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Close life variants

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Re: Close life variants

Postby BlinkerSpawn » December 31st, 2015, 9:29 am

Compactified version of M. I. Wright's ship:
x = 33, y = 86, rule = B35j_S23
12b3o3b3o$11bo3bobo3bo$15bobo$10bo4bobo4bo$10bo11bo$10bo3bo3bo3bo$11b
3o5b3o5$11bobo5bobo$11b3o5b3o$12bo7bo4$6bo$5b3o$4bo3b2o$3b2o4bo7b3o$2b
3o2bo2bo6b2o$9b2o6b2o$9b2o$8b3o4bo$8b2o5b3o$16b2o3$12b3o3b3o9b2o$12bob
o3bobo9bobo$11bo2bo3bo2bo9b2o$11bobo5bobo$11b3o5b3o2$9bo13bo$9bo13bo$b
2o8bo9bo$obo7b2obo5bob2o$2o9bo2bo3bo2bo$12b2o5b2o5$30b2o$30bobo$5b4o5b
o4b2o10b2o$4bo2b2o3b2o5b2o$3bo5bo9bo$4bo2b2o9bo$5b2o8bobo$6bo2bo4b2obo
$b2o4bobo4b2obo$obo5bo5b4o$2o13b2o3$12b3o3b3o$11bo3bobo3bo$15bobo$10bo
4bobo4bo$10bo11bo8b2o$10bo3bo3bo3bo8b2o$11b3o5b3o5$11bobo5bobo$2o9b3o
5b3o$2o10bo7bo2$9b2o3b2ob2o3b2o$8bobo3b2ob2o3bobo$7b2o5b2ob2o5b2o$23b
2o$14b2ob2o4bo$14bo3b5o8b2o$13b2o4b3o9b2o$4b2o14bo$2bo$6bo$2b2o3bo4bo$
3b2o7bo$4b3o!

EDIT: And reduction of the other half of the backrake:
x = 171, y = 120, rule = B35j_S23
18bo5bo27bo5bo$17b3o3b3o24b2ob2ob2ob2o$17bobo3bobo24b2ob2ob2ob2o$16bob
o5bobo24b2o5b2o22b3o3b3o25b3o3b3o26bo5bo$17bo7bo23b2ob2o3b2ob2o19bo3bo
bo3bo24bobo3bobo24b2ob2ob2ob2o$17bo7bo23b2ob2o3b2ob2o23bobo27bo2bo3bo
2bo23b2o7b2o$13bo15bo21bo7bo20bo4bobo4bo22bobo5bobo24bo7bo$13bobo11bob
o50bo11bo22b3o5b3o21bo3bobobobo3bo$50bo9bo19bo3bo3bo3bo53bobo11bobo$
14b3obo5bob3o22bo7bo21b3o5b3o21bo13bo18bo15bo$16b2obo3bob2o86bo13bo19b
2o11b2o$18bo5bo24bo2bo5bo2bo53bo9bo23bob2o3b2obo$50b3o5b3o53b2obo5bob
2o23b3o3b3o$115bo2bo3bo2bo$81bobo5bobo24b2o5b2o$81b3o5b3o$82bo7bo$18bo
$17bo3b2obo5b2o12b3o$17bo6bo4b2ob2o9bo3bo10bo92bobobo$18bo5bo7b2o8bo2b
ob2o8bo38bo53bo6bo$19bo8b3ob2o8bo3bobo7b2o37b3o11b4o5bo4b2o26bo4b2o5b
3o$20bobo8bo10bo4b2o44b2o3bo9bo2b2o3b2o5b2o21bo5b4o6b2obo$21b2o5b3o17b
o6bo2bo24b3o7bo4b2o7bo5bo9bo22bo15bo2bo$20bo3bo3b3o13bo3bo4bo4bo25b2o
6bo2bo2b3o7bo2b2o9bo39bobo$21bo2bo23bo6bo28b2o6b2o15b2o8bobo32b2o5b3o$
21b2o24bo7b2o35b2o16bo2bo4b2obo31bo2bo$87bo4b3o16bobo4b2obo32b3o$6b2o
77b3o5b2o17bo5b4o36bo$5bobo77b2o32b2o14bo$5b2o59bo3b3o61bob5o$65bob2o
64b2ob4obo$65b4o65bo$67bo4bobo60b2o2bo3bo$75bo60bo6bo$71bo3bo66bo$71bo
3bo$75bo$72bo2bo92b2o$73b3o92bobo$169b2o4$6b2o$5bobo58b2o$5b2o58bo2bo$
66bobo$67bo6$168b2o$168bobo$16b3o3b3o144b2o2$16bo2bobo2bo$17b3ob3o$6b
2o6bo11bo$5bobo5b4o7b4o38b2o$5b2o6bo3bo5bo3bo16b3o3b3o12bo2bo$43bo3bob
o3bo12bobo$15b3o5b3o21bobo17bo$42bo4bobo4bo$42bo11bo$42bo3bo3bo3bo$43b
3o5b3o$14b2ob2o3b2ob2o$15bobo5bobo142b2o$16bo7bo143bobo$169b2o$30bo12b
obo5bobo18bobo$28bo2bo11b3o5b3o21bo75b3o3b3o$27bo16bo7bo18bo3bo75bobo
3bobo$6b2o10bo7bo5b2o37bo3bo75bo2bobo2bo$5bobo10b2o6bo3b2o2bo31b2o7bo
78bobo$5b2o13bo4b2obo3bobo30bo2bo3bo2bo72b2o4bobo4b2o$19bo5b3o5bo4bo
27bobo4b3o71b2o13b2o$37b3o27bo52b3o3b3o21bobo5bobo$20bo15bo3b2o78bobo
3bobo21bobo5bobo$21b2o12b2o4bo7b3o68bo2bobo2bo22b2o5b2o$34b3o2bo2bo6b
2o72bobo$41b2o6b2o38b3o3b3o19b2o4bobo4b2o$6b2o33b2o45bo3bobo3bo17b2o
13b2o$40b3o4bo44bobo24bobo5bobo38b2o$3bob3o32b2o5b3o37bo4bobo4bo19bobo
5bobo19b2ob2o3b2ob2o6bobo$2bobo43b2o37bo11bo20b2o5b2o20bo3bo3bo3bo7b2o
$bo85bo3bo3bo3bo50b3o5b3o$bo3b2o81b3o5b3o$65b3o$bo2bob2o56bo3bo$o2bo2b
2o55bo4bo92b2o3b3o$b2o3b2o56bo2bo53b2o3b2o25b2o6b2o3bobo$6bo81bobo5bob
o53bo2bo5b2o2bo3bo$67b2o19b3o5b3o16bo6b2ob2o26bo7bo4b2obo$63bo3b2o20bo
7bo16bo2b2obo2bo2b2o3bobo27bo5b2o$64bo2bo45bo3b3o11bobo27bo$65bo20b2o
3b2ob2o3b2o13bo3b2o12bo$85bobo3b2ob2o3bobo13b7o$84b2o5b2ob2o5b2o15b2o
5bo$100b2o21b2o43b2o$91b2ob2o4bo18b5o44bobo$91bo3b5o20b2o18b2o27b2o$
90b2o4b3o21bo13b2o3bo2bo$97bo35b3o2bo3b2o$134bob3o3bo$137b2o3bo$89bo
46b2o$79b2o2b2o4bo$81b3o2$72bobo$75bo$71bo3bo$71bo3bo$75bo$72bo2bo$73b
3o!
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Re: Close life variants

