Thread for basic questions

[muzik]

I think I may have managed to enumerate the minimum outer-totalistic rule that simulates each of the 32 Margolus block CA which don't require B0. The binary numbers on the left represent the birth conditions, in the same order as is displayed on Eppstein's glider database (omitting the first term, which represents B0 rules).

Here we are: (hey I actually managed to do something by myself for once)

Code: Select all

00000 - B/S
00001 - B/S8
00010 - B5/S67
00011 - B5/S678
00100 - B4/S4
00101 - B4/S48
00110 - B45/S467
00111 - B45/S4678
01000 - B3/S5 (Familiar 2x2 rule oscillators)
01001 - B3/S58
01010 - B35/S567
01011 - B35/S5678
01100 - B34/S45
01101 - B34/S458
01110 - B345/S4567
01111 - B345/S45678
10000 - B12/S3
10001 - B12/S38
10010 - B125/S367
10011 - B125/S3678
10100 - B124/S34
10101 - B124/S348
10110 - B1245/S3467
10111 - B1245/S34678
11000 - B123/S35
11001 - B123/S358
11010 - B1235/S3567
11011 - B1235/S35678
11100 - B1234/S345
11101 - B1234/S3458
11110 - B12345/S34567
11111 - B12345/S345678

[Macbi]

I remember at some point seeing a "binary countdown" circuit that eventually emitted a glider after a long period of time. (In particular an amount of time exponential in the size of the counter.) Does anyone have a copy of it (or a circuit like that)? (Even better if it's constructable.)

[dvgrn]

I remember at some point seeing a "binary countdown" circuit that eventually emitted a glider after a long period of time. (In particular an amount of time exponential in the size of the counter.) Does anyone have a copy of it (or a circuit like that)? (Even better if it's constructable.)

Is this polynomial bomb structure any use? If it doesn't really have to self-destruct after absorbing 2^N gliders, then it can be reduced to a simple chain of semi-Snarks attached to any reasonable-period gun.

[M. I. Wright]

Yeah, you can construct this sort of circuit by chaining semi-snarks or even period-doubling herschel tracks:

Code: Select all

x = 45, y = 52, rule = LifeHistory
5.A.2A.3B$5.2A.A5B$10.5B$11.4B$12.4B$.4B2.B.3B.4B$.4B.18B$2A5B2A11BA
4B$2A5B2A9B3A4B$.B.15BABA4B$3.B2A12BA8B$4.2A7B2.13B$4.8B6.10B$6.7B7.
7B$5.10B6.8B$5.13B2.7B2A$6.21B2AB$8.22B.B$8.16B2A5B2A$8.16B2A5B2A$9.
18B.4B$16.4B.3B.B2.4B$17.4B$18.4B$19.4B8.2A$20.2BEB6.B2AB$21.2B2E5.4B
$22.2E2B5.2B$23.4B2.4B7.2A$24.4B.5B5.A.A$25.14B.A$26.14B$26.14B$15.2A
8.9B2A4B$14.B2AB6.10B2A5B$14.4B5.18B$15.2B5.4B2.11B.B2A$6.2A7.4B2.4B
5.8B2.BA.A$6.A.A5.5B.4B4.10B5.A$7.A.14B5.2A5.B.B5.2A$8.14B7.A4.3B$8.
14B4.3A5.B2AB$8.15B3.A8.2A$7.3B2A12B$7.3B2A13B$5.2AB.11B2.4B$4.A.AB2.
8B5.4B$4.A5.10B4.4B$3.2A5.B.B5.2A5.4B$11.3B4.A7.4B$10.B2AB5.3A5.4B$
11.2A8.A6.4B!

