ConwayLife.com

I was experimenting with some one-cell-thick patterns today, and found myself wondering the following:

Are there any one-cell-thick patterns that grow without bound orthogonally to the initial row of cells, while remaining bound on the other axis? E.g. if the initial cells are laid out in a horizontal line, can it grow to infinite height (in both directions, of course), while remaining within a finite range of x coordinates?

All it would take would be a pair of LWSSs and no errant gliders. Has anyone ever constructed such a pattern? Is there reason to believe it doesn't exist?

PaulKwiatkowski wrote: May 6th, 2025, 2:27 am [...] Are there any one-cell-thick patterns that grow without bound orthogonally to the initial row of cells, while remaining bound on the other axis? [...] All it would take would be a pair of LWSSs and no errant gliders. [...]

If I understand correctly, the second pattern quoted below answers your question (and I suggest to read the forum thread from which this is quoted):

AbhpzTa wrote: July 10th, 2017, 7:01 am [...]
2 pure LWSS generators:

Code: Select all

x = 172, y = 91, rule = B3/S23
6ob4ob3ob7ob5ob4ob4o14b5o5b4ob10ob3ob3ob3ob3o2b3o11b4o3b3o90$6ob4ob3ob
7ob5ob4ob4o24b5ob4o6b4o6b5ob3o7b5o5b4ob10ob3ob3ob3ob3o2b3o11b4o3b3o!

Another thread that's worth looking at for questions like this is the unidimensional spaceship thread.

The universal construction mechanism discussed there can produce a complete working unidimensional spaceship -- whenever someone gets around to finishing the tricky job of patching the remaining pieces together. That mechanism is eminently capable of building any glider-constructible object, in mirrored pairs on either side of an initial one-cell-thick line.

Thank you both so much for those replies!

Yes, that "2 pure LWSS generators" pattern does indeed answer my question, and those are now two of my favorite Life patterns ever. As for the thread, what a wonderful rabbit hole to fall into!

And that's amazing that any glider-constructable object can be built from a single row of live cells. Should these be referred to as "holograms"?