Hexagonal rules

[LLAMASKYWALKER]

I think hexagonal rules should have their own topic.
I'm going to start this thread with a rule that i tried to make similar to life.
B3/S12o3H
This rule has quite a few oscillators and still life's, but no spaceships yet.
OSCILATORS:
p2 blinker

Code: Select all

x = 2, y = 3, rule = B3/S12o3H 
o$bo$bo!

p2 that i am calling nucleotide because it can be chained a bit like DNA:

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x = 21, y = 16, rule = B3/S12o3H
2$7b2o2$9b2o$10b2o$11b2o$4b2o$13b2o$4b2o8b2o$15b2o2$15b2o$15b2o$15b2o
!

p3

Code: Select all

x = 11, y = 6, rule = B3/S12o3H
2$4bobo$4bo2bo$5bobo!

nucleotide and still life hassling each other p6 :

Code: Select all

x = 12, y = 6, rule = B3/S12o3H
2$4b2o2bo$8bo$6b2o!

nucleotide and still life on still life p7

Code: Select all

x = 5, y = 6, rule = B3/S12o3H
2b2o$2b2o2$2ob2o$4bo$2b2o!

p2

Code: Select all

x = 5, y = 3, rule = B3/S12o3H
obo$bobo$2bobo!

p4 "snowflake"

Code: Select all

x = 5, y = 5, rule = B3/S12o3H
bo$2obo$3bo$b2obo$3bo!

p6

Code: Select all

x = 10, y = 3, rule = B3/S12o3H
2o2b3o$bob4ob2o$3b3o2b2o!

[yujh]

No. And further more these rules do not escape their bounding hexagon, and plenty more are searched in catagolue. You can post these in thread for your unrecognized CA which doesn’t specify that it needs to be Moore neighbourhood(you can even see MAP rules in that which can be Hexagonal rules anyways) another example is Muzak posting Hex LTL in the LTL thread , which means it doesn’t need to be another part of the OCA.(yet another reason why I don’t want to split the OCA board. Great)

[bprentice]

I think hexagonal rules should have their own topic.

Good idea!

Download Hexagonal Cell here:

http://bprentice.webenet.net/Hexagonal% ... 20Cell.zip

and run the 25 patterns in ../Patterns/Mites

Brian Prentice

[LaundryPizza03]

What about B0 hexagonal rules?

Code: Select all

x = 7, y = 18, rule = B023/S012H
bo$3o$4o$b4o$bob3o$b4obo$2b2ob2o$3b2o5$2b3o$b3obo$2ob3o$b4o$b6o$2b5o!

[yujh]

I think hexagonal rules should have their own topic.

Good idea!

Download Hexagonal Cell here:

http://bprentice.webenet.net/Hexagonal% ... 20Cell.zip

and run the 25 patterns in ../Patterns/Mites

Brian Prentice

Don’t advertise your program too much. Golly and lifeviewer already supports hexagonal rules. (And there’s obviously a bunch of research into these rules and got documented in catagolue)

[bprentice]

yujh,

Please don't tell me or others what to do. You are becoming a domineering complainer which is made worse by your lack of knowledge and ability.

Brian Prentice

[LLAMASKYWALKER]

What about B0 hexagonal rules?

Code: Select all

x = 7, y = 18, rule = B023/S012H
bo$3o$4o$b4o$bob3o$b4obo$2b2ob2o$3b2o5$2b3o$b3obo$2ob3o$b4o$b6o$2b5o!

Cool! is there any hexagonal life equivilant?

[hotdogPi]

Golly and lifeviewer already supports hexagonal rules.

Golly does not support INT hexagonal rules.

[yujh]

Golly and lifeviewer already supports hexagonal rules.

Golly does not support INT hexagonal rules.

well, at least lifeviewer does and for golly that's just some ruletables. I remmember when there is actually there was actually a very old version of apgsearch that is golly script and it searches 22da, although I do not know any scripts that generate them. At least apgsearch(funnily, not ikpx2) support them

[bprentice]

What does Golly and LifeViewer support hexagonal rules mean? Can either of these programs perform 60 degree rotations?

Brian Prentice

[hotdogPi]

What does Golly and LifeViewer support hexagonal rules mean? Can either of these programs perform 60 degree rotations?