Code: Select all

x = 156, y = 55, rule = LifeHistory
5.A.2A.3B$5.2A.A5B$10.5B$11.4B$12.4B$.4B2.B.3B.4B$.4B.18B$2A5B2A11BA
4B115.3B$2A5B2A9B3A4B115.4B$.B.15BABA4B116.4B$3.B2A12BA8B38.A6.2A68.
4B$4.2A7B2.13B37.3A4.A2.A.A65.4B$4.8B6.10B40.A5.2A.3A64.4B$6.7B7.7B
18.A21.2A6.B4.A63.4B$5.10B6.8B16.3A7.2A10.5B.B2AB3A64.5B$5.13B2.7B2A
19.A5.B2AB11.3B.B2A.A65.9B$6.21B2AB17.2A6.3B8.8B69.9B$8.22B.B15.4B3.B
.B8.9B69.9B$8.16B2A5B2A15.4B.6B6.8B69.10B$8.16B2A5B2A16.10B4.10B68.
12B$9.18B.4B9.2A7.24B57.2A8.13B$16.4B.3B.B2.4B10.A8.23B58.A9.11B$17.
4B21.A.AB6.17B2D5B34.2A20.A.AB4.12B$18.4B10.A10.2AB.3B2.17B2D7B33.A6.
2A13.2AB.15B$19.4B7.3A12.34B32.A.AB.2B2AB14.17B$20.2BEB5.A15.36B25.2A
4.2AB.4B15.17B$21.2B2E4.2A15.34B26.A.A4.8B15.17B.B$14.2A6.2E7B14.33B
25.BA.A.3A3.9B12.19B2A$15.A7.6B14.31B8.4B14.2A.B2A5.A2.9B10.19B.B2A$
15.A.2A5.6B3.B2.2B2.20B3.12B.2B.3B.4B12.B2A2B6.2A.11B2.2B2.20B4.B$16.
A2.A4.19BD15B5.30B6.4B6.23BD16B$17.2AB3.20BDBD4B.7B6.13B2A16B3.6B8.
21BDBD4B.9B$18.14B2A9B3D4B2.6B7.12B2A16B2.6B7.12B2A9B3D4B2.7B$19.13B
2A11BD4B3.6B8.28B.7B6.13B2A11BD4B2.7B$20.29B6.4B6.39B5.30B4.6B$20.17B
.4B12.B2A2B6.2A.11B2.2B2.20B3.12B.2B.3B.B2.B10.7B$21.15B.6B12.2A.B2A
5.A2.9B10.31B24.6B$21.15B5.A2B.2A11.BA.A.3A3.9B12.33B20.7B$22.13B5.A.
A2B.A14.A.A4.8B15.34B18.6B$24.13B2.A.AB2.A15.2A4.2AB.4B15.36B17.5B$
23.8B4.2A.A.A3.A21.A.AB.2B2AB14.35B17.6B$23.6B6.2ABA2.4A.A19.A6.2A13.
2AB.3B2.17B2D7B19.4B$23.5B8.B2.A.A3.A.A17.2A20.A.AB6.17B2D5B21.2B2AB$
23.B.B9.2A.2A2.A2.A.A39.A8.23B25.2A$24.3B9.A.A2.2A3.A39.2A7.24B$23.B
2AB9.A.A55.10B4.10B$24.2A11.A55.4B.6B6.8B$92.4B3.B.B8.9B$92.2A6.3B8.
8B$93.A5.B2AB11.3B.B2A.A$90.3A7.2A10.5B.B2AB3A$90.A21.2A6.B4.A$113.A
5.2A.3A$110.3A4.A2.A.A$110.A6.2A!

[calcyman]

I have a question of my own: How many cells does it take for generation 1 to be different across every isotropic rule? outer-totalistic? asymmetric (MAP)?

A better way to phrase this is: how many cells does it take for every transition to be used in each of those rulespaces?

Or, equivalently, how large must a pattern be to contain all 512 different 3-by-3 regions?

If you're allowed a toroidal universe, then we know the exact minimum size of such a torus -- 512 squares in a 8-by-64 rectangular torus, as proved here:

J. C. Cock,
Toroidal tilings from de Bruijn-Good cyclic sequences,
Discrete Math. 70 (1988), 209-210.

[praosylen]

What is the smallest still life in B3/S23 that contains every isotropic S2 and S3 survival configuration? So far, I've found a 32-cell example, as well as 3 33-cell examples and a 34-cell one:

Code: Select all

x = 76, y = 14, rule = B3/S23
6bo19bo8bo$5bobo17bobo6bobo$4bobo17bobo8bo$4bo19bo11b3o$b2obo17bob2o
13bob2o8bo$b2ob2o10bob2obobo2bo11b2ob2o7bobo$4bo11b2ob2o2bob2o12bo10bo
bo14b2ob2ob2o$4bo18bo15bo9b2ob2o4b2o6bobob2obo$2bob2o16b2o13bob2o10bo
2bobo2bo5bo7bo$bobo2bo16bob2o9bobo2bo9bobob4o5bob6ob2o$o2bob2o15bo2b2o
8bo2bob2o8b2obo10bo4bo2bo2bo$b2o2bo16b2o12b2o2bo9bo2bob2o8b3o4bobo$5bo
bo32bobo8bobob2o10b2o4bo$6b2o33b2o9bo!

Related question: what about one containing all possible non-birth configuration as well?

[muzik]

Is mcell even compatible with windows 10? I just downloaded it and installed it which seemed to work fine, but when i try to run it, it leads off into this error right here:

Code: Select all

Exception EOleSysError in module MCell.exe at 000FD8D1.
Error accessing the OLE registry.