Postby bdm68 » January 1st, 2016, 4:17 am

I have found a ruleset similar to Conway's Game of Life with some differences. It uses a modification of the Moore neighbourhood to determine neighbours. As such, I don't know if it belongs here or if this thread is limited to cellular automata where all neighbours use the Moore neighbourhood with a weight of 1.

The family of automata I have been experimenting with modify the Moore neighbourhood by assigning orthogonal neighbours a weighting different to the diagonal neighbours. For example, Orthogonal = 3 and Diagonal = 1:

1 3 1
3 * 3
1 3 1

Using this modified Moore neighbourhood, I have found an automaton of particular interest with a ruleset of B578/S4567. Because the Moore neighbourhood is different, I will need to use an ad hoc extension to describe this rule completely: N31 (orthogonal cells have a weight of 3 and diagonal cells have a weight of 1). Under this extended notation, the ruleset is B578/S4567/N31. Life's ruleset is B3/S23/N11.
This modified Moore neighbourhood considers cells that are diagonally adjacent to be farther away.

It produces results similar to Life with some differences. For example, the glider, lightweight spaceship, middleweight spaceship and heavyweight spaceship all work normally but some still lifes behave differently.

The smallest pattern I have found so far that is different is the Tub. In the B578/S4567/N31 ruleset, the tub disappears after one generation. In general, diagonally-connected still lifes tend to die out. Some other patterns:

Block - same
Tub - disappears after one generation
Boat, Long Boat- turns into a Block after 2 generations
Aircraft Carrier - turns into two Blocks after 17 generations
Barge - disappears after one generation
Beehive - disappears after 3 generations
Ship - same
Snake - same
Eater1 - disappears after 10 generations
Loaf - turns into a Block after 3 generations
LongSnake - turns into a 3-state oscillator (2 Blocks) after 2 generations
R Pentomino - turns into two Blocks after 8 generations
Blinker - same

Interesting patterns found:
5 x 2 block: 12-period oscillator

It is interesting that the glider and spaceships work identically but many smaller patterns do not.

Another related ruleset that produces similar results is B789(10)/S5678/N32.
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Re: Close life variants

Postby BlinkerSpawn » January 1st, 2016, 10:22 am

Is this an accurate N31 template?
@RULE B578_S4567_N31
@TABLE
n_states:2
neighborhood:Moore
symmetries:rotate4reflect
#no B1
0010000000
#no B2
0010100000
0010001000
#no B3
0100000000
0010101000
#no B4
0110000000
0100100000
0010101010
#B5
0110100001
0110001001
0110000011
0100101001
#no B6
0101000000
0100010000
0110101000
0110100010
#B7
0111000001
0101100001
0101001001
0110010001
0110101011
#B8
0111100001
0111001001
0110110001
0110011001
0110010011
#no B9
0101010000
0111101000
0101101010
0110111000
#no B10
0111010000
0101011000
0111101010
0110111010
#no B11
0111110000
0111011000
0111010010
#no B12
0101010100
0111111000
0111011010
#no B13
0111010100
0111111010
#no B14
0111110100
0111011100
#no B15
0111111100
#no B16
0111111110
#no S0
1000000000
#no S1
1010000000
#no S2
1010100000
1010001000
#no S3
1100000000
1010101000
#S4
1110000001
1100100001
1010101011
#S5
1110100001
1110001001
1110000011
1100101001
#S6
1101000001
1100010001
1110101001
1110100011
#S7
1111000001
1101100001
1101001001
1110010001
1110101011
#no S8
1111100000
1111001000
1110110000
1110011000
1110010010
#no S9
1101010000
1111101000
1101101010
1110111000
#no S10
1111010000
1101011000
1111101010
1110111010
#no S11
1111110000
1111011000
1111010010
#no S12
1101010100
1111111000
1111011010
#no S13
1111010100
1111111010
#no S14
1111110100
1111011100
#no S15
1111111100
#no S16
1111111110
@COLORS

0 0 0 0
1 255 255 255
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Re: Close life variants

