Uber Breeders?

[greenaurorakitty]

Hey: I'm new here , so excuse my not knowing anything, but can anyone show me a rake/breeder? I really want to see that.
For example, is there a
Rake that spits out puffers that spits out guns ?

Is there also a Breeder that makes breeders? (or a breeder that can make itself, so that can make its, leading to countless exponential cells?) Thanks!!!

[greenaurorakitty]

I just want to see if this is possible. If this only works in the 3rd dimension, tell me, but maybe you could use a hyperbolic plane...

[biggiemac]

Unfortunately, a pattern beginning in a finite bounding box can experience at most quadratic population growth, just because nothing can turn on a cell of distance N from the edge of the bounding box until N generations have passed. However, there are some rakes/etc with sublinear growth that might afford a thing-makes-things-that-make-things-that-make-things pattern. I am not sure whether one has been explicitly constructed though.

To use a hyperbolic plane, one would need to set up a new system of nearest neighbors, and the rule would no longer be the well-researched Life we know.. Perhaps 4-coordinated pentagonal, or 3-coordinated heptagonal or octagonal rules on hyperbolic geometry would do incredible things..

At least to get the hang of what conventional breeders look like, there's a folder in Golly/Patterns/Life called Breeders that has a bunch of varieties.

Edit: In fact, I wouldn't be surprised if Conway himself thought to some degree about cellular automata on hyperbolic surfaces - this page where I went to visualize the 4-coordinated pentagonal tiling actually has a reference from a book he wrote.

[Tropylium]

To use a hyperbolic plane, one would need to set up a new system of nearest neighbors, and the rule would no longer be the well-researched Life we know.. Perhaps 4-coordinated pentagonal, or 3-coordinated heptagonal or octagonal rules on hyperbolic geometry would do incredible things..

I've done some very preliminary investigation on this, and a general problem with any hyperbolic spaceships is that the sides need to travel much faster than the bow. E.g. on a right pentagonal tiling, we can sketch numerous axes of paired cells; but already these cells' neighbors will be three cells apart from each other between different steps, rather than just one.

If you attempted to translate the moon into Hyperbolic Seeds for example, you'll discover that the bow still takes off at the speed of light, but the "wings" will lag behind and break off; after four generations you have only a domino left. From there on, the pattern stabilizes into a single-axis replicator.

Life-analogous B3 rules moreover cannot support spaceships, as any finite pattern can be encased inside a convex boundary where all edges have a length of at most 2.

I haven't proven this in detail, but this appears to be to be sufficient to show that one-state outer totalistic CA rules on a right pentagonal tiling are incapable of supporting spaceships: all patterns must either grow infinitely or settle into stationary ash. Some B2 rules might be able to support puffers, though…