Thread for basic non-CGOL questions

[2718281828]

What is the smallest (known) log-growth pattern in any isotropic non-totalistic Life-like cellular automaton (without B0)?
Bonus: And log(log)-growth?

[toroidalet]

What is the smallest (known) log-growth pattern in any isotropic non-totalistic Life-like cellular automaton (without B0)?

4 cells with a 2-cell predecessor:

Code: Select all

x = 41, y = 3, rule = B2ci3aer4eiqrz5i6cik8/S01c2cn3ek4nqtw5aekry6ekn78
39bo$obo35bobo$39bo!

source (obviously I remember everything I've created)

Where can I find the cblocks rule table?

I'm pretty sure cblocks allows unlimited instant pushing and so cannot be expressed by a rule table.

[Moosey]

What is the smallest (known) log-growth pattern in any isotropic non-totalistic Life-like cellular automaton (without B0)?

4 cells with a 2-cell predecessor:

Code: Select all

x = 41, y = 3, rule = B2ci3aer4eiqrz5i6cik8/S01c2cn3ek4nqtw5aekry6ekn78
39bo$obo35bobo$39bo!

source (obviously I remember everything I've created)

Long lifespan methuselah family:

Code: Select all

x = 27, y = 28, rule = B2ci3aer4eiqrz5i6cik8/S01c2cn3ek4nqtw5aekry6ekn78
26bo27$obo!

Where can I find the cblocks rule table?

I'm pretty sure cblocks allows unlimited instant pushing and so cannot be expressed by a rule table.

Oh. Where do I find it then, CA or no?

[GUYTU6J]

What is the highest (known) period for an unloopable (loopability 1) RRO in isotropic non-totalistic Life-like cellular automaton (without B0)?

[Hdjensofjfnen]

What is the highest (known) period for an unloopable (loopability 1) RRO in isotropic non-totalistic Life-like cellular automaton (without B0)?

I have a p1912 (or a predecessor of it) which is of loopability 1 in my signature.

[Moosey]

Are there any guns for hybrid Gs in Quadlife or Immigration?
For instance, these:

Code: Select all

x = 14, y = 3, rule = QuadLife
2B9.BC$A.B8.A.C$A10.A!

Or, perhaps my question would be better phrased:
Are there any synths for hybrid Gs in Quadlife? (since it can emulate immigration, I won't ask about immigration)

Here's a tricolor HF synth, to demonstrate that such things are possible:

Code: Select all

x = 15, y = 18, rule = QuadLife
2.C$3.C$.3C10$13.2B$12.2B$14.B$.2D$D.D$2.D!

EDIT:
This R surprised me:

Code: Select all

x = 3, y = 3, rule = QuadLife
.AD$DB$.B!

EDIT:
More proof of concept-- a BH with a foreign cell:

Code: Select all

x = 84, y = 42, rule = QuadLife
66.A$65.A$65.3A$24.A.A$25.2A$25.A9$54.2A$46.B6.A2.A$47.B5.A2.A$3.A41.
3B6.2A26.B$3.A.A75.B.B$3.2A76.B.A$82.B4$49.3A$2A49.A$.2A47.A$A12$40.
2A$41.2A$40.A!

Similar:

Code: Select all

x = 31, y = 24, rule = QuadLife
.A$2.A$3A9$17.A$18.A$16.3A2$24.A4.B$25.A2.B$23.3A2.3B4$23.3C2.3D$25.C
2.D$24.C4.D!

Code: Select all

x = 12, y = 10, rule = QuadLife
9.B$9.B.B$9.2B5$.2A$A.A$2.A!

Code: Select all

x = 8, y = 13, rule = QuadLife
.A$2.A$3A10$5.3B!

Anyways, back to my question. Can anyone make a synth of this?

Code: Select all

x = 3, y = 3, rule = QuadLife
A2B$A$.A!

