HexLife

[Saka]

This is hexlife, Life but on a hexagonal grid, still lifes are very common, here is the rule table:

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@RULE HexLife

@TABLE
n_states:2
neighborhood:hexagonal
symmetries:rotate6reflect

#Birth
0,1,1,1,0,0,0,1
#Death
1,0,0,0,0,0,0,0
1,1,0,0,0,0,0,0
1,1,1,1,1,0,0,0
1,1,1,1,1,1,0,0
1,1,1,1,1,1,1,1

Here are sample oscillators:
p2:

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x = 4, y = 4, rule = HexLife
2bo$b2o$o2bo$2o!

p8:

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x = 6, y = 6, rule = HexLife
3bo$3b2o$5bo$2ob3o$bobo$2b2obo!

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x = 9, y = 7, rule = HexLife
3o$bobo$4bo$5bo$5bo$5bobo$6b3o!

I have yet to find any spaceships

[John]

I'm new to this, but I think your rule is a restricted version of B3/S6H. I don't think hexagonal gliders are possible without some B2 because without, a pattern can't leave it's bounding box. Specifically, I think it needs 01100001.

[Saka]

I'm new to this, but I think your rule is a restricted version of B3/S6H. I don't think hexagonal gliders are possible without some B2 because without, a pattern can't leave it's bounding box. Specifically, I think it needs 01100001.

Hi john! Hexagonal gliders ARE possible, look at 22da

[gmc_nxtman]

Yes, hexagonal gliders are possible, but in 22da there is birth on 2 neighbors. Think about spaceships - in order for a spaceship to move, it has to leave its initial bounding box. With birth on three neighbors, it would normally allow for spaceships - but in a restricted, hexagonal neighborhood, b3 doesn't make spaceships possible. You have to add b2 or b1 (and b1 just explodes). Consider, in another lifelike rule, what happens to this pattern:

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x = 32, y = 20, rule = B45678/S012345678
2bo5b7o3bobo2bo3b2o2bo$4o6b2o2b2ob4o2bo2b3obo$4o2b4o2bo3b2ob2obo2bobob
o$2o3b3o2b5o4b2o2b4o$obo2bo2bobo6bo2b2ob2o6bo$4o6bo2bobo3bob2o2bo2bobo
$5b2obobob4o3bobob3o2b2o$3bo2bo4b3obob2ob2o4b3ob2o$o2bo5b3o2b3o2b2o6bo
b3o$4bo2bo5bo3bo3bobo2b4obo$b2o2b8ob2o3b4ob8o$2o3bo2bo5b2o6bob4o2bo$b
4o6bo4bobob2o2b6o$3ob2obob2obo2b2o2bo3b5obobo$3b4ob3o5b2obo5b5obo$bo2b
ob3o2b5obo4bobo3bo$3ob3o2bo4b3ob2ob4o2bobobo$2b2o2b5o3b2o2bo3bobo3bobo
$3o5b3o3b4o6bob2obo$o3b5o3b4obobo2b3o2b3o!

Note that the pattern's bounding box gets filled with cells, but no cells are born outside the box. This is because of the lack of b0,1,2, or 3. (b1 explodes, b0 is a special case). Now take the hexagonal neighborhood(marked in asterisks):

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.....
.**..
.*.*.
..**.
.....

There is no point at which B3 can allow bounding box escaping. Therefore, in a hexagonal rule without B1 or B2 gliders are not possible.

[wildmyron]

This is hexlife, Life but on a hexagonal grid, still lifes are very common, here is the rule table:

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@RULE HexLife

@TABLE
n_states:2
neighborhood:hexagonal
symmetries:rotate6reflect

#Birth
0,1,1,1,0,0,0,1
#Death
1,0,0,0,0,0,0,0
1,1,0,0,0,0,0,0
1,1,1,1,1,0,0,0
1,1,1,1,1,1,0,0
1,1,1,1,1,1,1,1

The rule table actually implements B3/S236 because of an erroneous 1 in the last row of the table.

There is an earlier thread which has some examples of spaceships in other semi-totalistic rules on hexagonal neighbourhoods, as well as links to other sites with relevant information. As already mentioned, hexagonal rules without B0, B1 or B2 can not support spaceships.

Also, please note that Golly's QuickLife algorithm is natively able to simulate these rules, as Andrew mentions on the old thread. Simply append H to the rulestring, e.g. B3/S23H

[John]

Oh, I forgot that for an unlisted set of inputs, the input cell remains unchanged. Thanks!