Postby drc » January 1st, 2016, 12:49 pm

BlinkerSpawn wrote:Is this an accurate N31 template?
@RULE B578_S4567_N31
@TABLE
n_states:2
neighborhood:Moore
symmetries:rotate4reflect
#no B1
0010000000
#no B2
0010100000
0010001000
#no B3
0100000000
0010101000
#no B4
0110000000
0100100000
0010101010
#B5
0110100001
0110001001
0110000011
0100101001
#no B6
0101000000
0100010000
0110101000
0110100010
#B7
0111000001
0101100001
0101001001
0110010001
0110101011
#B8
0111100001
0111001001
0110110001
0110011001
0110010011
#no B9
0101010000
0111101000
0101101010
0110111000
#no B10
0111010000
0101011000
0111101010
0110111010
#no B11
0111110000
0111011000
0111010010
#no B12
0101010100
0111111000
0111011010
#no B13
0111010100
0111111010
#no B14
0111110100
0111011100
#no B15
0111111100
#no B16
0111111110
#no S0
1000000000
#no S1
1010000000
#no S2
1010100000
1010001000
#no S3
1100000000
1010101000
#S4
1110000001
1100100001
1010101011
#S5
1110100001
1110001001
1110000011
1100101001
#S6
1101000001
1100010001
1110101001
1110100011
#S7
1111000001
1101100001
1101001001
1110010001
1110101011
#no S8
1111100000
1111001000
1110110000
1110011000
1110010010
#no S9
1101010000
1111101000
1101101010
1110111000
#no S10
1111010000
1101011000
1111101010
1110111010
#no S11
1111110000
1111011000
1111010010
#no S12
1101010100
1111111000
1111011010
#no S13
1111010100
1111111010
#no S14
1111110100
1111011100
#no S15
1111111100
#no S16
1111111110
@COLORS

0 0 0 0
1 255 255 255

No:

x = 5, y = 13, rule = B578_S4567_N31
3bo$4bo$o3bo$b4o7$bo$2bo$3o!
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Re: Close life variants

Postby BlinkerSpawn » January 1st, 2016, 4:43 pm

The sections of the template consisting of sum-8 neighbor sets seems to be the issue there.
I should have stated my earlier question differently: Could the rule table above be modified (by changing trailing zeros to ones and vice versa) to emulate any given N31 rule?
Evidently not due to the aforementioned error. If anyone can send me a fixed table (so I can edit in the correct template) or find another problem, that would be great.
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Re: Close life variants

Postby drc » January 1st, 2016, 9:14 pm

bdm68 wrote:I have found a ruleset similar to Conway's Game of Life with some differences. It uses a modification of the Moore neighbourhood to determine neighbours. As such, I don't know if it belongs here or if this thread is limited to cellular automata where all neighbours use the Moore neighbourhood with a weight of 1.

The family of automata I have been experimenting with modify the Moore neighbourhood by assigning orthogonal neighbours a weighting different to the diagonal neighbours. For example, Orthogonal = 3 and Diagonal = 1:

1 3 1
3 * 3
1 3 1

Using this modified Moore neighbourhood, I have found an automaton of particular interest with a ruleset of B578/S4567. Because the Moore neighbourhood is different, I will need to use an ad hoc extension to describe this rule completely: N31 (orthogonal cells have a weight of 3 and diagonal cells have a weight of 1). Under this extended notation, the ruleset is B578/S4567/N31. Life's ruleset is B3/S23/N11.
This modified Moore neighbourhood considers cells that are diagonally adjacent to be farther away.

It produces results similar to Life with some differences. For example, the glider, lightweight spaceship, middleweight spaceship and heavyweight spaceship all work normally but some still lifes behave differently.

The smallest pattern I have found so far that is different is the Tub. In the B578/S4567/N31 ruleset, the tub disappears after one generation. In general, diagonally-connected still lifes tend to die out. Some other patterns:

Block - same
Tub - disappears after one generation
Boat, Long Boat- turns into a Block after 2 generations
Aircraft Carrier - turns into two Blocks after 17 generations
Barge - disappears after one generation
Beehive - disappears after 3 generations
Ship - same
Snake - same
Eater1 - disappears after 10 generations
Loaf - turns into a Block after 3 generations
LongSnake - turns into a 3-state oscillator (2 Blocks) after 2 generations
R Pentomino - turns into two Blocks after 8 generations
Blinker - same

Interesting patterns found:
5 x 2 block: 12-period oscillator

It is interesting that the glider and spaceships work identically but many smaller patterns do not.

Another related ruleset that produces similar results is B789(10)/S5678/N32.


I wish there was a script to produce this.
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Re: Close life variants

Postby BlinkerSpawn » January 1st, 2016, 10:42 pm

drc wrote:
bdm68 wrote:(A bit about B578/S4567/N31)


I wish there was a script to produce this.

The script wouldn't be too complicated:
Obtain rulestring (with a-z representing 10-35, if necessary)
Write the ruletable to {rulestring}.rule up to where transitions begin (no symmetry)
For each possible set of neighbors:
      Write "0{neighbor set}", then 1 if ortho weight * ortho neighbors + diag weight * diag neighbors is included in the birth string, otherwise write 0.
      Write a newline character.
      Write "1{neighbor set}", then 1 if ortho weight * ortho neighbors + diag weight * diag neighbors is included in thesurvival string, otherwise write 0.
      Write a newline character.
Add a @COLORS file, if desired.

Unfortunately, I don't know Python yet, but I'd be surprised if this ran to more than, say, fifty lines.
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Re: Close life variants

Postby bdm68 » January 2nd, 2016, 5:42 am

drc wrote:
bdm68 wrote:(snip) long description of B578/S4567/N31.

I wish there was a script to produce this.

I wrote a quick and dirty script in PHP to simulate this rule. It took about an hour to write the first version and was about 150 lines before I started adding code to initialise the grid with specific patterns. (It would be somewhat smaller except my coding style eschews inline if statements). The script was general enough to allow simulation of a variety of rules by changing a few variables.