Brian Prentice

If you ignore two of the four diagonal connections, you get a hexagonal grid. Rotating 60° isn't possible, though.

LifeViewer will try to make it look like hexagons if you're not too far zoomed out.

Code: Select all

x = 3, y = 3, rule = none
2B$BAB$.2B!

[bprentice]

The hexagonal version of Mites has 5 states and is based on these rules:

viewtopic.php?f=11&t=1352

The java step function code is:

Code: Select all

  public int step(int c, int r)
  {
    int cell = hexagonalCell.getCell(c, r);
    int NWNW = hexagonalCell.getCell(c - 1, r - 2);
    int NENE = hexagonalCell.getCell(c + 1, r - 2);
    int WW =   hexagonalCell.getCell(c - 2, r    );
    int W =    hexagonalCell.getCell(c - 1, r    );
    int E =    hexagonalCell.getCell(c + 1, r    );
    int EE =   hexagonalCell.getCell(c + 2, r    );
    int SWSW = hexagonalCell.getCell(c - 1, r + 2);
    int SESE = hexagonalCell.getCell(c + 1, r + 2);
    int NW, NE, SW, SE;
    if ((r % 2) == 0)
    {
      NW =   hexagonalCell.getCell(c - 1, r - 1);
      NE =   hexagonalCell.getCell(c    , r - 1);
      SW =   hexagonalCell.getCell(c - 1, r + 1);
      SE =   hexagonalCell.getCell(c    , r + 1);
    }
    else
    {
      NW =   hexagonalCell.getCell(c    , r - 1);
      NE =   hexagonalCell.getCell(c + 1, r - 1);
      SW =   hexagonalCell.getCell(c    , r + 1);
      SE =   hexagonalCell.getCell(c + 1, r + 1);
    }
    if (cell == 0)
    {
      if (((NWNW == 2) && (NW == 1)) ||
          ((NENE == 2) && (NE == 1)) ||
          ((WW == 2) && (W == 1)) ||
          ((EE == 2) && (E == 1)) ||
          ((SWSW == 2) && (SW == 1)) ||
          ((SESE == 2) && (SE == 1)))
        return 1;
      if ((((W == 1) && (NW == 3)) || ((SE == 1) && (E == 3))) ||
          (((NW == 1) && (NE == 3)) || ((SW == 1) && (SE == 3))) ||
          (((NE == 1) && (E == 3)) || ((W == 1) && (SW == 3))) ||
          (((E == 1) && (SE == 3)) || ((NW == 1) && (W == 3))) ||
          (((SE == 1) && (SW == 3)) || ((NE == 1) && (NW == 3))) ||
          (((E == 1) && (NE == 3)) || ((SW == 1) && (W == 3))))
        return 1;
    }
    else if (cell == 1)
      return 2;
    else if (cell == 2)
      return 0;
    else if ((cell == 3) || (cell == 4))
      return cell;
    return 0;
  }

Hexagonal Cell does support 60 degree rotations.

Brian Prentice

[bprentice]

Cool! is there any hexagonal life equivilant?

Yes, Paul Callahan wrote a nice rule several years ago. You can run his patterns in Hexagonal Cell. They are in directory ../Patterns/Paul Callahan.

See also file ../Notes/Paul Callahan Hexagonal CA.txt

Brian Prentice

[LLAMASKYWALKER]

Cool! is there any hexagonal life equivilant?

Yes, Paul Callahan wrote a nice rule several years ago. You can run his patterns in Hexagonal Cell. They are in directory ../Patterns/Paul Callahan.

See also file ../Notes/Paul Callahan Hexagonal CA.txt

Brian Prentice

Can you just tell me the rulestring?

[GUYTU6J]

Cool! is there any hexagonal life equivilant?

Yes, Paul Callahan wrote a nice rule several years ago. You can run his patterns in Hexagonal Cell. They are in directory ../Patterns/Paul Callahan.

See also file ../Notes/Paul Callahan Hexagonal CA.txt

Brian Prentice

Can you just tell me the rulestring?