EDIT:
If it helps, the distinct 2-color 2G collisions. Two asymmetric ones have multicolored output objects:

Code: Select all

#C shamelessly copied from the golly pattern collection after edits
x = 379, y = 369, rule = QuadLife
154.A36.A18.A$58.A18.A19.A16.A19.A18.A19.A16.A18.A36.A$57.A18.A19.A
16.A19.A19.3A16.A17.3A16.3A15.A17.A$57.3A16.3A17.3A14.3A17.3A36.3A51.
A18.3A$226.3A4$190.B$58.3B17.3B89.B18.2B55.B$58.B19.B20.B17.B20.B13.
2B15.2B18.B.B14.2B20.B16.2B$59.B19.B18.2B16.2B19.2B13.B.B14.B.B34.B.B
18.2B16.B.B$98.B.B15.B.B18.B.B12.B53.B20.B.B$.A4.A3.A.A3.A.A.A2.A3.A
3.A3.A4.A4.A.A2$.A.A2.A2.A3.A4.A4.A3.A3.A3.A.A2.A2.A2$.A2.A.A2.A3.A4.
A4.A.A.A3.A3.A2.A.A2.A2.A.A2$.A4.A2.A3.A4.A4.A3.A3.A3.A4.A2.A4.A266.A
$269.A22.A21.A62.A$.A4.A3.A.A5.A4.A3.A3.A3.A4.A4.A.A182.A15.A21.A22.A
22.3A18.A22.A17.A$229.A15.A22.3A20.3A40.A22.A18.3A$86.A16.A17.A16.A
16.A15.A17.A16.A22.3A13.3A86.3A20.3A$66.A18.A16.A17.A16.A16.A15.A17.A
16.A$65.A19.3A14.3A15.3A14.3A14.3A13.3A15.3A14.3A$65.3A4$224.3B15.3B
59.2B$76.3B16.3B16.3B15.3B15.3B14.3B16.3B15.3B19.B17.B11.2B23.2B20.B.
B20.2B40.2B$54.3B21.B18.B18.B17.B17.B16.B18.B17.B18.B17.B13.2B23.2B
21.B21.2B12.2B26.2B$56.B20.B18.B18.B17.B17.B16.B18.B17.B50.B24.B44.B
15.2B24.B$55.B285.B23$106.A157.A$74.A30.A157.A38.A$2.A.A4.A6.A3.A4.A
2.A3.A2.A.A.A2.A.A28.A15.A15.3A119.A.A.A2.A28.3A14.A20.A$46.A26.3A12.
A190.A21.3A$2.A3.A2.A6.A3.A.A2.A2.A2.A3.A6.A45.3A138.A4.A44.3A$46.A$
2.A.A4.A6.A3.A2.A.A2.A.A4.A.A.A2.A.A184.A4.A2$2.A3.A2.A6.A3.A4.A2.A2.
A3.A6.A2.A183.A4.A$305.3B$2.A.A4.A.A.A2.A3.A4.A2.A3.A2.A.A.A2.A3.A61.
2B119.A4.A.A.A44.B21.B$108.B.B146.2B23.2B22.B$66.2B21.2B17.B149.2B22.
B.B$65.B.B21.B.B165.B$67.B21.B17$84.A15.A39.A153.A24.A19.A$.A.A4.A7.A
.A4.A.A3.A3.A28.A20.A15.A39.A88.A3.A2.A.A.A20.A16.A15.A24.A19.A$61.A
21.3A13.3A15.A21.3A17.A99.A16.A16.3A22.3A17.3A$.A3.A2.A6.A3.A2.A3.A2.
A2.A28.3A52.A41.A69.A3.A2.A23.3A14.3A$116.3A39.3A$.A.A4.A6.A3.A2.A6.A
.A196.A.A.A2.A.A.A2$.A3.A2.A6.A3.A2.A3.A2.A2.A195.A3.A2.A2$.A.A4.A.A.