$orthogonal_weight = 3;
$diagonal_weight = 1;
$survive = array(4, 5, 6, 7);
$birth = array(5, 7, 8);


Here is how neighbours are counted. It takes the weightings into account.
// xy is a two-dimensional array of cells, populated with 0 or 1
// x and y are the coordinates of the cell being tested
function neighbors($xy, $x, $y)
{
   global $maxc; // size of grid
   global $orthogonal_weight;
   global $diagonal_weight;
   
   $result = 0;
   for ($i = -1; $i <= 1; $i++)
   {
      if ($x + $i >= 0 && $x + $i < $maxc) // bounds check
      {
         for($j = -1; $j <= 1; $j++)
         {
            if ($y + $j >= 0 && $y + $j < $maxc && abs($i) + abs($j) > 0) // bounds check, also ignore current cell
            {
               if ($i == 0 || $j == 0) // orthogonal
               {
                  $result += $xy[$x + $i][$y + $j] * $orthogonal_weight;
               }
               else
               {
                  $result += $xy[$x + $i][$y + $j] * $diagonal_weight;
               }
            }
         }
      }
   }
   return $result;
}

Note that the neighbours function includes a bounds check and in common with many bounded grids doesn't work properly at the edges of the grid.

Here is the function that calculates the new state of the current cell. This also has a bounds check.
function newstate($xy, $x, $y)
{
   global $maxc;
   global $birth;
   global $survive;
   
   $result = 0;
   if ($x >= 0 && $x < $maxc && $y >= 0 && $y < $maxc) // bounds check
   {
      $n = neighbors($xy, $x, $y);
      
      if ($xy[$x][$y] == 0)
      {
         if (in_array($n, $birth))
         {
            $result = 1;
         }
      }
      else
      {
         if (in_array($n, $survive))
         {
            $result = 1;
         }
      }
   }
   return $result;
}

The rest of the code should not be particularly difficult to anyone who has written it before. I can post it if you want. It's about 450 lines of quick and dirty PHP (most of it is 300 lines for the "populate" initialisation function), it may have a few bugs and it requires a working Apache installation and web browser to use.
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Re: Close life variants

Postby bdm68 » January 2nd, 2016, 7:54 am

The four most common soup patterns with B578/S4567/N31 appear to be:

Old patterns: Block (very common) and Blinker.

Ship and "Twin Blinker" (2-state oscillator, more common than Blinker)
# # . . . . . . . # . #
# . # . . . . . . # . #
. # # . . . . . . # . #

Gliders are also fairly common.

Rarer patterns of interest:
3-state oscillator:
"Diblock"
. . . # #
# # . # #
# # . . .

4-state oscillator:
"Bowl"
# . . #
# . . #
. # # .

12-state oscillators:
"Brick"
# # # # #
# # # # #

"3/4 Circle"
. # # # .
# . . . #
. . . . #
. . . . #
. . . # .


Edit: corrected name of Ship.
Last edited by bdm68 on January 2nd, 2016, 4:22 pm, edited 1 time in total.
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Re: Close life variants

Postby drc » January 2nd, 2016, 12:23 pm

bdm68 wrote:The rest of the code should not be particularly difficult to anyone who has written it before. I can post it if you want. It's about 450 lines of quick and dirty PHP (most of it is 300 lines for the "populate" initialisation function), it may have a few bugs and it requires a working Apache installation and web browser to use.
[/quote][/quote]
I can't code python :(
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Re: Close life variants