I wouldn't be surprised if it has become incompatible over time - the last time it was updated I wasn't even breathing.

[Apple Bottom]

Is mcell even compatible with windows 10? I just downloaded it and installed it which seemed to work fine, but when i try to run it, it leads off into this error right here:

Code: Select all

Exception EOleSysError in module MCell.exe at 000FD8D1.
Error accessing the OLE registry.

I wouldn't be surprised if it has become incompatible over time - the last time it was updated I wasn't even breathing.

This is a bit of a stab in the dark, but try running it as Administrator; these errors can be caused by issues with permissions. Alternatively, try running the program in some suitable compatibility mode, e.g. for Windows XP.

Or better yet, just stick to Golly.

[muzik]

..well, there's a bunch of families of rules in MCell that Golly (currently) doesn't fully support, and I wanted to check those out.

[Apple Bottom]

..well, there's a bunch of families of rules in MCell that Golly (currently) doesn't fully support, and I wanted to check those out.

Why not use RuleLoader?

[Saka]

..well, there's a bunch of families of rules in MCell that Golly (currently) doesn't fully support, and I wanted to check those out.

Why not use RuleLoader?

MCell has range > 1 1D rules. That's just one of them. There are also native margolus, and special rules.

Oh and by the way, I needed to run with administrator mode. I love the old-fashioned download screen.

[AbhpzTa]

What is the smallest still life in B3/S23 that contains every isotropic S2 and S3 survival configuration? So far, I've found a 32-cell example, as well as 3 33-cell examples and a 34-cell one:

Code: Select all

x = 76, y = 14, rule = B3/S23
6bo19bo8bo$5bobo17bobo6bobo$4bobo17bobo8bo$4bo19bo11b3o$b2obo17bob2o
13bob2o8bo$b2ob2o10bob2obobo2bo11b2ob2o7bobo$4bo11b2ob2o2bob2o12bo10bo
bo14b2ob2ob2o$4bo18bo15bo9b2ob2o4b2o6bobob2obo$2bob2o16b2o13bob2o10bo
2bobo2bo5bo7bo$bobo2bo16bob2o9bobo2bo9bobob4o5bob6ob2o$o2bob2o15bo2b2o
8bo2bob2o8b2obo10bo4bo2bo2bo$b2o2bo16b2o12b2o2bo9bo2bob2o8b3o4bobo$5bo
bo32bobo8bobob2o10b2o4bo$6b2o33b2o9bo!

28-cell example:

Code: Select all

x = 8, y = 11, rule = B3/S23
b2o$bo2b2o$2bob2o$b2o$2bo$o2b2o$2obo$bobo2b2o$bobobobo$2bobo$3bo!

lower limit = 20 (4 S3a's, 2 S3j's)
upper limit = 28

[toroidalet]

What search programs would be used to find a helix made out of Ts? (In tlife, for example)

[gameoflifemaniac]

How to quickly create complicated still lifes?
Like this one?