A3.A.A4.A.A3.A3.A85.3B106.A3.A2.A$54.3B62.B17.2B16.B103.B35.2B35.2B$
56.B21.2B15.2B23.B16.B.B14.2B102.2B16.2B17.B.B11.2B22.2B$55.B23.2B15.
2B39.B16.B.B101.B.B15.B.B16.B14.2B20.B$78.B16.B180.B32.B6$73.2A19.2A$
74.A20.A152.2A$249.A7$64.A233.A$63.A20.A194.A17.A$63.3A17.A166.A27.A
18.3A$2.A.A3.A6.A3.A.A4.A.A.A2.A.A47.3A143.A.A17.A28.3A$37.A211.3A$A
7.A6.A3.A3.A2.A6.A195.A3.A$37.A275.2A$A2.A.A2.A6.A3.A3.A2.A.A.A2.A.A
193.A.A82.A$256.2A$A4.A2.A6.A3.A3.A2.A6.A2.A192.A3.A23.A$80.B$2.A.A3.
A.A.A2.A3.A.A4.A.A.A2.A3.A20.2B19.2B148.A.A18.B42.2B$57.B.B19.B.B167.
2B13.2B26.B.B$59.B189.B.B13.2B27.B$264.B14$252.2A24.2A$253.A25.A$258.
A15.A$257.A15.A26.A$61.A195.3A13.3A23.A$A.A5.A.A5.A4.A.A.A34.A167.A.A
4.A63.3A$60.3A169.A45.B24.3B$A3.A2.A3.A3.A.A5.A204.A6.A41.2B24.B$232.
A44.B.B24.B$A.A4.A3.A2.A3.A4.A204.A.A4.A19.2B37.2A$254.B.B38.A$A3.A2.
A3.A2.A.A.A4.A204.A6.A20.B2$A.A5.A.A3.A3.A4.A204.A6.A2$53.2B$54.2B$
53.B18$3.A3.A3.A3.A3.A2.A.A.A30.A169.A6.A.A3.A5.A18.A$56.A207.A$3.A3.
A3.A3.A3.A2.A33.3A168.A5.A3.A2.A.A.A.A17.3A2$3.A.A.A3.A3.A3.A2.A.A.A
200.A5.A3.A2.A2.A2.A2$3.A3.A3.A4.A.A3.A204.A5.A3.A2.A5.A2$3.A3.A3.A5.
A4.A.A.A32.3B165.A.A.A2.A.A3.A5.A$59.B203.B$60.B201.2B$262.B.B17$67.A
$66.A$4.A6.A.A5.A4.A.A.A37.3A157.A.A.A2.A.A.A4.A4.A.A4.A.A4.A.A5.A.A
3.A.A$251.A13.A13.A17.A$4.A5.A3.A3.A.A3.A203.A4.A7.A.A3.A6.A3.A2.A6.A
3.A2.A20.A$251.A13.A13.A16.3A$4.A5.A3.A2.A3.A2.A.A.A199.A4.A.A.A2.A3.
A2.A.A4.A3.A2.A.A4.A3.A2.A.A2$4.A5.A3.A2.A.A.A2.A203.A4.A6.A.A.A2.A2.
A3.A3.A2.A2.A3.A3.A2.A2$4.A.A.A2.A.A3.A3.A2.A203.A4.A.A.A2.A3.A2.A3.A
2.A.A4.A3.A3.A.A3.A$58.2B239.B$57.B.B238.2B$59.B238.B.B16$59.A$58.A$
58.3A264.A$3.A.A.A4.A4.A.A.A2.A.A.A2.A.A193.A3.A4.A2.A.A.A2.A.A.A2.A.
A5.A.A3.A3.A4.A4.A4.A4.A.A3.A.A.A22.A$35.A221.A66.3A$3.A7.A.A5.A4.A6.
A195.A3.A.A2.A4.A4.A6.A6.A3.A2.A3.A3.A.A3.A.A2.A2.A7.A$35.A221.A$3.A.
A.A2.A3.A4.A4.A.A.A2.A.A193.A3.A2.A.A4.A4.A.A.A2.A.A4.A6.A.A.A2.A3.A
2.A2.A.A2.A2.A.A2.A.A.A$57.B$3.A6.A.A.A4.A4.A6.A2.A21.2B169.A3.A4.A4.
A4.A6.A2.A3.A3.A2.A3.A2.A.A.A2.A4.A2.A4.A2.A26.3B$56.B.B265.B$3.A.A.A
