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Those phoenix patterns are fascinating. the width 8 one seems to have a few errors though. Aaaaargh! That means the rle routine isn't right in my code. ... Or that the phoenix finding part is bad. (I had checked the top of the pattern for a few generations, but evidently not for enough (446 * 2 or ...

B34/S03456 has no phoenixes with period = 3.

See viewtopic.php?f=11&t=1323#p11194

B34/S03456 has something in common with GoL: There are no phoenixes of period 3 here, either. (Since there are two birth rules, the proof is a little more complicated than Stephen Silver's proof in GoL, but it follows the same idea.) Theorem: There are no finite phoenixes in B34/S03456 of period >= ...

This is an accidental discovery if there ever was one. I started off by looking for a phoenix of period 2 in the CA B34/S03456, and I came up with the following: x = 8, y = 446, rule = B34/S03456 3b2o$$b2ob2o$5bo$bo$2o3b2o$6bo$bo$bo4b2o$3bobo$b2o3bo$o4bo$$2o3bobo$2bo2bobo$$2b2o2bo$bo4b o$6bo$b2o3bo$...

Those phoenix patterns are fascinating. the width 8 one seems to have a few errors though. Aaaaargh! That means the rle routine isn't right in my code. ... Or that the phoenix finding part is bad. (I had checked the top of the pattern for a few generations, but evidently not for enough (446 * 2 or ...

Just to keep things simple, let's say a "phoenix" is an oscillator in which no cells ever survive. In which rules can they exist, and which periods can they have? Are there any Life-like CAs where you'd like this question answered in particular, for period 2? Then there's the rule B345/S. There are...

Here's a phoenix of width 6 and period 2. (The narrowest phoenix in regular Life has width 8.) x = 6, y = 12, rule = B34/S03456 2bo$2bobo$o3bo$obobo$2bo2bo$2o$4b2o$o2bo$bobobo$bo3bo$bobo$3bo! and one of width 7 and period 2 which looks extendable: x = 7, y = 33, rule = B34/S03456 2b2o2$b2ob2o$bo$5bo...

Here's a few oscillators I've found of periods, 3,4,5,6, and 7. Have you found any phoenixes? (Phoenices?) Haven't found a spaceship yet, but while searching I did find this creature which extends at c/2. Neat ... It's something that grows, yet it isn't "tar" ... What software did you use to search?

...but then I noticed that you can put two of them together, to make: x = 7, y = 2, rule = B34/S03456 boboo$2o2bobo! but unfortunately, it also has period 2. I seem to be missing some key detail here. When I copy this into Golly, it appears to be period 4, as does any linear extension of it: I must...

The reason I started looking at this CA is because of Eppstein's "most wanted" page; https://www.ics.uci.edu/~eppstein/ca/wanted.html It lists several CAs which he thinks have gliders/space ships, but which he has been unable to find any. He says that it is "one of the rules studied by Wolfram. An e...

I can't remember exactly, back that far.

Most likely, it was in my junior high years, around the mid 1980s. I probably heard about it from someone via the first edition of Winning Ways.

This post also connects with the "useless discoveries" thread elsewhere in this forum. By looking at random fields and this rule, I found an oscillator that everyone has probably seen: x = 4, y = 2, rule = B34/S03456 bo$2obo! but then I noticed that you can put two of them together, to make: x = 7, ...