Code: Select all

x = 98, y = 98, rule = B3/S23
2obob2o3b2ob2o2bob2o3b2o3b2o2bo5bo8b2o2b2obob2ob2o3b2ob2o3b2o5b2ob2obo
3b2ob2obo$ob2obo5bobo2bob2o3bo2bobobo2b3o3b3o5bo2bo2bob2obobo4b2obobo
3bo2b2o2bobob2o2bobobob2o$6bo4bo2bobo4bo2bobobo7bo5bobo2bo2bobo5bobobo
6bo3bo3bob2o2bo3b3obobo$b6o5b2obobob2ob2obo2bo4b2obo2b4ob3ob3obob2ob2o
bob6obobo2b3o4b2ob2o4bobob3o$o12bo3b2obobo2bobob2o2bob2obo8bo3b2o2bobo
2bo6bobob2obo2b3o4bob2o2bobo3bo$b2ob2obobobobo2bo3bobo2bobo2bo7bob2ob
4o2bo3bobobobo2b3obo2bo4bo2bo2b4o4bobo2b2o$2bobob2ob2obo3bo3bobob2o2bo
2b6ob2obobo3b3ob2o2bobob3o2bob2obob3o4b2o3bob2obob2obo$2bobo7bobobob2o
3bo2b2o8bo7b3o3bo2b3obo4bobo4b2o3b4o2bo3bobobo4bo$b2obob6ob2o2bo6b2o2b
6o2bob6o4bo2bo5b4obobob2o4bo6bo2bobobobob3ob2obo$o3bobo4bo3bobo8bobo5b
obobo5b4ob2ob4o4bobobobob5ob4obob2o2bobobo4bob2o$b4o2b2o3bobo2bobo4b2o
2bobobobobo3bo2bo3bo2bo5b3o3bo2bo7bo3bobo3bobobo3b3o$5bobo3b2obobob2o
5bobob3obobob3obo2bo3bobob4o2b2o2b2obob4o2bob2o2bo3bobo2b3o3b4o$b5o2bo
5bobo7bo2bo5bobo2bo2bob2o2b2obobo3bo8bobo3bobo2bobob2obo2b2o2bobo4bo$o
5bobo2b4ob6o2bobo2b3obob2o3b2o2bobo2bobo2bobob6obobo2b2ob2obobo2bob3o
2bo3b3o$4o2bobobo11bobo2b2obo2bo3b3o2bobo2bo3bob2ob2o5bobob2o5bo2bob2o
5bob4o3bo$4bobobobo2b8obob3o5bob3o2bob2ob3o3bobo6b3obobo3b4obo3bo2b6o
5bob2o$2o2bobobobobo3bo3bobo4b2obob2o3bobo3bo3b4o3b5o2bobo2b3o3bo2b3o
2bo7b5obo$obobo2bobobob2o3bobo2b2obo2b2o4bobob4o2bo5b4o3bobo2bo5b2o2b
2o3b2ob7o6bo$2bo2bobobobobob4o2bobo3bo3b4obobo4b3ob2obo5bobobobo3b2obo
b2o2b2o2bobo7bob2ob2o$bobobobobobobobo3bobobob2ob3o5bo3b2o4bobob2o2b3o
bobobobo2bobo3bobob2o3b2ob6obo2bo$2bo2bo2bo2bobobo2b2obob2obo4b4ob4o2b
3o3bo4bo4bobobob2obobo3bo2bo6bobo8bo$3b3o5bobobobo3bo4bob2o4bo6bo3b4ob
3ob5obo2bo3bob3obo3bobo3bo4b6o$6b5obo2bobo3bob2obobob3o2bob3obobo6bo2b
o6bo3b2obo4bo3b2ob3ob6o$b4o5bobob2obob3obo2bo6b2o3bobobob5o2bobo2b2obo
b3o2bo2b2o4bo6bo7bob2o$bo2bob2o4bobo3bo5bobo2b4o2b2o4bo2bo3bob2obobobo
bobo2bo2b2ob2o3bob4obob5ob2obo2b2o$2bobobo5bo2b2obo2b2obobobo3bobo2b3o
bobo2bobo2bobobobobobobo9bobobo3bobobo2bo7b2o$3b2o2bo5bobob2obo2b2obob
o2bo2bobo2bobobob2obobo2bobob2obo2b11obobobo3bo4bob2obo$o4b3o4b2obo4b
2o4bobobo3bo2bobobobo2bo2b2ob2obo4bobo4bo7bobob5o2bobobob6o$5o10bob2o
3b4obobob3ob2obobobobobo4bo3bob2o2bo2bo4b2ob4o2bo5b3obobo6bo$4bob2o4b
4obob3o3bobobo5bo2bobobobob2o3bo3bobo4b7ob2o4bobo2b3o3bobob4o$3obo2bo
3bo5bo4b3o2bobob3obob2obobobobo2bob2ob2o2b4o11b3o2bobo3b3o2bo5bo$o2bob
2o4bob5ob2o3bobo2bobo2b2obo2bobobo2b3obo4b2o4bob2o2b5o3b2o2b3o4b2ob5o$
bobo5b2obo6bob3o2bobo3bo5b2o2bobo6bob2o3b2o2bobo2bo2bo2bobo2b2o3b4o3bo
