bobo$2o11bo!

... and a transient transparent blinker.

Code: Select all

x = 20, y = 26, rule = B3-jknr4ity5ijk6i8/S23-a4city6c7cHistory
.A$3A$A.2A17$18.A$17.A.A$18.A2$2.3C13.A$17.A.A$18.A!

Posted: **July 20th, 2023, 12:37 am**

Some people like to talk about mathematics.
Some people like to talk about construction.
Some people like to talk about history.
Some people like to talk about terminology.
Some people like to talk about CA patterns.
Some people like to talk about CA rules.
Some people like to talk about Life.
Some people like to talk about life.
Some people like to talk about other people.
Some people like to talk about themselves.

Posted: **July 22nd, 2023, 12:43 pm**

pzq_alex wrote: July 22nd, 2023, 5:20 am Some thoughts:

Taking it here since it didn't really fit that thread:

Consolidate existing information/techniques. There are countless people in this community with an incredible amount of experience in some field. However, their expertise are often not so well-exposited to others, thus participating the fun wouldn't be possible to them. Earlier posts of the same idea: viewtopic.php?p=4397#p4397, viewtopic.php?p=128861#p128861.

Posted: **July 27th, 2023, 1:30 am**

From my perspective, a superconductor operating at room temperature and ambient pressure is as "too good to be true" as a natural elementary c/61 spaceship in Conway's Life.

A revolution in computer designing stimulated by superconductors would surely enhance soup-searching speed, though.

Posted: **July 29th, 2023, 4:58 am**

I'm posting this here, because it is technically not directly relevant to the questions of Life-specific terminology. It is a reference to a real-world analogy.

However, this is definitely relevant,

as long as one is interested in keeping meanings of terms sufficiently close to their intuitive meanings,
and generally, as long as one is interested in keeping explanations / descriptions of patterns sufficiently easy to read, for those people who cannot be expected to be able to follow all the ambiguous ill-defined jargon that may go in conversations.

dvgrn wrote: July 17th, 2023, 8:55 am Possible influence from a real-world definition
I've been thinking about this a bit more, and it occurred to me that there's one real-world sense of the word "signal" that seems like a particularly good match for the p128 oscillator that Jormungant posted.

Here is a sample use of "signal" to describe the repeating cyclic fluctuation in the AC power grid:

Power grids vary by nation. In the US, the grid is based on a highly stable 60-hertz signal, meaning it cycles 60 times per second.
I like the analogy to the cycling of signals in the p128 oscillator. I think this has also always been the "signal" analogy that works best for me, for things like the dependent p5 and p6 signal sources and sinks mentioned above.

To me at least, those "power towers" are not signal circuitry. They carry power, not signals.

A question on electronics.stackexchange.com: What's the difference between a power rail and a signal line?

A partial quote from one of answers:

user253751 wrote:Yes, both of them are wires, and provide paths for electrons to flow, so they are the same thing. But you may be missing a subtlety: the purpose of a power rail is to carry power (= energy), and the purpose of a signal line is to carry information. That means when designing a power rail we are more concerned with things like voltage drop and heat dissipation; when designing a signal line we are more concerned with things like interference and reflections.

The difference between "real-world" signal lines and "real-world" power lines is certainly significant and useful.

Similarly, there is a significant, useful difference between Life signals (somehow carried by active objects, or carried by sets of active objects, or carried by evolving reactions, or carried by temporarily existing stationary objects, ...) and Life active objects (gliders, LWSSes, Herschels, B-heptominoes, ...)

---

Part of my position is that LifeWiki would do much better without all the ill-defined jargon that might sometimes be understandable in conversations. Just because someone can use "signal" informally to refer to a moving object (rather than to some interesting information carried by it), doesn't mean there is a well-defined term here.

Posted: **August 4th, 2023, 11:54 pm**

Disaster16439 wrote: August 4th, 2023, 11:42 pm Doesn't that mean Live Free Or Die has a critical mass of 3? Also, critical mass is quite hard to measure, for DryLife critical mass would probably be around 7 or so(probably), and checking 2^49(minus symmetry) patterns won't be easy, that's 562,949,953,421,312 patterns(minus symmetry) to evolve!

drylife is 6.

Code: Select all

x = 3, y = 4, rule = B37/S23
o$2o$b2o$2bo!

(also i dont think this is threadworthy but i shouldn't complain)
Edit: sorry, no. thrn its probably around 6.5

Posted: **August 7th, 2023, 4:29 am**

Disaster16439 wrote: August 7th, 2023, 3:59 am
Wyirm wrote: January 2nd, 2022, 3:52 pm
Code: Select all
x = 3, y = 3, rule = B2e3-a/S23
bo$o$b2o!
p100. This may already be known, but it hasn't been posted here.
My oscillator collection says I rediscovered it on 4/8/2023, so it is possible that someone has discovered it before

Found Dec 2017 or earlier, according to catagolue: http://catagolue.hatsya.com/haul/b2e3-a ... 7b6180b4cd

ConwayLife.com

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Explanation of the new single-cell ship

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