See thread viewtopic.php?f=11&t=4914.
While I am incrementing my post count unwillingly, I have to complain again:
Why, seriously, doesn't users follow the good habit of searching forums on the topic before creating a new one? It is not that hard to find relevant threads like
viewtopic.php?f=11&t=1328, viewtopic.php?f=11&t=1579, viewtopic.php?f=11&t=2015, viewtopic.php?f=11&t=2117, viewtopic.php?f=11&t=1319 within a couple of minutes. Respect academic standards AND utilize internet resources!

[hotdogPi]

If you want a non-relativistic rule with spaceships, you're going to need B2o.

[yujh]

If you want a non-relativistic rule with spaceships, you're going to need B2o.

why you asking me that in discord and posting lol

[hotdogPi]

If you want a non-relativistic rule with spaceships, you're going to need B2o.

why you asking me that in discord and posting lol

I got the answer from you. I wouldn't have been able to post that here if you didn't answer.

[calcyman]

More interestingly, is there an outer-totalistic hexagonal rule capable of (say) universal computation and construction?

Paul Callahan wrote the following:

I'm fairly certain that there is no totalistic rule on a hex grid that supports the variety of interesting reactions found in Life, because if there were it would be better known. In any case, I checked briefly and found nothing promising. In particular B3/S23 (birth on three live neighbors, survival on 2 or 3, like Life) settles down very fast and doesn't seem likely to have spaceships. Birth on 2 neighbors is useful, because an axis-parallel front of 3 neighbors cannot occur in a hex grid. However, always having birth on 2 neighbors seems likely to cause uncontrolled growth.

B2 alone doesn't cause uncontrolled growth on a hexagonal grid (unlike on a square grid, in which case you get Seeds). Indeed, the two rules B2/S3 and B2/S34 are both apgsearchable, and don't contain any known infinite-growth patterns.

They do, however, contain rare natural spaceships: there's a period-14 glide-reflecting spaceship that's common to both rules:

https://catagolue.hatsya.com/object/xq1 ... z102/b2s3h

and a period-5 symmetric spaceship that only occurs in B2/S3:

https://catagolue.hatsya.com/object/xq5 ... 2021/b2s3h

They're so rare, though, that there's no obvious way to construct them or use them for signal circuitry.

[Hdjensofjfnen]

More interestingly, is there an outer-totalistic hexagonal rule capable of (say) universal computation and construction?

Another intriguing possibility would be the B0 rule B023/S2H, which contains this fairly common spaceship:

Code: Select all

x = 7, y = 4, rule = B023/S2H
o$b2o$4bo$6bo!

It also contains plentiful infinite growth in the form of wickstretchers, which support a few simple reactions:

Code: Select all

x = 29, y = 27, rule = B023/S2H
b27o$2ob26o$2b17ob5ob3o$19bob4obo$20b7o$20b4o2b2o$20bob7o$21b2obo2b2o$
21b4o$21b3o$21b3o$21b3o$21b3o$21b3o$21b3o$21b3o$21b3o$21b3o$21bobo$22b
2o$22bo4$b27o$2ob26o$2b27o!

EDIT: Also intriguing is B023/SH's linear replicator, though I'm not sure if a replicator signal can be deleted in this rule:

Code: Select all

x = 1, y = 2, rule = B023/SH
o$o!

EDIT 2: B023/S0H might be a bit tamer, allowing for more regular replicator behavior:

Code: Select all

x = 2, y = 22, rule = B023/S0H
bo$bo9$o$bo9$o$o!

[bprentice]

A screenshot of Hexagonal Cell running Mites:

Screen Shot 2022-03-17 at 12.10.35 PM.png (1.02 MiB) Viewed 1333 times

The pattern on the left evolves to the pattern on the right in 32 generations.

Brian Prentice

[Sarah]

???

Code: Select all

x = 58, y = 10, rule = B023/S2H
44bo$43b4o10bo$37b7obobo3bobo$34b2ob7ob10o$38b8o3b3o$50b4o$50bob3o$b50o
b3ob2o$2ob48ob4obo$2b51o3b2o!

[LLAMASKYWALKER]

p2 oscillators from the first rule

Code: Select all

x = 15, y = 10, rule = B3/S12o3H
5$2b2ob3o$3bobobo$5b2o!

Code: Select all

x = 4, y = 4, rule = B3/S12o3H
4o$bobo$2bo$3bo!

p4

Code: Select all

x = 5, y = 5, rule = B3/S12o3H
3obo$4bo$2bobo$3bo$4bo!