Postby A for awesome » January 2nd, 2016, 2:41 pm

A rule table for B578/S4567/N31:
@RULE B578_S4567_N31
@TABLE
n_states:2
neighborhood:Moore
symmetries:none
var a={0,1}
var aa=a
var ab=a
var ac=a
var ad=a
var ae=a
var af=a
var ag=a
1,1,1,0,0,0,0,0,0,1
1,1,0,1,0,0,0,0,0,1
1,0,1,1,0,0,0,0,0,1
0,1,1,1,0,0,0,0,0,1
1,1,1,1,0,0,0,0,0,1
1,1,0,0,1,0,0,0,0,1
0,1,1,0,1,0,0,0,0,1
1,1,1,0,1,0,0,0,0,1
1,0,0,1,1,0,0,0,0,1
0,1,0,1,1,0,0,0,0,1
1,1,0,1,1,0,0,0,0,1
0,0,1,1,1,0,0,0,0,1
1,0,1,1,1,0,0,0,0,1
0,1,1,1,1,0,0,0,0,1
1,1,0,0,0,1,0,0,0,1
1,0,1,0,0,1,0,0,0,1
0,1,1,0,0,1,0,0,0,1
1,1,1,0,0,1,0,0,0,1
1,0,0,1,0,1,0,0,0,1
0,0,1,1,0,1,0,0,0,1
1,0,1,1,0,1,0,0,0,1
1,0,0,0,1,1,0,0,0,1
0,1,0,0,1,1,0,0,0,1
1,1,0,0,1,1,0,0,0,1
0,0,1,0,1,1,0,0,0,1
1,0,1,0,1,1,0,0,0,1
0,1,1,0,1,1,0,0,0,1
0,0,0,1,1,1,0,0,0,1
1,0,0,1,1,1,0,0,0,1
0,0,1,1,1,1,0,0,0,1
1,1,0,0,0,0,1,0,0,1
0,1,1,0,0,0,1,0,0,1
1,1,1,0,0,0,1,0,0,1
1,0,0,1,0,0,1,0,0,1
0,1,0,1,0,0,1,0,0,1
1,1,0,1,0,0,1,0,0,1
0,0,1,1,0,0,1,0,0,1
1,0,1,1,0,0,1,0,0,1
0,1,1,1,0,0,1,0,0,1
0,1,0,0,1,0,1,0,0,1
1,1,0,0,1,0,1,0,0,1
1,1,1,0,1,0,1,0,0,1
0,0,0,1,1,0,1,0,0,1
1,0,0,1,1,0,1,0,0,1
0,1,0,1,1,0,1,0,0,1
1,0,1,1,1,0,1,0,0,1
1,0,0,0,0,1,1,0,0,1
0,1,0,0,0,1,1,0,0,1
1,1,0,0,0,1,1,0,0,1
0,0,1,0,0,1,1,0,0,1
1,0,1,0,0,1,1,0,0,1
0,1,1,0,0,1,1,0,0,1
0,0,0,1,0,1,1,0,0,1
1,0,0,1,0,1,1,0,0,1
0,0,1,1,0,1,1,0,0,1
0,0,0,0,1,1,1,0,0,1
1,0,0,0,1,1,1,0,0,1
0,1,0,0,1,1,1,0,0,1
1,0,1,0,1,1,1,0,0,1
0,0,0,1,1,1,1,0,0,1
1,1,0,0,0,0,0,1,0,1
1,0,1,0,0,0,0,1,0,1
0,1,1,0,0,0,0,1,0,1
1,1,1,0,0,0,0,1,0,1
1,0,0,1,0,0,0,1,0,1
0,0,1,1,0,0,0,1,0,1
1,0,1,1,0,0,0,1,0,1
1,0,0,0,1,0,0,1,0,1
0,1,0,0,1,0,0,1,0,1
1,1,0,0,1,0,0,1,0,1
0,0,1,0,1,0,0,1,0,1
1,0,1,0,1,0,0,1,0,1
0,1,1,0,1,0,0,1,0,1
0,0,0,1,1,0,0,1,0,1
1,0,0,1,1,0,0,1,0,1
0,0,1,1,1,0,0,1,0,1
1,0,0,0,0,1,0,1,0,1
0,0,1,0,0,1,0,1,0,1
1,0,1,0,0,1,0,1,0,1
0,0,0,0,1,1,0,1,0,1
1,0,0,0,1,1,0,1,0,1
0,0,1,0,1,1,0,1,0,1
1,0,0,0,0,0,1,1,0,1
0,1,0,0,0,0,1,1,0,1
1,1,0,0,0,0,1,1,0,1
0,0,1,0,0,0,1,1,0,1
1,0,1,0,0,0,1,1,0,1
0,1,1,0,0,0,1,1,0,1
0,0,0,1,0,0,1,1,0,1
1,0,0,1,0,0,1,1,0,1
0,0,1,1,0,0,1,1,0,1
0,0,0,0,1,0,1,1,0,1
1,0,0,0,1,0,1,1,0,1
0,1,0,0,1,0,1,1,0,1
1,0,1,0,1,0,1,1,0,1
0,0,0,1,1,0,1,1,0,1
0,0,0,0,0,1,1,1,0,1
1,0,0,0,0,1,1,1,0,1
0,0,1,0,0,1,1,1,0,1
0,0,0,0,1,1,1,1,0,1
1,1,0,0,0,0,0,0,1,1
0,1,1,0,0,0,0,0,1,1
1,1,1,0,0,0,0,0,1,1
1,0,0,1,0,0,0,0,1,1
0,1,0,1,0,0,0,0,1,1
1,1,0,1,0,0,0,0,1,1
0,0,1,1,0,0,0,0,1,1
1,0,1,1,0,0,0,0,1,1
0,1,1,1,0,0,0,0,1,1
0,1,0,0,1,0,0,0,1,1
1,1,0,0,1,0,0,0,1,1
1,1,1,0,1,0,0,0,1,1
0,0,0,1,1,0,0,0,1,1
1,0,0,1,1,0,0,0,1,1
0,1,0,1,1,0,0,0,1,1
1,0,1,1,1,0,0,0,1,1
1,0,0,0,0,1,0,0,1,1
0,1,0,0,0,1,0,0,1,1
1,1,0,0,0,1,0,0,1,1
0,0,1,0,0,1,0,0,1,1
1,0,1,0,0,1,0,0,1,1
0,1,1,0,0,1,0,0,1,1
0,0,0,1,0,1,0,0,1,1
1,0,0,1,0,1,0,0,1,1
0,0,1,1,0,1,0,0,1,1
0,0,0,0,1,1,0,0,1,1
1,0,0,0,1,1,0,0,1,1
0,1,0,0,1,1,0,0,1,1
1,0,1,0,1,1,0,0,1,1
0,0,0,1,1,1,0,0,1,1
0,1,0,0,0,0,1,0,1,1
1,1,0,0,0,0,1,0,1,1
1,1,1,0,0,0,1,0,1,1
0,0,0,1,0,0,1,0,1,1
1,0,0,1,0,0,1,0,1,1
0,1,0,1,0,0,1,0,1,1
1,0,1,1,0,0,1,0,1,1
1,1,0,0,1,0,1,0,1,1
1,0,1,0,1,0,1,0,1,1
0,1,1,0,1,0,1,0,1,1
1,1,1,0,1,0,1,0,1,1
1,0,0,1,1,0,1,0,1,1
0,0,1,1,1,0,1,0,1,1
1,0,1,1,1,0,1,0,1,1
0,0,0,0,0,1,1,0,1,1
1,0,0,0,0,1,1,0,1,1
0,1,0,0,0,1,1,0,1,1
1,0,1,0,0,1,1,0,1,1
0,0,0,1,0,1,1,0,1,1
1,0,0,0,1,1,1,0,1,1
0,0,1,0,1,1,1,0,1,1
1,0,1,0,1,1,1,0,1,1
1,0,0,0,0,0,0,1,1,1
0,1,0,0,0,0,0,1,1,1
1,1,0,0,0,0,0,1,1,1
0,0,1,0,0,0,0,1,1,1
1,0,1,0,0,0,0,1,1,1
0,1,1,0,0,0,0,1,1,1
0,0,0,1,0,0,0,1,1,1
1,0,0,1,0,0,0,1,1,1
0,0,1,1,0,0,0,1,1,1
0,0,0,0,1,0,0,1,1,1
1,0,0,0,1,0,0,1,1,1
0,1,0,0,1,0,0,1,1,1
1,0,1,0,1,0,0,1,1,1
0,0,0,1,1,0,0,1,1,1
0,0,0,0,0,1,0,1,1,1
1,0,0,0,0,1,0,1,1,1
0,0,1,0,0,1,0,1,1,1
0,0,0,0,1,1,0,1,1,1
0,0,0,0,0,0,1,1,1,1
1,0,0,0,0,0,1,1,1,1
0,1,0,0,0,0,1,1,1,1
1,0,1,0,0,0,1,1,1,1
0,0,0,1,0,0,1,1,1,1
1,0,0,0,1,0,1,1,1,1
0,0,1,0,1,0,1,1,1,1
1,0,1,0,1,0,1,1,1,1
0,0,0,0,0,1,1,1,1,1
1,a,aa,ab,ac,ad,ae,af,ag,0