2.A3.A4.A4.A.A.A2.A3.A191.A3.A4.A4.A4.A.A.A2.A3.A3.A.A3.A3.A2.A3.A2.A
4.A4.A.A3.A.A.A23.B11$305.2A$306.A9$55.A16.A237.A$2.A.A5.A.A3.A4.A2.A
.A27.A16.A155.A.A.A2.A14.A.A3.A6.A3.A.A4.A.A.A2.A.A26.A$6.A47.3A14.3A
210.A24.3A$2.A6.A3.A2.A.A2.A2.A3.A200.A4.A7.A4.A7.A6.A3.A3.A2.A6.A$6.
A277.A$2.A.A4.A3.A2.A2.A.A2.A3.A200.A4.A5.A.A.A2.A2.A.A2.A6.A3.A3.A2.
A.A.A2.A.A2$2.A6.A3.A2.A4.A2.A3.A200.A4.A7.A4.A4.A2.A6.A3.A3.A2.A6.A
2.A26.3B$310.B$2.A7.A.A3.A4.A2.A.A46.B155.A4.A.A.A10.A.A3.A.A.A2.A3.A
.A4.A.A.A2.A3.A26.B$50.2B20.2B$51.2B19.B.B$50.B19$2.A.A5.A7.A.A4.A7.A
.A4.A.A3.A3.A2$2.A3.A3.A7.A3.A2.A6.A3.A2.A3.A2.A2.A28.A239.A$77.A239.
A$2.A.A5.A2.A.A2.A.A4.A6.A3.A2.A6.A.A28.3A237.3A$229.A.A4.A.A3.A.A.A
3.A.A3.A5.A3.A3.A4.A3.A.A$2.A3.A3.A7.A3.A2.A6.A3.A2.A3.A2.A2.A$228.A
3.A2.A3.A4.A4.A3.A2.A.A.A.A3.A3.A.A2.A2.A3.A$2.A.A5.A7.A.A4.A.A.A3.A.
A4.A.A3.A3.A$228.A3.A2.A8.A4.A3.A2.A2.A2.A3.A3.A2.A.A2.A3.A$77.3B$77.
B150.A3.A2.A3.A4.A4.A3.A2.A5.A3.A3.A4.A2.A3.A$78.B$229.A.A4.A.A5.A5.A
.A3.A5.A3.A3.A4.A3.A.A26.2B$307.B.B$309.B7$276.2A37.2A$277.A38.A6$
112.A13.A$2.A6.A.A5.A4.A.A.A9.A.A4.A6.A3.A4.A2.A3.A2.A.A.A2.A.A32.A
13.A$80.A30.3A11.3A$2.A5.A3.A3.A.A3.A8.A4.A3.A2.A6.A3.A.A2.A2.A2.A3.A
6.A$80.A$2.A5.A3.A2.A3.A2.A.A.A2.A.A.A2.A.A4.A6.A3.A2.A.A2.A.A4.A.A.A
2.A.A2$2.A5.A3.A2.A.A.A2.A8.A4.A3.A2.A6.A3.A4.A2.A2.A3.A6.A2.A2$2.A.A
.A2.A.A3.A3.A2.A13.A.A4.A.A.A2.A3.A4.A2.A3.A2.A.A.A2.A3.A$107.2B21.2B
195.A$107.B.B20.B.B193.A$107.B22.B98.A.A.A9.A.A3.A6.A3.A.A4.A.A.A2.A.
A7.A5.A2.A.A.A3.A.A3.A.A16.3A$278.A$233.A7.A7.A6.A3.A3.A2.A6.A9.A.A.A
.A2.A6.A5.A$278.A$229.A.A.A2.A.A2.A2.A.A2.A6.A3.A3.A2.A.A.A2.A.A7.A2.
A2.A2.A.A.A3.A.A3.A.A2$229.A11.A4.A2.A6.A3.A3.A2.A6.A2.A6.A5.A2.A10.A
5.A$324.B$229.A.A.A9.A.A3.A.A.A2.A3.A.A4.A.A.A2.A3.A5.A5.A2.A.A.A3.A.
A3.A.A13.2B$323.B.B7$69.A$68.A$46.A21.3A34.A$3.A5.A3.A3.A.A4.A.A18.A
58.A$45.3A56.3A$3.A.A.A.A3.A2.A6.A3.A2$3.A2.A2.A3.A3.A.A3.A2$3.A5.A3.
A6.A2.A3.A19.3B$47.B24.2B17.3B177.2A32.2A$3.A5.A3.A3.A.A4.A.A21.B23.B
.B18.B178.A33.A$72.B19.B!