Code: Select all

x = 7, y = 4, rule = B3/S12o3H
2obo$bobo$2b4o$3b3o!

[confocaloid]

Partition the range-2 hexagonal neighbourhood into three 'layers' in the following way:

Code: Select all

    3 2 3
   2 1 1 2
  3 1 0 1 3
   2 1 1 2
    3 2 3

Let a cell in layer 3 have weight 1, let a cell in layer 2 have weight 7, and let a cell in layer 1 have weight 49. With this weighted neighbourhood, the rule B2/S34H has the following rulestring:

Code: Select all

R2,C0,S147-244,B98-146,NW01070100000731310700013100310100073131070000010701H

What is possible with toggling just one birth or survival condition (out of 343 x 2 possible conditions) away from this?

Adding S49 allows a common c/8 diagonal spaceship:

Code: Select all

x = 3, y = 4, rule = R2,C0,S49,147-244,B98-146,NW01070100000731310700013100310100073131070000010701H
2bo$obo2$2bo!

Adding S112 allows two common spaceships, a c/2o and a c/5o:

Code: Select all

x = 11, y = 5, rule = R2,C0,S112,147-244,B98-146,NW01070100000731310700013100310100073131070000010701H
bo6bo$8bo$2o6bo$2o7bo$2bo7bo!

Adding S21 allows this p73 oscillator:

Code: Select all

x = 3, y = 6, rule = R2,C0,S21,147-244,B98-146,NW01070100000731310700013100310100073131070000010701H
bo$o$obo$obo$2bo$bo!

Adding S64 results in a slightly explosive rule with this c/6o:

Code: Select all

x = 3, y = 5, rule = R2,C0,S64,147-244,B98-146,NW01070100000731310700013100310100073131070000010701H
o$o2$bo$2bo!

Adding S9 enables this symmetric explosion:

Code: Select all

x = 5, y = 5, rule = R2,C0,S9,147-244,B98-146,NW01070100000731310700013100310100073131070000010701H
obobo$2b2o$2b3o2$4bo!

Edit: changed weights of layers to simplify the rulestrings.

[confocaloid]

15c/30 orthogonal forerake, emits c/5 orthogonal gliders:

Code: Select all

x = 150, y = 35, rule = R2,C0,S21,112,147-244,B98-146,NW01070100000731310700013100310100073131070000010701H
57bobo$42bo9bo6b2o$39bob3o5bo3bo4bo2bo8bo$48b2o11b2o3b3o61bobo$42b2o5b
obo8b4o8b2o41bo9bo6b2o$43bo5bo9b3obo6b2ob2o37bob3o5bo3bo4bo2bo8bo$42bo
9bo6bo2bo3b2o4b2o47b2o11b2o3b3o$51bo63b2o5bobo8b4o8b2o$33bo26bobo53bo
5bo9b3obo6b2ob2o$115bo9bo6bo2bo3b2o4b2o$31bo2bo89bo$33bo72bo26bobo2$
56bo47bo2bo$4bo19bo33bo47bo$4bobo49bo2b2o23bo$o14bo6bo2bo4bo14bo13bo
23bo$5bobo16bo29bo3b3o5bo17bo12bo$bo4bo9bo14bo14bo24bo11b2o$54bo12bo3b
3o11b3o7bo2bo$25bo14bo15bo2bo6b3o3bo12bobo9bo$27bo14bo27bo4bo10bo9b2o$
60b2o6bo5bo6bo6bo$57bobobo6bo2bo9bo13b3o$58bobo7bobo2bo2bo21bo$58b2obo
12b6o19bo$56bobo19b2o48bo$6bo8bo8bo8bo8bo15bob3o13b2o47bo4bobo$6bo8bo
8bo8bo8bo14b2o17b2o52bo5bo3bo$7b2o7b2o7b2o7b2o7b2o14bobobo46b3o17bo10b
o4b2o$7bo8bo8bo8bo8bo15bob2o50bo12bo3bob3o5bobo2b2ob2o$8bo8bo8bo8bo8bo
16bo52bo10bo2b3o2bo8bo5b2o$127bob2o3bo9b2o$125bo2bobo3b4o2bo7bo$125bo
5bo4bo3bo!