And the script that generated it:
import golly as g
def bits(n):
    l = []
    for i in xrange(8):
        l.append((n&2**i)/2**i)
    return l
rule = g.getstring("Enter rule in B_S_N format")
parsed = rule.replace("B","").replace("S","").replace("N","").split("_")
for i in xrange(3):
    parsed[i] = [int(j) for j in parsed[i]]
table = "@RULE "+rule+"""
@TABLE
n_states:2
neighborhood:Moore
symmetries:none
var a={0,1}
var aa=a
var ab=a
var ac=a
var ad=a
var ae=a
var af=a
var ag=a"""
for i in xrange(256):
    b = bits(i)
    b2 = [str(n) for n in b]
    ws = 0
    for i in xrange(len(b)/2):
        ws += b[2*i]*parsed[2][0]
        ws += b[2*i+1]*parsed[2][1]
    if ws in parsed[0]:
        table += "\n0,"+",".join(b2)+",1"
    if ws in parsed[1]:
        table += "\n1,"+",".join(b2)+",1"
table += "\n1,a,aa,ab,ac,ad,ae,af,ag,0"
g.setclipstr(table)

Be warned, it copies the table directly to the clipboard without asking first.
x₁=ηx
V ⃰_η=c²√(Λη)
K=(Λu²)/2
Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)

$$x_1=\eta x$$
$$V^*_\eta=c^2\sqrt{\Lambda\eta}$$
$$K=\frac{\Lambda u^2}2$$
$$P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$

http://conwaylife.com/wiki/A_for_all

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Re: Close life variants

Postby rowett » March 18th, 2016, 8:21 am

The next version of LifeViewer contains support for Alan Hensel's isotropic non-totalistic rule format (from neighbors2).
I've added two aliases already:
  • tlife B3/S2-i34q
  • dlife 23/3-n
If you want your favourite Hensel-format alias supported then please give me the alias name and the Hensel string.
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Re: Close life variants

Postby ygh » June 15th, 2016, 9:43 pm

New B578_S4567_N31 oscillator!

x = 5, y = 5, rule = B578_S4567_N31
2bo$2ob2o$2bo$2ob2o$2bo!


Toads still work:
x = 2, y = 4, rule = B578_S4567_N31
o$2o$2o$bo!


Triple Blinker?
x = 4, y = 5, rule = B578_S4567_N31
bo$bo$o2bo$bobo$bobo!


LWSS works:
x = 4, y = 5, rule = B578_S4567_N31
3o$o2bo$o$o$bobo!
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Re: Close life variants

Postby Rhombic » August 7th, 2016, 6:31 am

This close life variant has a similar "ant" (or beetle, since it's a bit larger) to tlife, quite common:
x = 5, y = 5, rule = B34k5i/S23
4bo$4bo$bo2bo$o2bo$b2o!


There is a recurring pattern, a familiar -five-:
x = 4, y = 3, rule = B34k5i/S23
3o$o2bo$b2o!
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Re: Close life variants

Postby Rhombic » August 8th, 2016, 4:52 am

A common xp30 in a tLife-like rule:
x = 4, y = 3, rule = B36ci7c/S2-i34q
3o$2obo$3o!
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Re: Close life variants

Postby Rhombic » August 9th, 2016, 3:12 pm

Nice oscillators:
x = 5, y = 5, rule = B2n3/S2-i34j
3b2o$3bo$4bo$2o2bo$ob3o!

x = 6, y = 6, rule = B2n3/S2-i34j
2o$2o$2bobo$3bobo$2bo2bo$3b2o!
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Re: Close life variants

Postby LVGuy » August 15th, 2016, 9:14 pm

p12 in B578/S4567/N31 is just a 2x5 block

x = 2, y = 5, rule = B578_S4567_N31
2o$2o$2o$2o$2o!
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Re: Close life variants

Postby Rhombic » August 16th, 2016, 4:32 am

LVGuy wrote:p12 in B578/S4567/N31 is just a 2x5 block

x = 2, y = 5, rule = B578_S4567_N31
2o$2o$2o$2o$2o!


In fact, it closely resembles a phi spark that never dies :) but without the phi phase!

--

Two gliders are an oscillator:
x = 6, y = 6, rule = B578_S4567_N31
bo$b2o$obo$3b2o$4b2o$3bo!


Natural LWSS:
x = 50, y = 50, rule = B578_S4567_N31
2obob4o3bo2b4o3b7obobo2b2obob2o3b2o$2bo8bobo2bobo3b2ob2o2b2obob3obo3bo
bo2bobo$5b2o4b4o2b2ob3o3b3o2bo3b6ob2o2bo2bo$5b2obo5bob3o3b2obo2b2o2bob
3o2bobob3o2bo$b2ob4obo6b2o2bob2o2b2ob2o2bob3o4b4ob3o$b3o2b2ob2ob5ob11o
2b4o4b3obo2bo2bo$2bobobo2bobo2bo3bo4bo7b9o2b2o2bo$2b2ob2ob2ob2o2b2o4bo
bob3o2b2obo2bob3ob2obobobo$4b2obob3obo5b2o3b3o3bobobob5o2bo2b3o$b6o2bo
6bo3bo3b4ob6o2bobo3bo2b2obo$b3obobobo2b2o2bob2obo3bo9b3ob2ob2o3bobo$ob
o2bob4ob2o2b2obobob4ob4obob5obo3bobo$bob5o2bobo3b2o2bob2obobobo2b3obo
3bo2b2o3bo$4bo2bobobobobo3b2o4bobo2bob2o3b2o2bo3b4o$3obobob4o5b2obob2o
b3o2b4o2bob2o2bo2b2ob2o$obo3bo2b3obo2bob2ob2o2bo2b2o2b2ob2ob2obobo4b2o
$5obobob3ob3o2b2o5bo2bo2bob2o5bob3o2bo$obobobob3obobo2bo2b3obo2b3ob2o
2bo3bobo2bob3o$4b3o2b2o2bo2bo2b5o3b3o4bo4b2o2bobobobo$bob3obobob2obo2b
2ob4obo2bo5b5o4bo2bo2bo$o4bo2bo2b2ob3o3b2o4b2ob7o3bo9bo$obo4bobobo6bob
2obo2bo3b2obobob3o2b3o3bo$2b3o2bob3o3bob2ob2ob3o2bob3o6b2o2bob2o$5o3b
3o2bo2b2o2b2o2bo10b2ob6obo3bo$bob4obo2bobobo2bo2b2o2bo6b2obob3obobob2o
b2o$o3b3ob3o3bob2o3b4o5bo2bob3o2bobobo$bo7b2o2bobo5b2o2bo2bo2bobobobob
ob2obo3b2o$b2o2bo4b2o3bo6bobob2o2bo4b2ob2obobob4o$bo3bo3b7o2bob2obobob
ob4obob3ob2o4b3o$bobobo2b6obo2bobobo6b3obo6bo2bo2bo2bo$2o2b3o2bo2b2ob
3o2bob3o2bob2o3bob2obob2o2bo2b2o$3b4obo2b6obob2obo3bo2b2o2b2o3b2ob3ob
2obo$2b3obobob3obobobobo2bobob5obo2b4obobo2bobo$b3o4bo6bobob3o6bo2b3o
2b4obo3b2o2bo$2ob4o5bob2obob3o2bob2ob2ob2obo2bo2bo3bobobo$2b2o7b3ob6o
3bob3o2b4o4bo2b2o$ob2obo2b3o6bo3bo2bob2ob4obo2b4ob3o3b2o$o2b2obob2o2bo
2bo2b2obob2o2bob2o2b2obo2bo5b3obo$b2o4bo2b4o4bob9obo2bobo2b2o2b2o2b2o$
b2o2bobo3bo3b5ob3o3b2o8bo2b4obo2b2o$2o4bo4b3ob4ob2ob3obo2bob4o2bobob2o
b3obo$2o5b2ob2obobob2o2bob4o4b4ob7o3bo$2obobobob2ob4o3b2o2b2ob2o2bobo
2b2o3bo2bobobobo$2ob4o2bobo2b3o2b2obo3b4ob8obob2o$2b2o7bob2ob3o2b4obob
obobobo2bo4bob5o$2b2ob2o2b3obobob2o2bo3bobob2o3b2o2b2o3bo3bo$2bob3o2b
2ob2o2bo2bo2b7o2bobo2b6o3bobobo$b2o2b4o3b2o2bo2bob3obob3ob3obobo2b3ob
2ob3o$obobo3bob2ob3ob4o2b6o5bob2ob8o2bo$obo4b4obobo2bo2b2o3bob2o3bo5bo
b3obobo2bo!
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Re: Close life variants

Postby LVGuy » August 16th, 2016, 11:16 am

p2 in B578/S4567/N31 evolves from a herschel and is just 2 blinkers next to eachother :D
x = 3, y = 3, rule = B578_S4567_N31
obo$obo$obo!

p3 is a beacon
x = 4, y = 4, rule = B578_S4567_N31
2o$2o$2b2o$2b2o!
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Re: Close life variants

Postby Bullet51 » August 16th, 2016, 12:08 pm

Useless P10:
x = 8, y = 5, rule = B578_S4567_N31
2bo2bo$2bo2bo$b2o2b2o$3o2b3o$3o2b3o!
Still drifting.
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Re: Close life variants

Postby Rocknlol » August 16th, 2016, 9:55 pm

A collection of oscillators in B578/S4567/N31 (which the rule below is identical to):
x = 174, y = 156, rule = B3-ce4aikqtwz5e/S2-cn3-ce4cny5e
159b2o2b2o$159bobo2bo$163bo$156b2o2bo5b2o$156bobo3bobo2bo$160bo5bo$
153b2o2bo5bo5b2o$117bo9bo10bobo12bobo3bobo3bobo2bo$7bobobo85bo18bo2bo
5bo2bo9bobobo14bo5bo5bo$97bobo6b2o2b2o4bo2bo5bo2bo7bo13b2o2bo5bo5bo5b
2o$11bo45b3o17bo7bobo7bo10bo2bobo5bo2bo5bo16b2o5bobo3bobo3bobo3bobo2bo
$42bo6b3o14b3o6b2ob2o5bo2b2o10b2o5bo21b2o4b2o17bo5bo5bo5bo$7bobobo12b
3o5b3o7bobo13b2o17bo6bo2bo6b2o14bo8b2o22b2o6bo5bo5bo5bo$33b3o5bobo5b3o
14b2ob2o4b2ob2o5bo2b2o10bo5bobo2bo17b2o4b2o13bo2bobo3bobo3bobo3bobo$7b
o35bo14b3o7bo8bo7bobo8bobo7b2o2b2o5bo2bo5bo16bo6b2o5bo5bo5bo2b2o$98bo
17bo2bo5bo2bo8bobobo12bo5bo5bo$7bobobo104bo2bo5bo2bo10bobo11bo2bobo3bo
bo3bobo$117bo9bo25b2o5bo5bo2b2o$157bo5bo$156bo2bobo3bobo$156b2o5bo2b2o
$160bo$159bo2bobo$159b2o2b2o5$7bobobo2$11bo12b2o5b2o$24b2o5bo$7bobobo
22bo$25b2o6b2o$11bo13b2o2$7bobobo12$7bo3bo2$7bo3bo$32bo$7bobobo13b2o5b
2obo$24b4o4bob2o$11bo23bo2$11bo12$7bobobo$29b2o$7bo3bo16bo$28bo$7bobob
o15bo2bo$25b2o2bo$7bo3bo12bo3bo$24bo2bo$7bobobo12$4bo2bobobo$25b4o$4bo
2bo3bo12b2o2b2o$24bo4bo$4bo2bo3bo13bo2bo$26b2o$4bo2bo3bo2$4bo2bobobo
12$4bo2bobobo$37bo$4bo6bo24bo$24b5o7bo$4bo2bobobo12b5o7bo3bo$37b3o$4bo
2bo2$4bo2bobobo11$31b2o11b2o$30bobo11bobo$29bo2bo11bo2bo22b3o$30b2o13b
2o22bo3bo$31bo13bo$26bo23bo$25bobo21bobo17bo3bo$24bo2b2o19b2o2bo17b3o$
24b3o23b3o12b2o9b2o$65bo11bo2$obobo2bo3bo$60bo2bo15bo2bo$4bo2bo3bo47bo
4bo13bo4bo$59bo4bo13bo4bo$obobo2bobobo47bo4bo13bo4bo$60bo2bo15bo2bo$o
10bo2$obobo6bo53bo11bo$24b3o23b3o12b2o9b2o$24bo2b2o19b2o2bo17b3o$25bob
o21bobo17bo3bo$26bo23bo$31bo13bo$30b2o13b2o22bo3bo$29bo2bo11bo2bo22b3o
$30bobo11bobo$31b2o11b2o!


A knightship!
x = 8, y = 8, rule = B3-ce4aikqtwz5e/S2-cn3-ce4cny5e
2bo$bobo$o3bo$2bob2o$3bobo$3b2obo$6b2o$5bo!
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Re: Close life variants

Postby BlinkerSpawn » August 16th, 2016, 10:13 pm

You were probably aware that the p24 block hassler didn't need fourfold symmetry to work:
x = 15, y = 15, rule = B3-ce4aikqtwz5e/S2-cn3-ce4cny5e
11b3o$10bo3bo3$10bo3bo$11b3o$6b2o$6bo3$bo2bo$o4bo$o4bo$o4bo$bo2bo!

Less evident, however, is that the other p24 has a smaller form as well:
(EDIT: Smaller)
x = 12, y = 20, rule = B3-ce4aikqtwz5e/S2-cn3-ce4cny5e
8b3o$7bo3bo3$7bo3bo$8b3o6$2b3o$2o2bo$bobo$2bo2$8b3o$7bo3bo$7bo3bo$8b3o
!
LifeWiki: Like Wikipedia but with more spaceships. [citation needed]

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Re: Close life variants

Postby AbhpzTa » August 18th, 2016, 4:55 pm

BlinkerSpawn wrote:Less evident, however, is that the other p24 has a smaller form as well:
(EDIT: Smaller)
x = 12, y = 20, rule = B3-ce4aikqtwz5e/S2-cn3-ce4cny5e
8b3o$7bo3bo3$7bo3bo$8b3o6$2b3o$2o2bo$bobo$2bo2$8b3o$7bo3bo$7bo3bo$8b3o
!


Much smaller:
x = 22, y = 5, rule = B3-ce4aikqtwz5e_S2-cn3-ce4cny5e
o20bo$2obo7bo6bob2o$ob2o7b3o4b2obo$3bo9bo4bo$11b3o!
Iteration of sigma(n)+tau(n)-n [sigma(n)+tau(n)-n : OEIS A163163] (e.g. 16,20,28,34,24,44,46,30,50,49,11,3,3, ...) :
965808 is period 336 (max = 207085118608).
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Re: Close life variants

Postby Rocknlol » August 18th, 2016, 5:03 pm

c/4 and c/5 ships:
x = 54, y = 31, rule = B3-ce4aikqtwz5e/S2-cn3-ce4cny5e
10b2o$10b2o2$9bo2bo$9bo2bo$9bo2bo$5b2o8b2o$4bo5b2o5bo$8bo4bo$7b2o4b2o$
5b3o6b3o$3b2obobo4bobob2o$3bo5bo2bo5bo$2obo5bo2bo5bob2o21bo4bo$b2o6bo
2bo6b2o22b2o2b2o$3bo5bo2bo5bo21bobobo2bobobo$2b2obo3bo2bo3bob2o19bo4bo
2bo4bo$o2bo2bo2bo2bo2bo2bo2bo16bo14bo$o2bo4bo4bo4bo2bo17b2o10b2o$3b2o
3b2o2b2o3b2o20bo3bo4bo3bo$bo2b2o2b6o2b2o2bo22bo4bo$3b3o2b6o2b3o23b2o4b
2o$8b6o27b3o4b3o$3bo4b6o4bo23b2o4b2o$4bo3b2o2b2o3bo$2bobo3b2o2b2o3bobo
$bo6b2o2b2o6bo22b6o$obo4b2o4b2o4bobo20bobo2bobo$2bo4bo6bo4bo$2bo16bo
22b8o$3o16b3o22b4o!
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Pi Heptomino is replicator?

Postby PHPBB12345 » November 22nd, 2016, 7:56 am

pirep.zip
(620 Bytes) Downloaded 131 times
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