On Sun Mar 3, 2002 3:15pm, Gabriel Nivasch wrote:Subject: P3 agar search results

I used my toroidal adaptation of Lifesrc to search for period-3 agars. I

covered rectangles with the following dimensions:

base = 1: up to height = 18,

base = 2: up to height = 12,

base = 3: up to height = 8,

base = 4: up to height = 6,

base = 5: up to height = 5,

base = 6: up to height = 4,

base = 7 through 14: up to height = 2.

In each case, I covered all possible toroidal shifts.

I saved the interesting-looking results. All the patterns shown here can be

extended arbitrarily by simply repeating the given pattern orthogonally in the

x and y directions.

First, here's the agar from LifeLine with a similar-looking relative:

Code: Select all

```
x = 59, y = 28, rule = B3/S23
3b2o5b2o5b2o13b2o4b2o6b2o4b2o$o5b2o5b2o5bo14b2o4b2o6b2o4b2o$2b2o5b2o5b
2o13bo6b2o4b2o6b2o4bo$5b2o5b2o5b2o12b2o6b2o4b2o6b2o$b2o5b2o5b2o14bo4b
2o6b2o4b2o6bo$4b2o5b2o5b2o13b2o4b2o6b2o4b2o$2o5b2o5b2o20b2o4b2o6b2o4b
2o$3b2o5b2o5b2o12b2o6b2o4b2o6b2o$o5b2o5b2o5bo13b2o6b2o4b2o6b2o$2b2o5b
2o5b2o13b2o4b2o6b2o4b2o$5b2o5b2o5b2o13b2o4b2o6b2o4b2o$b2o5b2o5b2o20b2o
4b2o6b2o4b2o$4b2o5b2o5b2o12b2o6b2o4b2o6b2o$2o5b2o5b2o19b2o6b2o4b2o6b2o
$3b2o5b2o5b2o13b2o4b2o6b2o4b2o$o5b2o5b2o5bo14b2o4b2o6b2o4b2o$2b2o5b2o
5b2o13bo6b2o4b2o6b2o4bo$5b2o5b2o5b2o12b2o6b2o4b2o6b2o$b2o5b2o5b2o14bo
4b2o6b2o4b2o6bo$4b2o5b2o5b2o13b2o4b2o6b2o4b2o$2o5b2o5b2o20b2o4b2o6b2o
4b2o$31b2o6b2o4b2o6b2o$34b2o6b2o4b2o6b2o$31b2o4b2o6b2o4b2o$34b2o4b2o6b
2o4b2o$37b2o4b2o6b2o4b2o$32b2o6b2o4b2o6b2o$35b2o6b2o4b2o6b2o!
```

The following agar turns out to be a lattice of 2c/3 signal tracks, so it has

an infinite number of trivial variations:

Code: Select all

```
x = 24, y = 24, rule = B3/S23
obo2bob2obo2bob2obo2bobo$4bobo5bobo5bobo$b2obo2bob2obo2bob2obo2bo$o5bo
bo5bobo5bo$bob2obo2bob2obo2bob2obo$obo5bobo5bobo$o2bob2obo2bob2obo2bob
2o$2bobo5bobo5bobo$obo2bob2obo2bob2obo2bobo$4bobo5bobo5bobo$b2obo2bob
2obo2bob2obo2bo$o5bobo5bobo5bo$bob2obo2bob2obo2bob2obo$obo5bobo5bobo$o
2bob2obo2bob2obo2bob2o$2bobo5bobo5bobo$obo2bob2obo2bob2obo2bobo$4bobo
5bobo5bobo$b2obo2bob2obo2bob2obo2bo$o5bobo5bobo5bo$bob2obo2bob2obo2bob
2obo$obo5bobo5bobo$o2bob2obo2bob2obo2bob2o$2bobo5bobo5bobo!
```

You can get agars that consist of independent oscillators, like this agar of

loading docks:

Code: Select all

```
x = 34, y = 34, rule = B3/S23
obobobobo4bobobobobobobo4bobo$2bobobobobobobo4bobobobobobobo$bobo4bobo
bobobobobo4bobobobobo$bobobobobo4bobobobobobobo4bobo$3bobobobobobobo4b
obobobobobobo$obobo4bobobobobobobo4bobobobo$obobobobobo4bobobobobobobo
4bo$4bobobobobobobo4bobobobobobobo$bobobo4bobobobobobobo4bobobobo$bobo
bobobobo4bobobobobobobo4bo$o4bobobobobobobo4bobobobobobo$obobobo4bobob
obobobobo4bobobo$obobobobobobo4bobobobobobobo$bo4bobobobobobobo4bobobo
bobobo$bobobobo4bobobobobobobo4bobobo$bobobobobobobo4bobobobobobobo$ob
o4bobobobobobobo4bobobobobo$obobobobo4bobobobobobobo4bobo$2bobobobobob
obo4bobobobobobobo$bobo4bobobobobobobo4bobobobobo$bobobobobo4bobobobob
obobo4bobo$3bobobobobobobo4bobobobobobobo$obobo4bobobobobobobo4bobobob
o$obobobobobo4bobobobobobobo4bo$4bobobobobobobo4bobobobobobobo$bobobo
4bobobobobobobo4bobobobo$bobobobobobo4bobobobobobobo4bo$o4bobobobobobo
bo4bobobobobobo$obobobo4bobobobobobobo4bobobo$obobobobobobo4bobobobobo
bobo$bo4bobobobobobobo4bobobobobobo$bobobobo4bobobobobobobo4bobobo$bob
obobobobobo4bobobobobobobo$obo4bobobobobobobo4bobobobobo!
```