Code: Select all

x = 13, y = 40, rule = QuadLife
11.A$10.A$10.3A9$2.2B$.B.B$3.B16$3.A$2.A$2.3A6$.B$2B$B.B!

Can someone apgsearch quadlife?


EDIT:
Is there a thread for this rule? There was discussion of it while back in rules with interesting failed reps:

Code: Select all

x = 3, y = 3, rule = B3-cky6cik/S23-ce4n7e
b2o$obo$b2o!

[Gustone]

Is there a thread for this rule? There was discussion of it while back in rules with interesting failed reps:

Code: Select all

x = 3, y = 3, rule = B3-cky6cik/S23-ce4n7e
b2o$obo$b2o!

IT NEEDS TO BE
more normal rake

Code: Select all

x = 80, y = 27, rule = B3-cky6cik/S23-ce4n7e
27bo$26bobo$2bo23bobo28bo5b2o3bo$2obo12b3o5b2o3b2o25b4ob2o2bobobo2b3ob
4o$o3bo11bob2o3bo7bo23b2obobo3bobo3bobobob2obo$2obo12b3o5b2o3b2o25b4ob
2o2bobobo2b3ob4o$2bo23bobo28bo5b2o3bo$26bobo$27bo3$23b3o$2b2o6bo12bobo
$b4o4bob2o8b2o3b2o$o3b2o2bo3bo8bo5bo$b4o4bob2o8b2o3b2o$2b2o6bo12bobo$
23b3o5$43bo5b2o3bo$42b4ob2o2bobobo2b3ob4o$41b2obobo3bobo3bobobob2obo$
42b4ob2o2bobobo2b3ob4o$43bo5b2o3bo!

Code: Select all

x = 70, y = 29, rule = B3-cky6cik/S23-ce4n7e
28bo$27bobo$2b2o14bo8bobo$b4o12bob2o4b2o3b2o15bo5b2o3bo$o3b2o10bo3bo3b
o7bo13b4ob2o2bobobo2b3ob4o$b4o12bob2o4b2o3b2o13b2obobo3bobo3bobobob2ob
o$2b2o14bo8bobo16b4ob2o2bobobo2b3ob4o$27bobo17bo5b2o3bo$28bo4$2bo$2obo
4b3o6b2o$o3bo3bob2o4bob2o$2obo4b3o6b2o$2bo4$28bo$27bobo17bo5b2o3bo$2b
2o14bo8bobo16b4ob2o2bobobo2b3ob4o$b4o12bob2o4b2o3b2o13b2obobo3bobo3bob
obob2obo$o3b2o10bo3bo3bo7bo13b4ob2o2bobobo2b3ob4o$b4o12bob2o4b2o3b2o
15bo5b2o3bo$2b2o14bo8bobo$27bobo$28bo!

???

Code: Select all

x = 151, y = 42, rule = B3-cky6cik/S23-ce4n7e
92bo$63bo5b2o3bo19bo$62b4ob2o2bobobo2b3ob4obobo4bo$61b2obobo3bobo3bobo
bob2obo2bo3b4o11b2o$62b4ob2o2bobobo2b3ob4obobo4bo10bo3bo4bo$51b2o10bo
5b2o3bo19bo4b2o2bo11bo8b2o$52bo39bo6bobo12b3o6bo2bo$49bo49b2o2bo11bo8b
2o$49b2o10b2o14b2o14b2o10bo3bo4bo$38b3o20b2o14b2o14b2o12b2o$28b2o8bobo
3b2o$28bobo7bobo3bobo11b2o14b2o14b2o14b2o$29bo9bo5bo11bo2bo12bo2bo12bo
2bo12bo2bo$19bo17bo3bo16bobo13bobo13bobo13bobo$18b3o16bobobo17bo15bo
15bo15bo$b2o14b2o2bo$o3b4o10bob3o$o3bo2bo9b4obo$o3b4o9b2o2b2o$b2o17bob
obo12bo3bo11bo3bo11bo3bo11bo3bo11bo3bo11bo15bo15bo$13b2o3b3ob2obo2b2o
6bobobobo9bobobobo9bobobobo9bobobobo9bobobobo9bobo13bobo13bobo$13b2o3b
3ob2obo2b2o6bobobobo9bobobobo9bobobobo9bobobobo9bobobobo9bobo13bobo13b
obo$b2o17bobobo12bo3bo11bo3bo11bo3bo11bo3bo11bo3bo11bo15bo15bo$o3b4o9b
2o2b2o$o3bo2bo9b4obo$o3b4o10bob3o$b2o14b2o2bo$18b3o16bobobo17bo15bo15b
o15bo$19bo17bo3bo16bobo13bobo13bobo13bobo$29bo9bo5bo11bo2bo12bo2bo12bo
2bo12bo2bo$28bobo7bobo3bobo11b2o14b2o14b2o14b2o$28b2o8bobo3b2o60b2o$
38b3o20b2o14b2o14b2o10b2o$49b2o10b2o14b2o14b2o8bo3bo4bo$49bo47b2o2bo
11bo8b2o$52bo39bo4bobo12b3o6bo2bo$51b2o10bo5b2o3bo19bo2b2o2bo11bo8b2o$
62b4ob2o2bobobo2b3ob4obobo4bo8bo3bo4bo$61b2obobo3bobo3bobobob2obo2bo3b
4o9b2o$62b4ob2o2bobobo2b3ob4obobo4bo$63bo5b2o3bo19bo$92bo!

