ConwayLife.com

Posted: **September 28th, 2019, 7:27 pm**

All of the following may not apply to non-INT rules.

For a pattern to escape its bounding box, it must have one of the following:

Code: Select all

B0, B1e, B1c, B2a, B2c, B3i

For a pattern to escape its bounding diamond, it must have one of the following:

Code: Select all

B0, B1e, B1c, B2a, B2e, B3a

If a pattern cannot escape its bounding box or diamond, it does not support spaceships.

For lightspeed spaceships to exist, a rule needs one of the following:

Code: Select all

B0, B1e, B1c, B2a

For no-survival spaceships to exist: a rule needs one of the following (CONJECTURE, PLEASE PROVE/DISPROVE):

Code: Select all

B0, B1e, B1c, B2a, B2c

B1c cannot support spaceships, unless B0 is present.

At least one death transition is required for spaceships or oscillators to exist.

If a pattern has XY symmetry, it cannot be a spaceship.
If a pattern has less than 3 cells, it must have XY symmetry.
If a pattern is smaller than 2x2, it must have XY symmetry.

All spaceships that are not diagonal or orthogonal must be asymmetrical.

Posted: **September 29th, 2019, 6:26 am**

Heavpoot wrote:All of the following may not apply to non-INT rules.

For a pattern to escape its bounding box, it must have one of the following:
Code: Select all
B0, B1e, B1c, B2a, B2c, B3i
For a pattern to escape its bounding diamond, it must have one of the following:
Code: Select all
B0, B1e, B1c, B2a, B2e, B3a
If a pattern cannot escape its bounding box or diamond, it does not support spaceships.

I remember seeing a rule without all those requirements which nonetheless escaped is bounding box/diamond and had a ship somewhere. It had b4a, I think

Posted: **September 29th, 2019, 7:15 am**

Moosey wrote: I remember seeing a rule without all those requirements which nonetheless escaped is bounding box/diamond and had a ship somewhere. It had b4a, I think

You'll have to find it.

Meanwhile, I've made a spreadsheet to see what survival single transitions (e.g. 4a) and double-transitions (e.g. 2a4i) are needed to support c/2o spaceships in rules with no lightspeed ships and no B2c (and B0).
It can be found at:
https://docs.google.com/spreadsheets/d/ ... sp=sharing

Yes, some rules don't support c/2o ships but do support slower speeds such as c/3o, but I can't really be bothered to do the searches again right now.

You can contribute by running LLS searches for period 2 c/2o spaceships with a 15x15 (or larger) bounding box. If you decide to run searches for c/3o or some other speed and do find one, make the box green with the text "c/3o", but please only run those c/3o searches for transition / transition combinations that have no c/2o spaceships (AKA the red-boxed ones).

For the double-transition table, only fill the boxes in the bottom half.

Template LLS command

Code: Select all

./lls -S lingeling -s p2 x1 -b 15 15 -p ">0" -r pB2-ac345678/S

Remember you have to exclude the transitions you don't want, instead of only putting the transition you want (So for S2i it's not pB2-ac345678/S2i but pB2-ac345678/S2-cekan)

Posted: **September 30th, 2019, 7:50 am**

Earlier well-known results are "published" here by D. Eppstein:

https://www.ics.uci.edu/~eppstein/ca/glider.c

Posted: **September 30th, 2019, 12:43 pm**

Surely spaceships couldn't at all exist in B1c (no B0) rules since all patterns explode in every direction?

Posted: **October 1st, 2019, 8:36 am**

Moosey wrote:
Heavpoot wrote:All of the following may not apply to non-INT rules.

For a pattern to escape its bounding box, it must have one of the following:
Code: Select all
B0, B1e, B1c, B2a, B2c, B3i
For a pattern to escape its bounding diamond, it must have one of the following:
Code: Select all
B0, B1e, B1c, B2a, B2e, B3a
If a pattern cannot escape its bounding box or diamond, it does not support spaceships.
I remember seeing a rule without all those requirements which nonetheless escaped is bounding box/diamond and had a ship somewhere. It had b4a, I think

I was wrong, but there was a ship in a rule with S0123 or whatever utilizing a lack of S4a

ConwayLife.com

Some theories I have, feel free to contribute

Some theories I have, feel free to contribute

Re: Some theories I have, feel free to contribute

Re: Some theories I have, feel free to contribute

Re: Some theories I have, feel free to contribute

Re: Some theories I have, feel free to contribute

Re: Some theories I have, feel free to contribute