$2obob2o2bo2bo2b3o8bob3ob6o2b3o2b4ob2obob3o2bobo2b3o5bob3o2b3o3bob2o2b
o$3bobobobob2obo3b9o4bo5bobo3bobo2bobo8b2ob3o9bo3bobo2b2obo2bob2o2bo$
3bobobobo4b4o9b3obobobobo2bo2bo2bobo2b8o6b5o6b3o2bobobobobo3b3o$b2obo
2bobob2o5bo2b2o2bo3bobob2obobobo3b2obobobo7bob4o5bob4o3bobo3bobo2bobo$
bo2bob2ob2ob2ob2obo2bo2bob3o2bo4bobob2o3bobobo2b8obo3b2o2b2obo3bobo2bo
3bob2obobob2o$2bobobo9bob2obob2o4b2ob4obobo2bo2bobobo12b2o3bo4bo2b2ob
2ob2ob2o4bobobo$b2obo2b5ob2obo2bobo4b2o2bobo4bobobo2b2obob4ob4ob2obob
2ob5o3bo2bo2bo5b3o2bobo$2bobo7b2o2b3o2b4obo3bobo2b3obob3o3bo4bobo2bobo
2bo2bo10b2o2bo2b5o2b3ob2o$2bobobobobo4bo3b2o3bobo2b2obobo3bobo3b2o2b4o
3bobo2bobobo2b7o7b3o5bo4bo$b2o2bob2ob4obo2bo2b2obobobo2bobob2obo3bobo
7b4ob4o2bob2obo4b8o5b2obo2b2o2bo$o2bobo8b2obobobo2bobobobo2bobo2b5o2b
6obo8bobo2bo3bo9bob2o2bo2bobo2b2obo$b2obobob5o4bobobo2bobobo2b3obobo5b
obo4bo3b2ob2o2bob2obo2b10obobobobo2bob2obo2bo$4bobobo4b4o2bob2obobob3o
5bobob2obo2b2o3b3obobobobo2bobobo10b2obobob2obo2bobobo$b2obobo2b3o5b2o
5bobo4bob2obob2obobo4bo6bo3bobobo2bobo2b3ob3o4bobo4bobo2bob2o$o2bo2b3o
3b4obo6bobob4obo2bo5bob4o2bob2obobo2bo2bobo2bobo2bobo2b3obo2b4obo3bo$b
o2b2o3b3o3bobobob2obobobo5b3ob3obobo3b4obobob3o3bobobo2b2o3bobo2bob2ob
o3bo3b2ob2o$2b2o3b2o4bobobob2obobobo2b5o3bo2bobo2b3o5bobo4b4obobobo5bo
b2obo2bobobo6bob2o$5b2o2b6obobo3bobob2obo4b2obobo2b3o3b6obob2obo4bobob
5obo2bob2obobob2o5bo$2b3o2bobo6bo2bob2obo4bob2o3b2obobo3b2o9bobo2b4o2b
2o4bob3o5bobo3bo3b2o$bo3bobobob4ob3o3bobob2obobob2o3b2obob2o2b5ob3o3b
2o3bobo3b2obo4b5obob3obo3bob2o$bobo2bo2bobo2b2o3b2o3bob2ob2o2bob2o4b2o
bobo4bobo2b3o2bobo2bob2obobob2obo3bobo3bo2bo2bob2o$2ob2obobo3bo4bo3b4o
8bobob4o3bo2b2o2bobobo3bobobobobo4bo2bo2bobo4b2obo3bobo$6bob5ob2ob4o4b
9obobo2bob2obobobobobo2bobo2bobobobob2obobo2b2ob4obobob3o2bo$2ob2o2bo
6bobo5b3o4bo4bo3bobobo2bo3bobob4obobobo2b2obobo2bob2o6bobobo4b2ob2o$bo
bo4b6o2bob4o4bo4b2obob3obo2b3obobobo5bo2bobobo3bo2bobo2bob4obobob5o2bo
2bo$o2bobo7bobobo5bob2o5bo2bo4b3o3bobo3b5o3bobo2bobob3o2bobobo2bobobo
5bo2bobo$2obob7o3bo3b5obo6bo3b4o3b2obobob2o5b3o2b4obo4b2o2bo2bobobobob
2o2bob2ob2o$bob2o7b3ob3obo5bo3bob4o3bobo2bobobobo2b3o4b2o6b4o4b2obobob
obobobobobo$o5bob2o2bo3bo5b4obobobo4b2obob3o2bobo3b2o2b3obo2bob3o4b4o
2bobob2obo3bobobo$4ob2obo7bob4obo3bobo3b2obobo5b2obobo6bo2bo2b2obo2b3o
bo3bobobo4b4o3bob2o$3bobo2bo2bo3b2obo8bob4obobobob4o3bob4obobobo4bobob
o2bobo2b2obo2b4o4b2obobo$2obo2bobobobobo6b2o2b2obo3bobobobobo3bob2o5b
2obob2o3bo2bob2o2bobo2bobobo4bo2bob2obo$obobobobobobob2ob5o4bobob2o3bo
2bo2bob2obo2b3o3bobo3b2obobobo3bobo2bobobob3obobo4b2o$2bobobobobobo2bo
bo5bo2bo2bo2b3o3b3o3bo3b2o2b2obobob2obobobobo2b2o2b3obo2bo2bobob4obo2b
o$2bobobobobob2obo2b6o3bobobo9b2obo6bo2bobobobobobobobobo2b2o4b2obobo
2bo4bobob2o$b2ob2obo2bobo2b3o2bo7bo2b4o2bobo2bobob4obobo2bobobobobob2o
bobo4bobo3bobobo2b2o3bobo$bo5bobo2bobo3bo3b2o2bobobo3b4ob3o2bobo2bobob
3o2bo2bo2bo4bob6obob2obobob2o2b4o2bo$2b6ob2obo2bobo3b2o2bobobob2o5bo5b
obobo2b2o3b2obobobo2b3obo7bobo2bobo3b2o4b3o$11bob3ob2o5b2obo2bo2b4obob
obobo2bob2o3bo4bobo2b2o2bobob5obo2bobo2bobo3bobo$4ob5obo13bob2obobo4bo
b2ob2obobo2bob2ob4obob2o2b2o2bobo3bo2bobobob2ob4ob2ob2o$o2bobo3bo2b4ob
2o6bo2bobob4obo7bob2obo2bo6bo2bobo2b2o2bobo2bobobobo7bo3bobo$5bobo2b2o
3bobo2bo2bob2obo2bo4bo2b2ob4obo2bobo2b3obobobo2bo5bob4obobobob5o3b2o$
4bobob2o2bo2bo2bob4o2bo2bobob2o5bobo4bobobob2o2bobobob2obob5o5bo2bobob
o4b3o2b2o$3bo2bobo2bobob2obo5bo3b2ob2o2b5o2bob2obobobo3bobobob2o3bobo
5b3obobo2bo3b2obo2bo2bo$3b4obob2obo4b5o2b3o6bo4bobobo2bobobo2b3obo2bo
3b3obo2b3o3b2obobob4o2bobob2o$o7bo2bobob3o5b2o4b6ob2obobobobo2bo2b2o3b
ob2o2b2o4bobo4bo3b2obo6bo2bo$4ob4o2bobobo2b5o3b3obo5b2obo2b2obobobobo
2bo2bo2b2o2b4o2b5ob2o3bobob3ob2obo$3bobo3b2o2bo2bo6b3o6b3o4bo4bobo2bo
2bob2obobo2bo5b2o6bob3o2bobo2bo3b2o$2obo3bo2bobob2ob4obo2bob5o2bob2ob
5o2bobobobo2bobobobob5o3bob2obo3bob2o2bobob2o2bo$obo2bob2o3bo3bo3bobo
3bo5bo2bobo5bobobobobobo4bob2obo4b4obo2bo3bo3b3o2bobobobo$3b3o3b3ob2ob
o2bo3b3o2b3o2b2o2bob3obobobobo2bob3obo5b4o5bo2b2o3b3o3bobobobo2bo$6bob
o4bo2bobob3o3b2o3b2o2b2obo2bobobobo2bobo4bobob2obo3bob3ob2o3bobo3b2o2b
obob2obo$b4obob4obob2obobo2bobo2b2o4bo3bobo2bobob2obob4o3b2obo4b2obo2b
o2b4o3b2obob2obobo2b2o$o4bo5bobobo2bobo2bobobo2b5ob2obob3obo3bo6b3o3bo
bo3bobobo2bo4b3obobo2bobobobo$4obob4o2bobob2o2b3ob2o2bo5bobo2bo4b3o2b
4obo3bobo2b4o2bob2obob2o3bobob2obobobo2b2o$3bobobo2bob2o2bo2b2o9b4obob
o4b3o3b2o3bob5obobo6bo4bobob2obobo3bo2bo2bobo$2obobo2bo2bo2bobobo2bob
7o3bob2ob4o2bobo3bo2bo7bo2bob5ob4obo3bobobobo3bob2o2bo$o2bo2bob2obo2bo
bob2obobo6b2obo4bo3bo3b3o2bob6obo2b2obo4bo5b3obo3bobobobo2bob2o$bob4o
4b4obo4bobob4obobob3obob2ob3o3b3o6bob2obo2bob2obob4o3bob4obob2obo3bo$
2o5b4o5bob3obo2bo2bo3bo4bobo3bo2b3o3b5obo4bob2obo2bobo4bobo5b2o4b2o2bo
$2b4obo2bob2obo2bo3bobo3bobo2b3obo2b2obobo3b2o6b2ob2obo4bobo3b4obobob
2o4b3o2bob2o$2bo2bo2bobobo3b2o4bo2b4ob3o3bob2o2bo2b2o2bob5o4bo2b6ob4o
3bobobobob4o3bobo$6bobobobob2o4b2obobo7bo2bo3bobobo2bobobo2bo5bobo6bo
4bo4bobobobo3bobo2bob2o$5b2obobo2bo2bobo2bobobob2ob3o2b2o3bobob2o2bobo
5bobobobobob2obob3o5bobobo2bo2bobobo2b2o$9b2o4b2ob2o4b2ob2obo10bo7bo5b
2ob2o3b2obob2obo6b2ob2o2b2o3b2ob2o!

[dvgrn]

How to quickly create complicated still lifes?
Like this one?

Hmm, that doesn't really need to be in Golly's pattern collection any more, does it? (Patterns/Life/Still-Lifes/random.rle). Gabriel Nivasch made that one -- either with lifesrc/WinLifeSearch, or with an algorithm like the one used in Paul Callahan's "Still Life Generator" Java applet.

It's a little painful to get the applet running these days, at least in a browser. It would be fairly straightforward to port the code to a Golly Python or Lua script, if anyone wants to undertake that.

A WLS/JLS search could probably be set up to produce things like random.rle fairly quickly, even at large sizes like this. I haven't tried it so I don't really know what I'm talking about... You might have to seed it with random ON cells to get anything interesting, since the most obvious solution for an NxN pattern that is its own parent would be nice simple empty space.

[Saka]

Do "inner totalistic" rules exist and what are they?

[Apple Bottom]

Do "inner totalistic" rules exist and what are they?

No. (Not to my knowledge anyway!)

The classes usually considered are, in descending order of generality:

1. Anisotropic non-totalistic
2. Isotropic non-totalistic
3. Outer-totalistic (=semi-totalistic)
4. Totalistic

EDIT: changed "non-isotropic" to "anisotropic", to make it clear that this isn't the negation of isotropicity as much as the lack thereof as a positive trait.

[Saka]

What about a CA in which a cell's next state depends on the neighbor's previous state? What are those called?

[dvgrn]

Do "inner totalistic" rules exist and what are they?

No. (Not to my knowledge anyway!)

@Saka, they exist now that you've brought them into existence by asking that question. So now you're responsible for investigating them. Unfortunately you may not find them very interesting.

"Outer totalistic" means "transitions are based on state of center cell, and sum of states of outer cells (neighbors)."

So "inner totalistic" must mean "transitions are based on state of center cell, and sum of states of center cells". So there's no information flow possible between neighboring cells.

There seem to be only four inner-only totalistic rules, which we could call DIE AND STAY DEAD, EVERYBODY LIVE FOREVER, NEVER CHANGE ANYTHING, and HORRIBLE STROBE.

I suppose if we adjusted the analogy a little bit, "inner totalistic" could be taken to mean "transitions are based on states of individual outer cells, and sum of states of center cells". But that's just the same as standard anisotropic non-totalistic MAP rules, and we probably don't really need another confusing alias for MAP rules.

[praosylen]

Do "inner totalistic" rules exist and what are they?

I've heard rules where the center cell is counted in the total but there being no distinction between birth and survival rules (MCell's Vote rule family) referred to as inner-totalistic. Also see my 3ITVN thread in OCA for a generalization to higher states, but in the von Neumann neighborhood.

[dvgrn]

Do "inner totalistic" rules exist and what are they?

I've heard rules where the center cell is counted in the total but there being no distinction between birth and survival rules (MCell's Vote rule family) referred to as inner-totalistic. Also see my 3ITVN thread in OCA for a generalization to higher states, but in the von Neumann neighborhood.

Yeah, that's a much more serious answer than mine. There are plenty of uses of "inner-totalistic" out there using that sense of the term.

Assuming I have my story straight, inner-totalistic rules in this sense are a tiny subset of outer-totalistic rules -- just not quite as tiny a subset as the four rules I mentioned above. (Those can be the "inner-only-totalistic rules", or some such thing, and since they're completely boring they should be studiously ignored.)

You can create an outer-totalistic rule that does the same thing as any inner-totalistic rule, just as you can create a nominally non-totalistic MAP rule that's equivalent to any Life-like or isotropic rule.

Fredkin's rule for example is "13579" in MCell's inner-totalistic Vote syntax. You chop off the impossible "9" for the birth part of the rulestring, and subtract one from every number for the survival part of the rulestring (to account for the ON center cell). Result: B1357/S02468.

EDIT: If there's a difference between this sense of "inner-totalistic" and just plain "totalistic", could somebody please explain it? If there's no difference, then it seems clearer to avoid the "inner-" prefix.

[Apple Bottom]

Fredkin's rule for example is "13579" in MCell's inner-totalistic Vote syntax. You chop off the impossible "9" for the birth part of the rulestring, and subtract one from every number for the survival part of the rulestring (to account for the ON center cell). Result: B1357/S02468.

EDIT: If there's a difference between this sense of "inner-totalistic" and just plain "totalistic", could somebody please explain it? If there's no difference, then it seems clearer to avoid the "inner-" prefix.

Going by the above example, "inner-totalistic" is indeed equivalent to "totalistic". (And FWIW the wiki also gives 13579 as Fredkin's "totalistic rulestring".)

Probably no sense in coining a new term that's more likely than anything else to just sow additional confusion, but if it's already been used, the wiki could note that "inner-totalistic" is a synonym for "totalistic".

[muzik]

Have any more intuitive and easier to understand notations for non-isotropic non-totalistic rules been invented? I've been thinking of making some but I'm not the best at that kind of stuff.

[dvgrn]

Have any more intuitive and easier to understand notations for non-isotropic non-totalistic rules been invented? I've been thinking of making some but I'm not the best at that kind of stuff.

You can't really boil down anisotropic rules to anything less than five hundred and twelve 1's and 0's, so it's kind of hard to figure out how to make that intuitive or easy to understand.

And then MAP encoding just makes things harder. The base64 encoding doesn't line up with the natural boundaries of the data; you'd really want base 256 for that -- or base 16 would be pretty good, except you'd need 128 characters instead of 86 which is already painfully long.

The most intuitive thing I can think of would be a visual notation, something like what Stephen Wolfram uses in A New Kind of Science and mathworld.wolfram.com. That way you could directly look up the neighborhoods that correspond to each 1 and 0 in the 512-bit binary rulestring:

The first sixteenth of a visual notation for MAP rules

MapRuleVisualNotation.png (14.17 KiB) Viewed 10927 times

EDIT: Fixed a binary counting mistake in the diagram above and pattern file below.

The above is just a Golly screenshot of LifeHistory reversed with Ctrl+B, by the way -- you could complete the diagram with 30 more lines:

Code: Select all

x = 63, y = 13, rule = LifeHistory
3B.3B.3B.3B.3B.3B.3B.3B.3B.3B.3B.3B.3B.3B.3B.3B$BDB.BDB.BDB.BDB.BDB.B
DB.BDB.BDB.BDC.BDC.BDC.BDC.BDC.BDC.BDC.BDC$3B.2BC.BCB.B2C.C2B.CBC.2CB
.3C.3B.2BC.BCB.B2C.C2B.CBC.2CB.3C8$3B.3B.3B.3B.3B.3B.3B.3B.3B.3B.3B.
3B.3B.3B.3B.3B$BEB.BEB.BEB.BEB.BEB.BEB.BEB.BEB.BEC.BEC.BEC.BEC.BEC.BE
C.BEC.BEC$3B.2BC.BCB.B2C.C2B.CBC.2CB.3C.3B.2BC.BCB.B2C.C2B.CBC.2CB.3C!

It might be worth writing a script to generate this table automatically for whatever MAP rule is currently set in Golly. But then you'd have to come up with some way of showing the outcomes -- maybe just a single ON or OFF cell under each 3x3 grouping. (I just drew in the four sample +'s and x's by hand in Paint, but you could do that with custom icons in a custom rule, I suppose.)

[muzik]

I was thinking more of something along the lines of extending the notation used for isotropic non-totalistic rules.

For example, if I wanted a non-isotropic rule including certain variations of B2a, they could be picked from a set of possible rotations:

Code: Select all

x = 38, y = 11, rule = LifeHistory
3D3.D3.3D2.3D2.D.D2.3D2.3D2.3D$D.D3.D5.D4.D2.D.D2.D4.D6.D$D.D3.D3.3D
2.3D2.3D2.3D2.3D4.D$D.D3.D3.D6.D4.D4.D2.D.D4.D$3D3.D3.3D2.3D4.D2.3D2.
3D4.D4$2EB2.B2E2.2BE2.3B2.3B2.3B2.3B2.E2B$BCB2.BCB2.BCE2.BCE2.BCB2.BC
B2.ECB2.ECB$3B2.3B2.3B2.2BE2.B2E2.2EB2.E2B2.3B!

One possible notation using this system would be B2a(0246)/S2a(1357), which would only allow for birth on the displayed B2a conditions marked as 0, 2, 4 and 6, and survival on those marked 1, 3, 5 and 7. Like with non-totalistic rules, a - to negate unwanted orientations could also be used.

This notation probably isn't optimal when it comes to the lengths of rulestrings, but at least it could be interpreted a bit easier, and understanding what a rulestring symbolises at a glance is what i'm really after.