[muzik]

How many different conditions does the range-1 Moore 3D isotropic non-totalistic rulespace have?

[Gustone]

Is PCA margolus

[Moosey]

Is PCA margolus

I don't think so--the graphics don't help, but you may want to check golly's ruletable repository for Reversible world, which is a PCA. I don't believe it's margolus.

[wildmyron]

Is PCA margolus

No. Partitioned CA do not use an alternating neighbourhood such as Margolus rules do. Instead, each cell is divided up (partitioned) into as many parts as the cell has neighbours. So for a 4-neighbour PCA, each cell has 4 parts. These parts are denoted as U(p), R(ight), D(own), and L(eft) in the paper referenced by the PCA thread. Each part has it's own state (0 or 1 for a 2 state PCA). A 2 state PCA with 4 neighbours is denoted as a 2PCA(4) cellular automata. The evolution of the CA is determined by a local function which maps from 1 part of each of the 4 neighbour cells to the 4 parts of the centre cell. Here's a little diagram which shows the four parts of a central cell and it's 4 neighbours. The state of the four parts in the central cell (u, r, d, and l) is entirely determined by the four parts labelled U, R, D, and L from the neighbouring cells (i.e. a cells current state does not influence it's resulting state)

Code: Select all

       .               .     
      . .             . .    
       D               .     
   .   .   .       .   u   . 
  . R . . L . --> . . l r . .
   .   .   .       .   d   . 
       U               .     
      . .             . .    
       .               .     

Because there are four parts which can take 2 states, every 2PCA(4) CA is equivalent to a regular CA with 2^4 states on a von Neumann neighbourhood.

The diagrams in the referenced papers make this easier to understand than I am able to explain here, so I suggest you have a look at them:

3-neighbour: http://bprentice.webenet.net/PCA/Two%20 ... e%20CA.pdf
4-neighbour: http://bprentice.webenet.net/PCA/16%20S ... tomata.pdf

[wildmyron]

How many different conditions does the range-1 Moore 3D isotropic non-totalistic rulespace have?

I believe the answer is 8548, given by the sequence A054247: Number of n X n binary matrices under action of dihedral group of the square D_4.

This includes birth and survival configurations, so the number of neighbourhood configurations is 4274.

Edit: This is almost certainly wrong, see below

[FWKnightship]

Are there any guns for hybrid Gs in Quadlife or Immigration?

P22:

Code: Select all

x = 45, y = 21, rule = QuadLife
18.2A$19.A7.A$19.A.A14.2A$20.2A12.2A2.A$24.3A7.2A.2A$24.2A.2A7.3A$24.
A2.2A12.2A$25.2A14.A.A$35.A7.A$43.2A2$2A$.A$.A.A13.3B$2.2A3.B8.B3.B$
6.B.2B6.B4.B$5.B4.B6.2B.B$6.B3.B8.B3.2A$7.3B13.A.A$25.A$25.2A!

P30:

Code: Select all

x = 36, y = 25, rule = QuadLife
26.2B$9.2A14.B3.B$9.A.A12.B5.B$4.2A6.A11.B3.B.2B2.2A$2A.A2.A2.A2.A11.
B5.B3.2A$2A2.2A6.A12.B3.B$9.A.A14.2B$9.2A8$16.5A$15.A.3A.A$16.A3.A$
17.3A$18.A4$18.2A$18.2A!

