In B01245/S01245, I found a class of stable and unstable spaceships that I call spearheaders. Most spearheaders are c/2 orthogonal—but there is a very interesting exception. Here are three examples:
Code: Select all
x = 50, y = 4095, rule = B01245/S01245
4048$46b3o$45bobobo$45b5o$45b5o$47bo$47bo$46b3o$46bobo31$b3o20b3o$obobo18bobobo$5o17bob3obo$5o17b7o$b2obo17b7o$2bo19b7o$22b7o$22b7o$24b5o!
The spearheders on the left and right are stable, but the middle one is not. Playing the LifeViewer to when the spaceships going direction up go off the screen reveals that the spearheader family includes a replicator.
Many spearheaders are methuselahs. For example, the middle spearheader in the above LifeViewer takes 24,987 generations to stabilize—if the word stabilize is even applicable given that it spawned a replicator beforehand. The spearheader that lasts the longest that I know of lasts for 40,126 generations before dying.
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x = 7, y = 6, rule = B01245/S01245
2b3o$bobobo$ob3obo$7o$7o$6o!
It starts with four eyes, but it goes down to three eyes around generation 38870 (just after birthing another three-eyed spearheader, which soon dies from crashing into some debris that its parent had left) then two eyes around generation 39890. (Spearheaders with more eyes tend to be more stable, but they can have a maximum of four eyes. In fact, the two times that the spearheader loses the eye are because it tried to get three eyes on one side.) Also, the spearheader birthed several other spearheaders before dying (although most died shortly afterward), so there might also be another replicator. It's actually fairly common for spearheaders that live for long enough to birth other spearheaders. For example, there's another spearheader that I found that may be a methuselah lasting longer than the one above, but I gave up on tracking it after it became four spearheaders.
Code: Select all
x = 7, y = 13, rule = B01245/S01245
2b3o$bobobo$b5o$b5o$b5o$b5o$3b4o$4b2o$ob2o$2o3b2o$o2bob2o$bobo$4b2o!
Here are two more interesting spearheaders. The first is a stable spaceship with a large period.
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x = 23, y = 48, rule = B01245/S01245
3$10b3o$9bobobo$8bob3obo$8b7o$8b6o$9b4o$8b5obo$7b7o$10bo3bo$9b4ob2o$13bo$8bobo2bo$8b6o$9b4o$9bo2bo8$8b4o$7b5o$4b9o$6b5o$4b7o$6b3ob2o$4b2o2b5o$6b3o8$11bo$10b2o$10bo$11bo$11bo!
The other starts out with two eyes but then gains two more. This is relatively rare because a two-eyed spearheader will typically die before it has time to do that.
Code: Select all
x = 7, y = 13, rule = B01245/S01245
2b3o$bobobo$b5o$b5o$b5o$b5o$3b4o$4b2o$ob2o$2o3b2o$o2bob2o$bobo$4b2o!
Because four-eyed spearheaders tend to last longer, this is also a methuselah lasting for over 15,000 generations. (I don't know the exact number for the same reason as before: It became multiple spearheaders traveling in different directions.)
I'd be interested in seeing any stable rakes or a second replicator.
I am tentatively considering myself back.