This agar has hollow 3x3 squares in one phase:

Code: Select all

```
x = 22, y = 22, rule = B3/S23
b4o2b4ob4o2b4o$bobo8bobo$4ob4o2b4ob4o$5bobo8bobo$2o2b4ob4o2b4ob2o$o8bo
bo8bo$ob4o2b4ob4o2b3o$2bobo8bobo$b4ob4o2b4ob4o$6bobo8bobo$3o2b4ob4o2b
4obo$bo8bobo8bo$2ob4o2b4ob4o2b2o$3bobo8bobo$2b4ob4o2b4ob4o$7bobo8bobo$
4o2b4ob4o2b4o$obo8bobo$3ob4o2b4ob4o2bo$4bobo8bobo$o2b4ob4o2b4ob3o$8bob
o8bobo!
```

Here are a few more:

Code: Select all

```
x = 115, y = 36, rule = B3/S23
b2o3b2o3b2o3b2o11bo2bobo2bobo2bobo2bo10bo3b5o3b5o3b4o9bo3b3o3b3o3b3o3b
2o$2b2o3b2o3b2o3b2o10bo2bobo2bobo2bobo2bo10bobobobobobobobobobobobo11b
obobobobobobobobobobobo$3b2o3b2o3b2o3b2o10bo4bo4bo4bo17bobo5bobo5bobo
10bobo3bobo3bobo3bobo$o3b2o3b2o3b2o3bo10b4ob4ob4ob4o9b5o3b5o3b5o12b2o
3b3o3b3o3b3o3bo$3b2o3b2o3b2o3b2o13bo4bo4bo4bo9bobobobobobobobobobobobo
10bobobobobobobobobobobobo$2b2o3b2o3b2o3b2o10bobo2bobo2bobo2bobo12bobo
5bobo5bobo15bobo3bobo3bobo3bobo$3b2o3b2o3b2o3b2o9bobo2bobo2bobo2bobo
11bo3b5o3b5o3b4o9b3o3b3o3b3o3b3o$o3b2o3b2o3b2o3bo12bo4bo4bo4bo10bobobo
bobobobobobobobobo11bobobobobobobobobobobobo$2o3b2o3b2o3b2o12b2ob4ob4o
b4ob2o14bobo5bobo5bobo12bobo3bobo3bobo3bobo$o3b2o3b2o3b2o3bo10bo4bo4bo
4bo12b5o3b5o3b5o13b3o3b3o3b3o3b3o$3b2o3b2o3b2o3b2o11bobo2bobo2bobo2bob
o9bobobobobobobobobobobobo10bobobobobobobobobobobobo$o3b2o3b2o3b2o3bo
11bobo2bobo2bobo2bobo10bobo5bobo5bobo13bo3bobo3bobo3bobo3bo$2o3b2o3b2o
3b2o12bo4bo4bo4bo13bo3b5o3b5o3b4o11b3o3b3o3b3o3b3o$b2o3b2o3b2o3b2o11b
4ob4ob4ob4o10bobobobobobobobobobobobo11bobobobobobobobobobobobo$2o3b2o
3b2o3b2o15bo4bo4bo4bo15bobo5bobo5bobo10bo3bobo3bobo3bobo3bo$o3b2o3b2o
3b2o3bo10bo2bobo2bobo2bobo2bo9b5o3b5o3b5o15b3o3b3o3b3o3b3o$2o3b2o3b2o
3b2o13bo2bobo2bobo2bobo2bo9bobobobobobobobobobobobo10bobobobobobobobob
obobobo$b2o3b2o3b2o3b2o13bo4bo4bo4bo12bobo5bobo5bobo13bobo3bobo3bobo3b
obo$2b2o3b2o3b2o3b2o10bob4ob4ob4ob3o9bo3b5o3b5o3b4o9bo3b3o3b3o3b3o3b2o
$b2o3b2o3b2o3b2o11bo4bo4bo4bo13bobobobobobobobobobobobo11bobobobobobob
obobobobobo$2o3b2o3b2o3b2o13bobo2bobo2bobo2bobo15bobo5bobo5bobo10bobo
3bobo3bobo3bobo$b2o3b2o3b2o3b2o12bobo2bobo2bobo2bobo10b5o3b5o3b5o12b2o
3b3o3b3o3b3o3bo$2b2o3b2o3b2o3b2o14bo4bo4bo4bo9bobobobobobobobobobobobo
10bobobobobobobobobobobobo$3b2o3b2o3b2o3b2o9b3ob4ob4ob4obo10bobo5bobo
5bobo15bobo3bobo3bobo3bobo$2b2o3b2o3b2o3b2o12bo4bo4bo4bo44b3o3b3o3b3o
3b3o$92bobobobobobobobobobobobo$94bobo3bobo3bobo3bobo$92b3o3b3o3b3o3b
3o$91bobobobobobobobobobobobo$91bo3bobo3bobo3bobo3bo$93b3o3b3o3b3o3b3o
$92bobobobobobobobobobobobo$92bo3bobo3bobo3bobo3bo$94b3o3b3o3b3o3b3o$
91bobobobobobobobobobobobo$91bobo3bobo3bobo3bobo!
```

The last one is a p3/3 with displacement.