P36:

Code: Select all

x = 75, y = 50, rule = QuadLife
25.A$25.3A$28.A$27.2A7$39.2A$38.A2.A$30.A6.A.A.A$29.3A3.3A2.A$28.2A2.
A$30.3A4.2A$38.A6$27.A$27.2A4.3B$33.B2.2B$25.A2.3A3.3B$24.A.A.A6.B26.
2A$24.A2.A33.A2.A$25.2A35.A.A$41.A16.4A.A$41.A16.2A.2A$42.A7.2A9.A$
11.2A36.2A$10.A2.A36.2A$10.A.A38.A$11.A3.2A42.A$12.2A.A43.2A$13.A6.3A
37.2A$13.A5.2A.2A25.A9.2A$19.2A2.A24.2A.2A18.2A$21.2A24.A.4A18.A.A$
16.2A28.A.A24.A$15.A2.2A26.A2.A23.2A$15.2A.2A5.A21.2A$16.3A6.A$2.2A
19.A.2A$.A.A18.2A3.A$.A24.A.A$2A23.A2.A$26.2A!

[wildmyron]

How many different conditions does the range-1 Moore 3D isotropic non-totalistic rulespace have?

I believe the answer is 8548, given by the sequence A054247: Number of n X n binary matrices under action of dihedral group of the square D_4.

This includes birth and survival configurations, so the number of neighbourhood configurations is 4274.

Actually, this is clearly not the desired sequence, though I'm presuming that the term for n=2 matches the 1D case coincidentally. I'm fairly sure there'll be no such coincidence for n=4 - I see no reason why the number of 4x4 binary matrices under D_4 should be the same as the number of 3x3x3 binary matrices under the octahedral group O_h, which is what we actually want to know.

[muzik]

For a 3D CA on a cubic honeycomb, would a spaceship with displacement (x,x,x) be described as diagonal, or would this apply to (x,x,0)? Is there a standardised nomenclature for these?

[Moosey]

For a 3D CA on a cubic honeycomb, would a spaceship with displacement (x,x,x) be described as diagonal, or would this apply to (x,x,0)?

I believe that's triagonal.

[muzik]

I personally would have suggested "paragonal" for (x,x,x), and maybe "metagonal" for (x,x,x,x).

[Moosey]

What happens if space is discrete and time is continuous? How would that effectively differ from discrete space + time?

[testitemqlstudop]

If time is continuous then space is necessarily also continuous since you can't have a cell sitting in between two discrete borders - or else what's the point of continuous time?

[wildmyron]

What happens if space is discrete and time is continuous? How would that effectively differ from discrete space + time?

Here's an example of a geophysical model which uses a discrete lattice but continuous time. Of course the implementation of the model is not actually continuous, but an approximation to it. The framework models continuous time by determining the probability of a transition occurring between every pair of neighbouring cells within a small dt, and stochastically (randomly) determining whether a transition occurred for each cell pair within every dt. With small enough dt this becomes a good approximation of continuous time. I've only skim read the paper so I hope I'm not misrepresenting it.

[Moosey]

How do Perrier loop programs work? Can anyone implement a (working) loop that counts in binary, say, or any other simpler patterns to demonstrate how Perrier loops work?

[dvgrn]

How do Perrier loop programs work? Can anyone implement a (working) loop that counts in binary, say, or any other simpler patterns to demonstrate how Perrier loops work?

Have you been through the original article from 1996? Here's a link just in case.

[NickGotts]

muzik wrote:
Would exponential growth be possible with a linearly expanding neighbourhood?

The most straightforward way to get exponential growth would be to work on a regular tiling of a hyperbolic surface (where the angles of a triangle sum to less than 180 degrees). For example, such a surface could support a tiling of regular octagons, where each cell has eight neighbours, but the number of cells at distances of 1,2,3... increases exponentially. See https://en.wikipedia.org/wiki/Uniform_t ... olic_plane.

[muzik]

Are b1357s1357, b1357s02468, b02468s1357 and b02468s02468 reversible? I've heard on multiple occasions that they are but given the way large patterns tend to immediately die out at generations 2^n it doesn't seem at all possible for an outer-totalistic rule to generate these patterns from a void.

[Hunting]

Are b1357s1357, b1357s02468, b02468s1357 and b02468s02468 reversible? I've heard on multiple occasions that they are but given the way large patterns tend to immediately die out at generations 2^n it doesn't seem at all possible for an outer-totalistic rule to generate these patterns from a void.

Because there is B1, there's no pattern that can die out.