ConwayLife.com

I want a rule with the most amount of unique spaceships found.
It needs to be categorized if it is totalistic or non-totalistic.
It should be non-explosive.
I would like rules with most unique speeds but it's fine even with the same velocity spaceships.
I like rules with still lives and oscillator but it's okay without them.
Example: Conway's game of life
or like this non-totalistic rule with many c/2: I don't actually know if these are unique spaceships: That rule also contains a still life and some oscillators along with an accidental discovery of two new oscillators with the glider synthesis: EDIT: I would like rules with many common spaceships from random soups just like the above example but it is fine even if the spaceships are not natural (found with searching).
Remember, most amount of unique spaceships.

Now how about your examples?
EDIT: I want most spaceships small in the rule and something not adjustable but you can ignore this suggestion.

Life has ℵ_0 speeds (for instance, caterloopillars), which is the maximum cardinality possible (since all speeds are triples of natural numbers). I'm also pretty sure that HighLife has that number of replicator ship speeds, too.

There are also a great deal of non-totalistic rules with an infinite series of spaceship speeds (see this thread for examples).

I'm not so sure about the rule with the most natural spaceships, but it's probably a rule where there are a ton of fast spaceship components that can be combined together in all sorts of was (like an S4i rule).

JP21's phrasing suggests they are not looking for rules with adjustable but rather rules with the most known distinct spaceship mechanisms. Hive (B3-ry4ckn/S2-in3-cjn4it5aiky6-a7e8) seems like it would be a good example of a rule in this direction.

Among totalistic rules, Day and Night is probably among the most prolific for different (non-adjustable) speeds. There are elementary spaceships at 16 different speeds, although most of them are not natural.

I'm sure there are also numerous isotropic NT rules which have spaceships of many different speeds, but I can't think of any in particular off-hand. [Wrote this before 77topaz's post - Hive is a great example]. There will be some which have many different unique speeds findable with gfind/zfind and others which have many different natural spaceships found by apgsearch. Unfortunately there's any way to query Catagolue for how many unique speeds are present in any particular rule - Catagolue doesn't even really know a spaceship's speed so the best you could do is unique periods, but even for that there's no nice API to get that info.

One rule that does come to mind is this one found by AforAmpere. It has five different 3-cell spaceships - each with unique speeds. Being so small those spaceships are all natural and the rule is not explosive. There are many more spaceships known in the rule, but not as many different speeds as Day and Night.

wildmyron wrote: December 18th, 2019, 3:18 amOne rule that does come to mind is this one found by AforAmpere. It has five different 3-cell spaceships - each with unique speeds. Being so small those spaceships are all natural and the rule is not explosive. There are many more spaceships known in the rule, but not as many different speeds as Day and Night.

What a very amazing rule!!!
It is so incredible!!!
Now, is there anymore of them?

BUMP!
I made a rule with 4 unique c/3 spaceships: Edit: Boring few spaceships rule lol: