Margolus Media

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muzik
Posts: 4155
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

Margolus Media

Post by muzik » April 18th, 2021, 9:20 pm

This thread is to consolidate all information relevant to rules that support certain isotropic Margolus simulations exhibited by higher cellular automata. There's quite a few of these known, so I want to keep track of them as well as encourage the sharing of further types.

The most known class of such block CA are detailed in this blog post (sourced from this forum post) by Nathaniel: http://www.njohnston.ca/2009/05/rectang ... automaton/

and are explored further in the following paper: http://www.njohnston.ca/wp-content/uplo ... 01/2x2.pdf

A starter list of known media:
muzik wrote:
January 10th, 2018, 12:33 pm
Margolus rule being simulated by all five possible media (empty doesn't count) coexisting in a single rule:

Code: Select all

x = 84, y = 12, rule = B2c3i4i5i/S2c3i4i5i
2o18b2o20bo19bo19bo$bo18b2o20bo40bo$2o18b2o20bo19bo19bo$bo18b2o20bo40b
o$2o18b2o20bo19bo19bo$bo18b2o20bo40bo$2o18b2o20bo19bo19bo$bo18b2o20bo
40bo$2o18b2o20bo19bo19bo$bo18b2o20bo40bo$2o18b2o20bo19bo19bo$bo18b2o
20bo40bo!
bprentice wrote:
July 16th, 2016, 2:39 pm
I'm surprised that the young members of the forum did not explore the rule introduced here:

http://www.conwaylife.com/forums/viewto ... 125#p32973

A beautiful period 4194302 oscillator:

Code: Select all

x = 48, y = 48, rule = B2ae3i/S
.A.A3.A.A.A5.A.A.A7.A.A3.A5.A.A.A$A3.A.A5.A3.A5.A5.A3.A.A.A3.A5.A$9.
A3.A.A3.A3.A3.A7.A.A.A3.A3.A$A3.A.A.A.A7.A.A3.A.A5.A3.A5.A.A$.A.A5.
A.A.A.A.A.A.A9.A.A5.A.A.A.A.A$6.A3.A7.A.A.A.A.A3.A.A.A.A.A3.A.A$.A.
A.A.A5.A.A3.A.A5.A.A.A.A9.A3.A$A5.A.A.A.A3.A3.A3.A5.A.A3.A.A7.A$3.A
3.A9.A5.A.A.A3.A3.A3.A3.A.A$A.A.A5.A.A5.A.A.A.A3.A5.A5.A.A$3.A.A.A.
A3.A9.A5.A.A.A11.A$A3.A9.A3.A.A19.A.A.A.A$.A5.A.A5.A.A3.A.A5.A.A.A5.
A5.A.A$2.A.A.A3.A13.A3.A5.A3.A3.A3.A$11.A3.A.A3.A3.A.A3.A3.A.A3.A.A
$2.A.A.A5.A.A3.A.A.A7.A.A7.A.A.A.A$.A5.A13.A.A.A.A.A.A.A.A.A.A.A.A3.
A$A3.A3.A3.A.A3.A3.A7.A.A7.A.A$3.A.A3.A.A3.A.A.A5.A.A3.A3.A.A3.A5.A
$A.A.A.A11.A.A.A.A3.A5.A3.A7.A$3.A.A.A.A.A3.A3.A9.A.A.A5.A.A3.A$A3.
A.A5.A.A.A5.A.A17.A.A$.A3.A3.A5.A.A.A.A3.A3.A.A.A5.A$2.A5.A.A.A3.A9.
A.A5.A3.A.A.A.A$3.A.A.A.A3.A5.A.A9.A3.A.A.A5.A$8.A5.A.A.A3.A3.A.A.A
.A5.A3.A3.A$3.A.A17.A.A5.A.A.A5.A.A3.A$2.A3.A.A5.A.A.A9.A3.A3.A.A.A
.A.A$.A7.A3.A5.A3.A.A.A.A11.A.A.A.A$A5.A3.A.A3.A3.A.A5.A.A.A3.A.A3.
A.A$5.A.A7.A.A7.A3.A3.A.A3.A3.A3.A$A3.A.A.A.A.A.A.A.A.A.A.A.A13.A5.
A$.A.A.A.A7.A.A7.A.A.A3.A.A5.A.A.A$4.A.A3.A.A3.A3.A.A3.A3.A.A3.A$.A
3.A3.A3.A5.A3.A13.A3.A.A.A$A.A5.A5.A.A.A5.A.A3.A.A5.A.A5.A$.A.A.A.A
19.A.A3.A9.A3.A$2.A11.A.A.A5.A9.A3.A.A.A.A$5.A.A5.A5.A3.A.A.A.A5.A.
A5.A.A.A$2.A.A3.A3.A3.A3.A.A.A5.A9.A3.A$.A7.A.A3.A.A5.A3.A3.A3.A.A.
A.A5.A$A3.A9.A.A.A.A5.A.A3.A.A5.A.A.A.A$3.A.A3.A.A.A.A.A3.A.A.A.A.A
7.A3.A$A.A.A.A.A5.A.A9.A.A.A.A.A.A.A5.A.A$3.A.A5.A3.A5.A.A3.A.A7.A.
A.A.A3.A$A3.A3.A.A.A7.A3.A3.A3.A.A3.A$.A5.A3.A.A.A3.A5.A5.A3.A5.A.A
3.A$2.A.A.A5.A3.A.A7.A.A.A5.A.A.A3.A.A!
Brian Prentice

Code: Select all

x = 64, y = 10, rule = B2e/S
63bo$42bobo17bo$25bobo13bo3bo15bo$12bobo9bo3bo11bo5bo13bo$3bobo5bo3bo
7bo5bo9bo7bo11bo$obo3bo3bo5bo5bo7bo7bo9bo9bo$7bobo7bo3bo9bo5bo11bo7bo$
18bobo11bo3bo13bo5bo$33bobo15bo3bo$52bobo!
wwei47 wrote:
March 29th, 2021, 10:46 pm
GUYTU6J wrote:
March 29th, 2021, 10:22 pm
Is there any more interesting rule than muzik's example with the five media?
For margolus media that can have the cool oscillators, I know of three other types.

Code: Select all

x = 91, y = 77, rule = B2i3ai4qt5i/S1e2ik3ij4w5i
4o17bo3bo14b12o9bo3bo3bo3bo3bo3bo$4o16b3ob3o13b12o8b3ob3ob3ob3ob3ob3o$
21bo3bo35bo3bo3bo3bo3bo3bo18$8o13bo3bo3bo3bo$8o12b3ob3ob3ob3o$21bo3bo
3bo3bo8$40b16o5bo3bo3bo3bo3bo3bo3bo3bo$40b16o4b3ob3ob3ob3ob3ob3ob3ob3o
$61bo3bo3bo3bo3bo3bo3bo3bo8$8o13bo3bo3bo3bo$8o12b3ob3ob3ob3o$8o13bo3bo
3bo3bo$8o15bo7bo$21bo3bo3bo3bo$20b3ob3ob3ob3o$21bo3bo3bo3bo24$40b16o5b
o3bo3bo3bo3bo3bo3bo3bo$40b16o4b3ob3ob3ob3ob3ob3ob3ob3o$40b16o5bo3bo3bo
3bo3bo3bo3bo3bo$40b16o7bo7bo7bo7bo$61bo3bo3bo3bo3bo3bo3bo3bo$60b3ob3ob
3ob3ob3ob3ob3ob3o$61bo3bo3bo3bo3bo3bo3bo3bo!

Code: Select all

x = 266, y = 10, rule = B2en3ijq4w6aen/S2cek3aceny4ejqr5jk6a
b2o4b2o22b2o4b2o4b2o4b2o20b2o4b2o4b2o4b2o20b2o4b2o4b2o4b2o4b2o4b2o18b
2o4b2o4b2o4b2o4b2o4b2o4b2o4b2o16b2o4b2o4b2o4b2o4b2o4b2o4b2o4b2o$o2bo2b
o2bo20bo2bo2bo2bo2bo2bo2bo2bo18bo2bo2bo2bo2bo2bo2bo2bo18bo2bo2bo2bo2bo
2bo2bo2bo2bo2bo2bo2bo16bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo
14bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo$o2bo2bo2bo20bo2bo2bo
2bo2bo2bo2bo2bo18bo2bo2bo2bo2bo2bo2bo2bo18bo2bo2bo2bo2bo2bo2bo2bo2bo2b
o2bo2bo16bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo14bo2bo2bo2bo
2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo$b2o4b2o22b2o4b2o4b2o4b2o20b2o4b2o
4b2o4b2o20b2o4b2o4b2o4b2o4b2o4b2o18b2o4b2o4b2o4b2o4b2o4b2o4b2o4b2o16b
2o4b2o4b2o4b2o4b2o4b2o4b2o4b2o3$71b2o4b2o4b2o4b2o130b2o4b2o4b2o4b2o4b
2o4b2o4b2o4b2o$70bo2bo2bo2bo2bo2bo2bo2bo128bo2bo2bo2bo2bo2bo2bo2bo2bo
2bo2bo2bo2bo2bo2bo2bo$70bo2bo2bo2bo2bo2bo2bo2bo128bo2bo2bo2bo2bo2bo2bo
2bo2bo2bo2bo2bo2bo2bo2bo2bo$71b2o4b2o4b2o4b2o130b2o4b2o4b2o4b2o4b2o4b
2o4b2o4b2o!
muzik wrote:
January 6th, 2020, 9:36 pm
Other media that can support M10:

Code: Select all

x = 55, y = 25, rule = DeficientSeeds
A.A19.A.A27.A.A6$A.A19.A.A27.A.A6$22.A.A27.A.A6$22.A.A27.A.A6$52.A.A!

Code: Select all

x = 25, y = 9, rule = B1c/S1c|B2a/S1c2e
24bo$21bo$18bo$15bo$12bo$9bo$6bo$3bo$o!
muzik wrote:
January 30th, 2020, 5:04 pm
Here's another rule that exhibits that same kind of Margolus behaviour:

Code: Select all

 x = 48, y = 48, rule = R2,C0,M0,S5..5,B3..3,NN
bo$obo$bo$4bo$3bobo$4bobo$5bobo$6bo$9bo$8bobo$9bobo$10bobo$11bobo$12bo
bo$13bo$16bo$15bobo$16bobo$17bobo$18bobo$19bobo$20bobo$21bobo$22bo$25b
o$24bobo$25bobo$26bobo$27bobo$28bobo$29bobo$30bobo$31bobo$32bobo$33bo$
36bo$35bobo$36bobo$37bobo$38bobo$39bobo$40bobo$41bobo$42bobo$43bobo$
44bobo$45bobo$46bo!
The following is a non-totalistic rule that can simulate these block CA at twice the speed:
AbhpzTa wrote:
June 30th, 2016, 12:53 pm
B3i4int5ey6k7e/S1e2k3ey4irt5i

Code: Select all

x = 319, y = 95, rule = B3i4int5ey6k7e_S1e2k3ey4irt5i
17b2o19b2o54b2o23b2o25b2o71b2o22b2o27b2o3b2o26b2o$bo17bo20bo21bo2bo27b
o24bo26bo2bo66bo2bo26bo2bo22bo7bo24bo5bo3bo$bo17bo20bo21bo2bo27bo24bo
26bo2bo66bo2bo26bo2bo22bo7bo24bo5bo3bo$17b2o19b2o23b2o29b2o23b2o98b2o
22b2o27b2o3b2o26b2o$bo14bo23bo24bo30bo21bo2bo26bo66bo5bo23bo2bo22bo2bo
4bo27bo2bo3bo$bo14bo23bo24bo30bo21bo2bo26bo66bo5bo23bo2bo22bo2bo4bo27b
o2bo3bo$17b2o19b2o54b2o23b2o98b2o22b2o27b2o3b2o26b2o14$2o14b4o17b4o20b
7o26b2o20b8o20b6o61b14o16b10o19b12o19b18o$16b4o40bo7bo25b2o20b8o$60bo
7bo25b2o$60bo7bo25b2o$61b7o26b2o$89b5o2b5o$88bo5b2o5bo$87bob5o2b5obo$
88bo5b2o5bo$89b5o2b5o$94b2o$94b2o$94b2o$94b2o$94b2o$37b4o$37b4o$37b4o$
34b3o4b3o$33bo3b4o3bo$32bob3o4b3obo97b8o59b16o$33bo3b4o3bo$34b3o4b3o$
37b4o$37b4o$37b4o5$92b6o$92b6o$90b2o6b2o$90b2o6b2o$90b2o6b2o$87b3o2b6o
2b3o$87b3o2b6o2b3o$87b3o2b6o2b3o$84b3o3b2o6b2o3b3o$84b3o3b2o6b2o3b3o$
84b3o3b2o6b2o3b3o$84b3o3b2o6b2o3b3o$80b4o3b3o2b6o2b3o3b4o$80b4o3b3o2b
6o2b3o3b4o$78b2o4b3o3b2o6b2o3b3o4b2o$77bo2b4o3b3o2b6o2b3o3b4o2bo$77bo
2b4o3b3o2b6o2b3o3b4o2bo$77bo2b4o3b3o2b6o2b3o3b4o2bo$74b3ob2o4b3o3b2o6b
2o3b3o4b2ob3o$73bo3bo2b4o3b3o2b6o2b3o3b4o2bo3bo$72bob3ob2o4b3o3b2o6b2o
3b3o4b2ob3obo$71bobo3bo2b4o3b3o2b6o2b3o3b4o2bo3bobo$70bobob3ob2o4b3o3b
2o6b2o3b3o4b2ob3obobo$71bobo3bo2b4o3b3o2b6o2b3o3b4o2bo3bobo$72bob3ob2o
4b3o3b2o6b2o3b3o4b2ob3obo$73bo3bo2b4o3b3o2b6o2b3o3b4o2bo3bo$74b3ob2o4b
3o3b2o6b2o3b3o4b2ob3o$77bo2b4o3b3o2b6o2b3o3b4o2bo$77bo2b4o3b3o2b6o2b3o
3b4o2bo$77bo2b4o3b3o2b6o2b3o3b4o2bo$78b2o4b3o3b2o6b2o3b3o4b2o$80b4o3b
3o2b6o2b3o3b4o$80b4o3b3o2b6o2b3o3b4o$84b3o3b2o6b2o3b3o$84b3o3b2o6b2o3b
3o$84b3o3b2o6b2o3b3o$84b3o3b2o6b2o3b3o$87b3o2b6o2b3o$87b3o2b6o2b3o$87b
3o2b6o2b3o$90b2o6b2o$90b2o6b2o$90b2o6b2o$92b6o$92b6o!
EDIT:

Code: Select all

x = 193, y = 84, rule = B3i4int5ey6k7e_S1e2k3ey4irt5i
b2o13bo2bo13b2o21b2o52b2o65b2o$3bo12bo2bo12bo22bo2bo50bo2bo60bo2bo2bo$
3bo13b2o13bo22bo2bo50bo2bo60bo2bo2bo$b2o16bo13b2o21b2o52b2o$o18bo12bo
2bo19bo2bo53bo60bo2bo2bo$o31bo2bo19bo2bo53bo60bo2bo2bo$b2o30b2o21b2o
52b2o65b2o6$b3o10b8o$o3bo9b8o$b3o10b8o9b7o$14b8o8bo7bo$31b7o4$50b15o
43b6o57b11o$49bo15bo41bo6bo55bo11bo$49bo15bo41bo6bo55bo11bo$49bo15bo
41bo6bo55bo11bo$49bo15bo38b3ob6ob3o52bo11bo$49bo15bo38b3ob6ob3o52bo11b
o$49bo15bo36b2o3bo6bo3b2o50bo11bo$49bo15bo36b2o3bo6bo3b2o50bo11bo$50b
15o37b2o3bo6bo3b2o43b7ob11ob7o$102b2o3bo6bo3b2o42bo7bo11bo7bo$102b2o3b
o6bo3b2o41bob7ob11ob7obo$97b5o2b3ob6ob3o2b5o35bobo7bo11bo7bobo$96bo5b
2o3bo6bo3b2o5bo35bob7ob11ob7obo$96bo5b2o3bo6bo3b2o5bo36bo7bo11bo7bo$
94b2ob5o2b3ob6ob3o2b5ob2o35b7ob11ob7o$93bo2bo5b2o3bo6bo3b2o5bo2bo41bo
11bo$93bo2bo5b2o3bo6bo3b2o5bo2bo41bo11bo$93bo2bo5b2o3bo6bo3b2o5bo2bo
41bo11bo$90b3ob2ob5o2b3ob6ob3o2b5ob2ob3o38bo11bo$89bo3bo2bo5b2o3bo6bo
3b2o5bo2bo3bo37bo11bo$88bob3ob2ob5o2b3ob6ob3o2b5ob2ob3obo36bo11bo$88bo
b3ob2ob5o2b3ob6ob3o2b5ob2ob3obo36bo11bo$86b2obo3bo2bo5b2o3bo6bo3b2o5bo
2bo3bob2o35b11o$85bo2bob3ob2ob5o2b3ob6ob3o2b5ob2ob3obo2bo$84bob2obo3bo
2bo5b2o3bo6bo3b2o5bo2bo3bob2obo$83bobo2bob3ob2ob5o2b3ob6ob3o2b5ob2ob3o
bo2bobo$82bobob2obo3bo2bo5b2o3bo6bo3b2o5bo2bo3bob2obobo$81bobobo2bob3o
b2ob5o2b3ob6ob3o2b5ob2ob3obo2bobobo$80bobobob2obo3bo2bo5b2o3bo6bo3b2o
5bo2bo3bob2obobobo$81bobobo2bob3ob2ob5o2b3ob6ob3o2b5ob2ob3obo2bobobo$
49b16o17bobob2obo3bo2bo5b2o3bo6bo3b2o5bo2bo3bob2obobo$49b16o18bobo2bob
3ob2ob5o2b3ob6ob3o2b5ob2ob3obo2bobo$49b16o19bob2obo3bo2bo5b2o3bo6bo3b
2o5bo2bo3bob2obo$49b16o20bo2bob3ob2ob5o2b3ob6ob3o2b5ob2ob3obo2bo$49b
16o21b2obo3bo2bo5b2o3bo6bo3b2o5bo2bo3bob2o38b4o$49b16o23bob3ob2ob5o2b
3ob6ob3o2b5ob2ob3obo40b4o$49b16o23bob3ob2ob5o2b3ob6ob3o2b5ob2ob3obo40b
4o$49b16o24bo3bo2bo5b2o3bo6bo3b2o5bo2bo3bo41b4o$90b3ob2ob5o2b3ob6ob3o
2b5ob2ob3o42b4o$93bo2bo5b2o3bo6bo3b2o5bo2bo45b4o$93bo2bo5b2o3bo6bo3b2o
5bo2bo45b4o$93bo2bo5b2o3bo6bo3b2o5bo2bo45b4o$94b2ob5o2b3ob6ob3o2b5ob2o
46b4o$96bo5b2o3bo6bo3b2o5bo48b4o$96bo5b2o3bo6bo3b2o5bo38b10o4b10o$97b
5o2b3ob6ob3o2b5o39b10o4b10o$102b2o3bo6bo3b2o42b2o10b4o10b2o$102b2o3bo
6bo3b2o42b2o10b4o10b2o$102b2o3bo6bo3b2o40b2o2b10o4b10o2b2o$102b2o3bo6b
o3b2o40b2o2b10o4b10o2b2o$102b2o3bo6bo3b2o42b2o10b4o10b2o$104b3ob6ob3o
44b2o10b4o10b2o$104b3ob6ob3o46b10o4b10o$107bo6bo49b10o4b10o$107bo6bo
59b4o$107bo6bo59b4o$108b6o60b4o$174b4o$174b4o$174b4o$174b4o$174b4o$
174b4o$174b4o!
Last edited by muzik on April 21st, 2021, 9:00 pm, edited 5 times in total.

User avatar
muzik
Posts: 4155
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

Re: Margolus Media

Post by muzik » April 18th, 2021, 9:29 pm

There is also a 3-state equivalent to the usual 2D margolus rules, which follow the analogous 1D rule, break down according to a different sequence than the powers of two, and generally do not have lower mods than periods.
muzik wrote:
February 3rd, 2020, 10:21 am
Here are the 3-state equivalents of the block CA found in 2x2:

Code: Select all

x = 268, y = 2, rule = marg3
2A2.4A2.6A2.8A2.10A2.12A2.14A2.16A2.18A2.20A2.22A2.24A2.26A2.28A2.30A
$2A2.4A2.6A2.8A2.10A2.12A2.14A2.16A2.18A2.20A2.22A2.24A2.26A2.28A2.
30A!
Currently working on the rule so that any arrangement of blocks can work. Sometimes it breaks down with more complex ones but we can see the gist of the effects here. I haven't been able to find any of these in the wild yet. Yet to see anyone try to generalize these up to any (prime) number - I assume it'd be easy since it's just the modulo of the sum of neighbouring cells.

Comparison to 2 state:

Code: Select all

x = 268, y = 2, rule = B3/S5
2o2b4o2b6o2b8o2b10o2b12o2b14o2b16o2b18o2b20o2b22o2b24o2b26o2b28o2b30o$
2o2b4o2b6o2b8o2b10o2b12o2b14o2b16o2b18o2b20o2b22o2b24o2b26o2b28o2b30o!
Some squares, p4n 4nx4n:

Code: Select all

 x = 40, y = 12, rule = marg3
28.12A$28.12A$10.8A10.12A$10.8A10.12A$4A6.8A10.12A$4A6.8A10.12A$4A6.
8A10.12A$4A6.8A10.12A$10.8A10.12A$10.8A10.12A$28.12A$28.12A!
muzik wrote:
February 3rd, 2020, 12:50 pm
A diagonal version of the 3-state version of the commonly encountered margolus rule which follows rule 6:

Code: Select all

x = 50, y = 61, rule = marg3diag
13.A.A$12.A3.A21.A.A$11.A5.A19.A3.A$10.A7.A17.A5.A$9.A9.A15.A7.A$8.A
11.A13.A9.A$7.A13.A11.A11.A$6.A15.A9.A13.A$5.A17.A7.A15.A$4.A19.A5.A
17.A$3.A21.A3.A19.A$2.A23.A.A$.A47.A$48.A$.A45.A$2.A43.A$3.A41.A$4.A
39.A$5.A37.A$6.A35.A$7.A33.A$8.A17.A.A$9.A15.A3.A9.A$10.A13.A5.A7.A$
11.A11.A13.A$12.A17.A5.A$13.A7.A7.A5.A$14.A5.A13.A$19.A7.A5.A$14.A3.A
13.A$13.A3.A$12.A17.A$11.A5.A11.A$10.A7.A9.A$9.A9.A7.A$8.A11.A5.A$7.A
13.A3.A$6.A15.A.A$5.A$4.A$3.A$2.A$.A$A$33.A$A31.A$.A29.A$2.A27.A$3.A
25.A$4.A23.A$5.A21.A$6.A19.A$7.A17.A$8.A15.A$9.A13.A$10.A11.A$11.A9.A
$12.A7.A$13.A5.A$14.A3.A$15.A.A!
This one follows 3 state rule 8229. Failed oscillators follow A048473 and split into multiple smaller oscillators.

Can someone make a ruletable for the 5-state or 7-state versions of this?

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wwei47
Posts: 577
Joined: February 18th, 2021, 11:18 am

Re: Margolus Media

Post by wwei47 » April 18th, 2021, 9:55 pm

Code: Select all

x = 118, y = 88, rule = B1e2i3er4e5i6cn/S2ac:T120,90
3bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo3$o5bo5bo
5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo3$3bo5bo5bo5bo5bo5b
o5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo3$o5bo5bo5bo5bo5bo5bo5bo5bo
5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo3$3bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5b
o5bo5bo5bo5bo5bo5bo5bo5bo3$o5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo
5bo5bo5bo5bo5bo3$3bo5bo11bo5bo11bo5bo5bo5bo11bo5bo5bo11bo5bo5bo5bo5bo
3$o5bo5bo11bo5bo11bo5bo5bo17bo5bo5bo11bo5bo5bo5bo3$3bo5bo5bo5bo5bo5bo
11bo5bo5bo17bo5bo5bo11bo5bo5bo5bo3$o5bo5bo5bo5bo5bo5bo11bo5bo5bo17bo5b
o5bo11bo5bo5bo3$3bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo11bo5bo5bo5bo11bo5bo
5bo3$o5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo11bo5bo3$3bo5bo
5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo3$o5bo5bo5bo5bo
5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo3$3bo5bo5bo5bo5bo5bo5bo5b
o11bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo3$o5bo5bo5bo5bo5bo5bo5bo17bo5bo5bo
5bo5bo5bo5bo5bo5bo5bo3$3bo5bo11bo5bo5bo5bo5bo17bo5bo5bo5bo5bo5bo5bo5bo
5bo5bo3$o5bo5bo11bo5bo5bo5bo5bo17bo5bo5bo5bo5bo5bo5bo5bo5bo3$3bo5bo5bo
11bo5bo5bo5bo5bo17bo5bo5bo5bo5bo5bo5bo5bo5bo3$o5bo5bo5bo11bo5bo5bo5bo
5bo17bo5bo5bo5bo5bo5bo5bo5bo3$3bo5bo5bo5bo11bo5bo5bo5bo5bo17bo5bo5bo5b
o5bo5bo5bo5bo3$o5bo5bo5bo5bo11bo5bo5bo5bo5bo17bo5bo5bo5bo5bo5bo5bo3$3b
o5bo5bo5bo5bo11bo5bo5bo5bo5bo11bo5bo5bo5bo5bo5bo5bo5bo3$o5bo5bo5bo5bo
5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo3$3bo5bo5bo5bo5bo5bo5bo5b
o5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo3$o5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo
5bo5bo5bo5bo5bo5bo5bo5bo5bo3$3bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5b
o5bo5bo5bo5bo5bo5bo3$o5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo
5bo5bo5bo3$3bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5b
o3$o5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo!

Code: Select all

x = 19, y = 17, rule = Symbiosis
11.A$9.2A.A$3.A$2.3A3.A6.A$.A2.A3.2A5.A$A7.A.3A2.2A$A.3A4.A.4A.3A$.2A
2.B3.A4.A$B.B8.2A$13.A$12.2A$7.B3.2A4.2B$8.2A.A5.A$10.A3.A$9.2AB.B$8.
A2.2B4.B$8.B9.A!

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muzik
Posts: 4155
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Location: Scotland

Re: Margolus Media

Post by muzik » April 18th, 2021, 11:08 pm

This post and five posts that follow it mention a lot regarding these media:
A for awesome wrote:
January 8th, 2018, 11:37 pm
Something that I realized about these XOR oscillators: They're all actually 2x2 block oscillators, it's just that the 2x2 blocks have different contents. For the original 2x2 rule, the 2x2 blocks are completely full; for B2c/S and analogues, the blocks consist of one on cell and 3 off cells; and for rules such as that in the above post, the blocks look like this:

Code: Select all

oo
..
Obviously, they aren't all Margolus automata (at least range 1) — unlike 2x2 — but I feel like they still classify as 2x2 block oscillators, if not automata.

Here are two more families I've found based on this idea:

Code: Select all

x = 96, y = 2, rule = B2c/S2c
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobo$bobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobo!

Code: Select all

x = 90, y = 2, rule = B2c3i5i/S3i4i
90o$bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobo!
Unfortunately, patterns in rules supporting the latter family cannot escape their bounding box [EDIT: actually diamond].

EDIT 6-25-2020: Variants of the last kind of oscillator can actually function in rules where patterns can escape their bounding diamond, albeit following block automata with multiple types of off states:

Code: Select all

x = 90, y = 2, rule = B2ce3iy4a5i/S3i4i5y
90o$bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobo!
dvgrn wrote:
January 8th, 2018, 11:56 pm
A for awesome wrote:Something that I realized about these XOR oscillators: They're all actually 2x2 block oscillators, it's just that the 2x2 blocks have different contents. For the original 2x2 rule, the 2x2 blocks are completely full; for B2c/S and analogues, the blocks consist of one on cell and 3 off cells; and for rules such as that in the above post, the blocks look like this:

Code: Select all

oo
..
Yup, and clearly the dynamics of all these rules have to be exactly isomorphic in some sense, or the recognizable behavior couldn't happen.

I had this rule confused with Snowflakes for a while there, and posted the following in the wrong thread. Putting it here now with appropriate edits, so as not to waste it --

There seem to be oscillators out there with period (2^N-2)*2^k for any N>2 and k>=0. And then there are the exceptions-that-prove-the-rule ones at 174762 and 45 billion [one third of "standard" numbers, both -- (2^19-2)/3 and (2^37-2)/3 ]...

Code: Select all

#C period 45812984490 oscillator
x = 188, y = 1, rule = B2ci3ai4ci8/S02ae3eijkq4iz5a6i7e
188o!
... So can the pointy ends of these diamonds make gliders and suchlike, the way AbhpzTa did with the horiship guns in B2cek3i/S12cei?
muzik wrote:
January 9th, 2018, 12:11 pm
A for awesome wrote:Something that I realized about these XOR oscillators: They're all actually 2x2 block oscillators, it's just that the 2x2 blocks have different contents. For the original 2x2 rule, the 2x2 blocks are completely full; for B2c/S and analogues, the blocks consist of one on cell and 3 off cells; and for rules such as that in the above post, the blocks look like this:
I found this out a good few months ago. I tried looking for a rule where the last family worked though, with no success.

Here's more:

Code: Select all

x = 23, y = 6, rule = B2e/S
o3bo5bo6bo$bo3bo5bo6bo$6bo5bo6bo$7bo5bo6bo$14bo6bo$22bo!
The thread also mentioned this one:

Code: Select all

x = 65, y = 32, rule = B2-a3/S01c5i
o19bo19bo19bo$21bo19bo19bo$22bo19bo19bo$43bo19bo$64bo16$2o18b2o18b2o
18b2o$2o18b2o18b2o18b2o$2o18b2o18b2o18b2o$2o18b2o18b2o18b2o$20b2o18b2o
18b2o$20b2o18b2o18b2o$20b2o18b2o18b2o$20b2o18b2o18b2o$40b2o18b2o$40b2o
18b2o$60b2o$60b2o!
(referencing this post and this post)
muzik wrote:
January 9th, 2018, 12:44 pm
A type R(?) replicator, which fits in at least six of the seven rules:

Code: Select all

x = 1, y = 1, rule = B1c2n3c4c/S
o!

Code: Select all

x = 2, y = 1, rule = B1c2a3q6i/S
2o!

Code: Select all

x = 2, y = 2, rule = B1c2n/S1c2n4c
bo$o!

Code: Select all

x = 2, y = 2, rule = B1c2a3aq4qw8/S2a3q6i
2o$bo!

Code: Select all

x = 2, y = 2, rule = B1c2a4w/S3a4q8
2o$2o!

Code: Select all

x = 1, y = 1, rule = B1e2i3e4e/S
o!
A for awesome wrote:
January 9th, 2018, 7:08 pm
It also appears that the "off" block state can be replaced under some circumstances allowing for oscillators that are similar if not exactly the same:

Code: Select all

x = 15, y = 15, rule = B4c/S02en3ce4ci5e
15o$obobobobobobobo$2obobobobobob2o$obobobobobobobo$2obobobobobob2o$ob
obobobobobobo$2o9bob2o$obobobobobobobo$2obobobobobob2o$obobobobobobobo
$2obobobobobob2o$obobobobobobobo$2obobobobobob2o$obobobobobobobo$15o!

Code: Select all

x = 15, y = 15, rule = B4t5ey6ci/S2ek3cnr4cy5e
4b2o3b2o$b2obobobobob2o$bobobobobobobo$2bobobobobobo$2obobobobobob2o$o
bobobobobobobo$bob2obobobo2bo$2bobobobobobo$bobobobobobobo$obobobobobo
bobo$2obobobobobob2o$2bobobobobobo$bobobobobobobo$b2obobobobob2o$4b2o
3b2o!

Code: Select all

x = 17, y = 17, rule = B3a5i8/S3i4i6ci7e8
bobobobobobobobo$17o$bobobobobobobobo$17o$bobobobobobobobo$17o$bobobob
obobobobo$17o$b13obo$17o$bobobobobobobobo$17o$bobobobobobobobo$17o$bob
obobobobobobo$17o$bobobobobobobobo!
muzik wrote:
January 9th, 2018, 7:16 pm
This one seems to work for any even number not divisible by 4:

Code: Select all

x = 36, y = 16, rule = B2e3a4w/S1c3a4q
2o5b2o11b2o$2o5b2o11b2o$2b2o5b2o11b2o$2b2o5b2o11b2o$11b2o11b2o$11b2o
11b2o$13b2o11b2o$13b2o11b2o$28b2o$28b2o$30b2o$30b2o$32b2o$32b2o$34b2o$
34b2o!
Also, bilateral rules can allow for this:

Code: Select all

x = 31, y = 31, rule = B3i6i/S2i5i
2o28bo$2o28bo$2o28bo$2o28bo$2o28bo$2o28bo$2o28bo$2o28bo$2o28bo$2o28bo$
2o28bo$2o28bo9$2o28bo$2o28bo$2o28bo$2o28bo$2o28bo$2o28bo$2o28bo$2o28bo
$2o28bo$2o28bo$2o28bo!

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muzik
Posts: 4155
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

Re: Margolus Media

Post by muzik » April 20th, 2021, 1:13 am

Found in the alternating CA thread:

Code: Select all

x = 67, y = 1, rule = B12345678/S|B/S3
77bo3$76bo3$45bo29bo3$44bo29bo3$21bo21bo29bo3$20bo21bo29bo3$5bo13bo21b
o29bo3$4bo13bo21bo29bo10$o3bobo3bobobo3bobobobo3bobobobobo3bobobobobob
o3bobobobobobobo3bobobobobobobobo10$o9bo17bo25bo3$11bo17bo25bo3$12bo
17bo25bo3$31bo25bo3$32bo25bo3$59bo3$60bo!
And one I randomly came up wiTh while thinking about this:

Code: Select all

x = 148, y = 1, rule = B1/S|B2c/S
o4bo3bo4bo3bo3bo4bo3bo3bo3bo4bo3bo3bo3bo3bo4bo3bo3bo3bo3bo3bo4bo3bo3bo
3bo3bo3bo3bo4bo3bo3bo3bo3bo3bo3bo3bo!
Obvious variant:

Code: Select all

x = 148, y = 1, rule = B1/S0|B2c/S
o4bo3bo4bo3bo3bo4bo3bo3bo3bo4bo3bo3bo3bo3bo4bo3bo3bo3bo3bo3bo4bo3bo3bo
3bo3bo3bo3bo4bo3bo3bo3bo3bo3bo3bo3bo!
And this preserves the oblique versions

Code: Select all

x = 67, y = 1, rule = B12345678/S0|B/S4a
77bo3$76bo3$45bo29bo3$44bo29bo3$21bo21bo29bo3$20bo21bo29bo3$5bo13bo21b
o29bo3$4bo13bo21bo29bo10$o3bobo3bobobo3bobobobo3bobobobobo3bobobobobob
o3bobobobobobobo3bobobobobobobobo10$o9bo17bo25bo3$11bo17bo25bo3$12bo
17bo25bo3$31bo25bo3$32bo25bo3$59bo3$60bo!

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muzik
Posts: 4155
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

Re: Margolus Media

Post by muzik » April 20th, 2021, 2:19 am

Arbitrary-period Margolus media, using Andrew's alternating rule script:

Code: Select all

x = 16, y = 10, rule = B123/S12345678|B123/S12345678|B123/S12345678|B123/S12345678|B123/S12345678|B123/S12345678|B2c/S
o13bo13bo13bo13bo13bo13bo13bo13bo!

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muzik
Posts: 4155
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

Re: Margolus Media

Post by muzik » April 20th, 2021, 5:52 pm

The 5-state Margolus rule is now completed. Here are all three (2, 3, 5) prime modulo-based margolus rules so far:

Code: Select all

x = 96, y = 95, rule = B2e/S
14$14bobo57bo$13bo3bo21bobo33bo$12bo5bo19bo3bo33bo$11bo7bo17bo5bo33bo$
10bo9bo15bo7bo33bo$9bo11bo13bo9bo33bo$8bo13bo11bo11bo33bo$7bo15bo9bo
13bo33bo$6bo17bo7bo15bo33bo$5bo19bo5bo17bo33bo$4bo21bo3bo19bo33bo$3bo
23bobo55bo$2bo47bo35bo$49bo37bo$2bo45bo39bo$3bo43bo41bo$4bo41bo43bo$5b
o39bo45bo$6bo37bo47bo$7bo35bo49bo$8bo33bo51bo$9bo17bobo$10bo15bo3bo9bo
53bo$11bo13bo5bo7bo53bo$12bo11bo13bo53bo$13bo17bo5bo53bo$14bo7bo7bo5bo
53bo$15bo5bo13bo53bo$20bo7bo5bo53bo$15bo3bo13bo53bo$14bo3bo67bo$13bo
17bo53bo$12bo5bo11bo53bo$11bo7bo9bo53bo$10bo9bo7bo53bo$9bo11bo5bo53bo$
8bo13bo3bo53bo$7bo15bobo53bo$6bo71bo$5bo71bo$4bo71bo$3bo71bo$2bo$bo71b
o$34bobo35bo$bo31bo3bo33bo$2bo29bo5bo31bo$3bo27bo7bo29bo$4bo25bo9bo27b
o$5bo23bo11bo25bo$6bo21bo13bo23bo$7bo19bo15bo21bo$8bo17bo17bo19bo$9bo
15bo19bo17bo$10bo13bo21bo15bo$11bo11bo23bo13bo$12bo9bo25bo11bo$13bo7bo
27bo9bo$14bo5bo29bo7bo$15bo3bo31bo5bo$16bobo33bo3bo$53bobo!

Code: Select all

x = 94, y = 62, rule = marg3diag
13.A.A57.A$12.A3.A21.A.A33.A$11.A5.A19.A3.A33.A$10.A7.A17.A5.A33.A$9.
A9.A15.A7.A33.A$8.A11.A13.A9.A33.A$7.A13.A11.A11.A33.A$6.A15.A9.A13.A
33.A$5.A17.A7.A15.A33.A$4.A19.A5.A17.A33.A$3.A21.A3.A19.A33.A$2.A23.A
.A55.A$.A47.A35.A$48.A37.A$.A45.A39.A$2.A43.A41.A$3.A41.A43.A$4.A39.A
45.A$5.A37.A47.A$6.A35.A49.A$7.A33.A51.A$8.A17.A.A$9.A15.A3.A9.A53.A$
10.A13.A5.A7.A53.A$11.A11.A13.A53.A$12.A17.A5.A53.A$13.A7.A7.A5.A53.A
$14.A5.A13.A53.A$19.A7.A5.A53.A$14.A3.A13.A53.A$13.A3.A67.A$12.A17.A
53.A$11.A5.A11.A53.A$10.A7.A9.A53.A$9.A9.A7.A53.A$8.A11.A5.A53.A$7.A
13.A3.A53.A$6.A15.A.A53.A$5.A71.A$4.A71.A$3.A71.A$2.A71.A$.A$A71.A$
33.A.A35.A$A31.A3.A33.A$.A29.A5.A31.A$2.A27.A7.A29.A$3.A25.A9.A27.A$
4.A23.A11.A25.A$5.A21.A13.A23.A$6.A19.A15.A21.A$7.A17.A17.A19.A$8.A
15.A19.A17.A$9.A13.A21.A15.A$10.A11.A23.A13.A$11.A9.A25.A11.A$12.A7.A
27.A9.A$13.A5.A29.A7.A$14.A3.A31.A5.A$15.A.A33.A3.A$52.A.A!

Code: Select all

x = 94, y = 62, rule = marg5diag
13.A.A57.A$12.A3.A21.A.A33.A$11.A5.A19.A3.A33.A$10.A7.A17.A5.A33.A$9.
A9.A15.A7.A33.A$8.A11.A13.A9.A33.A$7.A13.A11.A11.A33.A$6.A15.A9.A13.A
33.A$5.A17.A7.A15.A33.A$4.A19.A5.A17.A33.A$3.A21.A3.A19.A33.A$2.A23.A
.A55.A$.A47.A35.A$48.A37.A$.A45.A39.A$2.A43.A41.A$3.A41.A43.A$4.A39.A
45.A$5.A37.A47.A$6.A35.A49.A$7.A33.A51.A$8.A17.A.A$9.A15.A3.A9.A53.A$
10.A13.A5.A7.A53.A$11.A11.A13.A53.A$12.A17.A5.A53.A$13.A7.A7.A5.A53.A
$14.A5.A13.A53.A$19.A7.A5.A53.A$14.A3.A13.A53.A$13.A3.A67.A$12.A17.A
53.A$11.A5.A11.A53.A$10.A7.A9.A53.A$9.A9.A7.A53.A$8.A11.A5.A53.A$7.A
13.A3.A53.A$6.A15.A.A53.A$5.A71.A$4.A71.A$3.A71.A$2.A71.A$.A$A71.A$
33.A.A35.A$A31.A3.A33.A$.A29.A5.A31.A$2.A27.A7.A29.A$3.A25.A9.A27.A$
4.A23.A11.A25.A$5.A21.A13.A23.A$6.A19.A15.A21.A$7.A17.A17.A19.A$8.A
15.A19.A17.A$9.A13.A21.A15.A$10.A11.A23.A13.A$11.A9.A25.A11.A$12.A7.A
27.A9.A$13.A5.A29.A7.A$14.A3.A31.A5.A$15.A.A33.A3.A$52.A.A!
Like how 2-state follows rule 6 and 3 state follows rule 8229, 5 states supports 205464118576052930. And where 2-state oscillators break down for the Mersenne numbers and 3 states for A048473, the 5 state oscillators appear to break down according to A081655 (thus implying h states break down at every 2*h^n - 1):

Code: Select all

x = 249, y = 249, rule = marg5diag
248.A$247.A$246.A$245.A$244.A$243.A$242.A$241.A$240.A$239.A$238.A$
237.A$236.A$235.A$234.A$233.A$232.A$231.A$230.A$229.A$228.A$227.A$
226.A$225.A$224.A$223.A$222.A$221.A$220.A$219.A$218.A$217.A$216.A$
215.A$214.A$213.A$212.A$211.A$210.A$209.A$208.A$207.A$206.A$205.A$
204.A$203.A$202.A$201.A$200.A$199.A$198.A$197.A$196.A$195.A$194.A$
193.A$192.A$191.A$190.A$189.A$188.A$187.A$186.A$185.A$184.A$183.A$
182.A$181.A$180.A$179.A$178.A$177.A$176.A$175.A$174.A$173.A$172.A$
171.A$170.A$169.A$168.A$167.A$166.A$165.A$164.A$163.A$162.A$161.A$
160.A$159.A$158.A$157.A$156.A$155.A$154.A$153.A$152.A$151.A$150.A$
149.A$148.A$147.A$146.A$145.A$144.A$143.A$142.A$141.A$140.A$139.A$
138.A$137.A$136.A$135.A$134.A$133.A$132.A$131.A$130.A$129.A$128.A$
127.A$126.A$125.A$124.A$123.A$122.A$121.A$120.A$119.A$118.A$117.A$
116.A$115.A$114.A$113.A$112.A$111.A$110.A$109.A$108.A$107.A$106.A$
105.A$104.A$103.A$102.A$101.A$100.A$99.A$98.A$97.A$96.A$95.A$94.A$93.
A$92.A$91.A$90.A$89.A$88.A$87.A$86.A$85.A$84.A$83.A$82.A$81.A$80.A$
79.A$78.A$77.A$76.A$75.A$74.A$73.A$72.A$71.A$70.A$69.A$68.A$67.A$66.A
$65.A$64.A$63.A$62.A$61.A$60.A$59.A$58.A$57.A$56.A$55.A$54.A$53.A$52.
A$51.A$50.A$49.A$48.A$47.A$46.A$45.A$44.A$43.A$42.A$41.A$40.A$39.A$
38.A$37.A$36.A$35.A$34.A$33.A$32.A$31.A$30.A$29.A$28.A$27.A$26.A$25.A
$24.A$23.A$22.A$21.A$20.A$19.A$18.A$17.A$16.A$15.A$14.A$13.A$12.A$11.
A$10.A$9.A$8.A$7.A$6.A$5.A$4.A$3.A$2.A$.A$A!

User avatar
muzik
Posts: 4155
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

Re: Margolus Media

Post by muzik » April 21st, 2021, 8:06 pm

7-state Margolus is now also done, resulting in four fundamental rule types having been constructed:

Code: Select all

x = 147, y = 165, rule = B2e/S
77bobo$76bo3bo$75bo5bo$74bo7bo$73bo9bo$72bo11bo$71bo13bo$70bo15bo$69bo
17bo$68bo19bo$67bo21bo$66bo23bo$65bo25bo$64bo27bo$63bo29bo$62bo31bo$
61bo33bo$60bo35bo$59bo37bo$58bo39bo$57bo41bo$56bo43bo$55bo45bo$54bo$
103bo$52bo51bo$51bo53bo$50bo55bo$49bo57bo$48bo59bo$47bo61bo$46bo63bo$
45bo65bo$44bo67bo$43bo69bo$42bo71bo$41bo73bo$40bo75bo$39bo77bo$38bo79b
o$37bo81bo$36bo83bo$35bo85bo$34bo87bo$33bo89bo$32bo91bo$31bo$30bo35bob
o57bo$29bo35bo3bo21bobo33bo$28bo35bo5bo19bo3bo33bo$63bo7bo17bo5bo33bo$
26bo35bo9bo15bo7bo33bo$25bo35bo11bo13bo9bo33bo$24bo35bo13bo11bo11bo33b
o$23bo35bo15bo9bo13bo33bo$22bo35bo17bo7bo15bo33bo$21bo35bo19bo5bo17bo
33bo$20bo35bo21bo3bo19bo33bo$19bo35bo23bobo55bo$18bo35bo47bo35bo$17bo
83bo37bo$16bo37bo45bo39bo$15bo39bo43bo41bo$14bo41bo41bo43bo$13bo43bo
39bo45bo$12bo45bo37bo47bo$11bo47bo35bo49bo$10bo49bo33bo51bo$9bo51bo17b
obo$8bo53bo15bo3bo9bo53bo$7bo55bo13bo5bo7bo53bo$6bo57bo11bo13bo53bo$5b
o59bo17bo5bo53bo$4bo61bo7bo7bo5bo53bo$3bo63bo5bo13bo53bo$2bo69bo7bo5bo
53bo$bo65bo3bo13bo53bo$66bo3bo67bo$bo63bo17bo53bo$2bo61bo5bo11bo53bo$
3bo59bo7bo9bo53bo$4bo57bo9bo7bo53bo$5bo55bo11bo5bo53bo$6bo53bo13bo3bo
53bo$7bo51bo15bobo53bo$8bo49bo71bo$9bo47bo71bo$10bo45bo71bo$11bo43bo
71bo$12bo41bo$13bo39bo71bo$14bo71bobo35bo$15bo37bo31bo3bo33bo$16bo37bo
29bo5bo31bo$17bo37bo27bo7bo29bo$18bo37bo25bo9bo27bo$19bo37bo23bo11bo
25bo$20bo37bo21bo13bo23bo$21bo37bo19bo15bo21bo$22bo37bo17bo17bo19bo$
23bo37bo15bo19bo17bo$24bo37bo13bo21bo15bo$25bo37bo11bo23bo13bo$26bo37b
o9bo25bo11bo$27bo37bo7bo27bo9bo$66bo5bo29bo7bo$27bo39bo3bo31bo5bo$26bo
41bobo33bo3bo$25bo79bobo$24bo$23bo$22bo$21bo$20bo$19bo$18bo$17bo$16bo$
15bo$14bo$13bo$12bo$11bo$10bo$9bo$8bo$7bo$6bo$5bo$4bo$3bo$2bo$bo$o$59b
obo$o57bo3bo$bo55bo5bo$2bo53bo7bo$3bo51bo9bo$4bo49bo11bo$5bo47bo13bo$
6bo45bo15bo$7bo43bo17bo$8bo41bo19bo$9bo39bo21bo$10bo37bo23bo$11bo35bo
25bo$12bo33bo27bo$13bo31bo29bo$14bo29bo31bo$15bo27bo33bo$16bo25bo35bo$
17bo23bo37bo$18bo21bo39bo$19bo19bo41bo$20bo17bo43bo$21bo15bo45bo$22bo
13bo47bo$23bo11bo49bo$24bo9bo51bo$25bo7bo53bo$26bo5bo55bo$27bo3bo57bo$
28bobo59bo$91bo!

Code: Select all

x = 147, y = 165, rule = marg3diag
77bobo$76bo3bo$75bo5bo$74bo7bo$73bo9bo$72bo11bo$71bo13bo$70bo15bo$69bo
17bo$68bo19bo$67bo21bo$66bo23bo$65bo25bo$64bo27bo$63bo29bo$62bo31bo$
61bo33bo$60bo35bo$59bo37bo$58bo39bo$57bo41bo$56bo43bo$55bo45bo$54bo$
103bo$52bo51bo$51bo53bo$50bo55bo$49bo57bo$48bo59bo$47bo61bo$46bo63bo$
45bo65bo$44bo67bo$43bo69bo$42bo71bo$41bo73bo$40bo75bo$39bo77bo$38bo79b
o$37bo81bo$36bo83bo$35bo85bo$34bo87bo$33bo89bo$32bo91bo$31bo$30bo35bob
o57bo$29bo35bo3bo21bobo33bo$28bo35bo5bo19bo3bo33bo$63bo7bo17bo5bo33bo$
26bo35bo9bo15bo7bo33bo$25bo35bo11bo13bo9bo33bo$24bo35bo13bo11bo11bo33b
o$23bo35bo15bo9bo13bo33bo$22bo35bo17bo7bo15bo33bo$21bo35bo19bo5bo17bo
33bo$20bo35bo21bo3bo19bo33bo$19bo35bo23bobo55bo$18bo35bo47bo35bo$17bo
83bo37bo$16bo37bo45bo39bo$15bo39bo43bo41bo$14bo41bo41bo43bo$13bo43bo
39bo45bo$12bo45bo37bo47bo$11bo47bo35bo49bo$10bo49bo33bo51bo$9bo51bo17b
obo$8bo53bo15bo3bo9bo53bo$7bo55bo13bo5bo7bo53bo$6bo57bo11bo13bo53bo$5b
o59bo17bo5bo53bo$4bo61bo7bo7bo5bo53bo$3bo63bo5bo13bo53bo$2bo69bo7bo5bo
53bo$bo65bo3bo13bo53bo$66bo3bo67bo$bo63bo17bo53bo$2bo61bo5bo11bo53bo$
3bo59bo7bo9bo53bo$4bo57bo9bo7bo53bo$5bo55bo11bo5bo53bo$6bo53bo13bo3bo
53bo$7bo51bo15bobo53bo$8bo49bo71bo$9bo47bo71bo$10bo45bo71bo$11bo43bo
71bo$12bo41bo$13bo39bo71bo$14bo71bobo35bo$15bo37bo31bo3bo33bo$16bo37bo
29bo5bo31bo$17bo37bo27bo7bo29bo$18bo37bo25bo9bo27bo$19bo37bo23bo11bo
25bo$20bo37bo21bo13bo23bo$21bo37bo19bo15bo21bo$22bo37bo17bo17bo19bo$
23bo37bo15bo19bo17bo$24bo37bo13bo21bo15bo$25bo37bo11bo23bo13bo$26bo37b
o9bo25bo11bo$27bo37bo7bo27bo9bo$66bo5bo29bo7bo$27bo39bo3bo31bo5bo$26bo
41bobo33bo3bo$25bo79bobo$24bo$23bo$22bo$21bo$20bo$19bo$18bo$17bo$16bo$
15bo$14bo$13bo$12bo$11bo$10bo$9bo$8bo$7bo$6bo$5bo$4bo$3bo$2bo$bo$o$59b
obo$o57bo3bo$bo55bo5bo$2bo53bo7bo$3bo51bo9bo$4bo49bo11bo$5bo47bo13bo$
6bo45bo15bo$7bo43bo17bo$8bo41bo19bo$9bo39bo21bo$10bo37bo23bo$11bo35bo
25bo$12bo33bo27bo$13bo31bo29bo$14bo29bo31bo$15bo27bo33bo$16bo25bo35bo$
17bo23bo37bo$18bo21bo39bo$19bo19bo41bo$20bo17bo43bo$21bo15bo45bo$22bo
13bo47bo$23bo11bo49bo$24bo9bo51bo$25bo7bo53bo$26bo5bo55bo$27bo3bo57bo$
28bobo59bo$91bo!

Code: Select all

x = 147, y = 165, rule = marg5diag
77bobo$76bo3bo$75bo5bo$74bo7bo$73bo9bo$72bo11bo$71bo13bo$70bo15bo$69bo
17bo$68bo19bo$67bo21bo$66bo23bo$65bo25bo$64bo27bo$63bo29bo$62bo31bo$
61bo33bo$60bo35bo$59bo37bo$58bo39bo$57bo41bo$56bo43bo$55bo45bo$54bo$
103bo$52bo51bo$51bo53bo$50bo55bo$49bo57bo$48bo59bo$47bo61bo$46bo63bo$
45bo65bo$44bo67bo$43bo69bo$42bo71bo$41bo73bo$40bo75bo$39bo77bo$38bo79b
o$37bo81bo$36bo83bo$35bo85bo$34bo87bo$33bo89bo$32bo91bo$31bo$30bo35bob
o57bo$29bo35bo3bo21bobo33bo$28bo35bo5bo19bo3bo33bo$63bo7bo17bo5bo33bo$
26bo35bo9bo15bo7bo33bo$25bo35bo11bo13bo9bo33bo$24bo35bo13bo11bo11bo33b
o$23bo35bo15bo9bo13bo33bo$22bo35bo17bo7bo15bo33bo$21bo35bo19bo5bo17bo
33bo$20bo35bo21bo3bo19bo33bo$19bo35bo23bobo55bo$18bo35bo47bo35bo$17bo
83bo37bo$16bo37bo45bo39bo$15bo39bo43bo41bo$14bo41bo41bo43bo$13bo43bo
39bo45bo$12bo45bo37bo47bo$11bo47bo35bo49bo$10bo49bo33bo51bo$9bo51bo17b
obo$8bo53bo15bo3bo9bo53bo$7bo55bo13bo5bo7bo53bo$6bo57bo11bo13bo53bo$5b
o59bo17bo5bo53bo$4bo61bo7bo7bo5bo53bo$3bo63bo5bo13bo53bo$2bo69bo7bo5bo
53bo$bo65bo3bo13bo53bo$66bo3bo67bo$bo63bo17bo53bo$2bo61bo5bo11bo53bo$
3bo59bo7bo9bo53bo$4bo57bo9bo7bo53bo$5bo55bo11bo5bo53bo$6bo53bo13bo3bo
53bo$7bo51bo15bobo53bo$8bo49bo71bo$9bo47bo71bo$10bo45bo71bo$11bo43bo
71bo$12bo41bo$13bo39bo71bo$14bo71bobo35bo$15bo37bo31bo3bo33bo$16bo37bo
29bo5bo31bo$17bo37bo27bo7bo29bo$18bo37bo25bo9bo27bo$19bo37bo23bo11bo
25bo$20bo37bo21bo13bo23bo$21bo37bo19bo15bo21bo$22bo37bo17bo17bo19bo$
23bo37bo15bo19bo17bo$24bo37bo13bo21bo15bo$25bo37bo11bo23bo13bo$26bo37b
o9bo25bo11bo$27bo37bo7bo27bo9bo$66bo5bo29bo7bo$27bo39bo3bo31bo5bo$26bo
41bobo33bo3bo$25bo79bobo$24bo$23bo$22bo$21bo$20bo$19bo$18bo$17bo$16bo$
15bo$14bo$13bo$12bo$11bo$10bo$9bo$8bo$7bo$6bo$5bo$4bo$3bo$2bo$bo$o$59b
obo$o57bo3bo$bo55bo5bo$2bo53bo7bo$3bo51bo9bo$4bo49bo11bo$5bo47bo13bo$
6bo45bo15bo$7bo43bo17bo$8bo41bo19bo$9bo39bo21bo$10bo37bo23bo$11bo35bo
25bo$12bo33bo27bo$13bo31bo29bo$14bo29bo31bo$15bo27bo33bo$16bo25bo35bo$
17bo23bo37bo$18bo21bo39bo$19bo19bo41bo$20bo17bo43bo$21bo15bo45bo$22bo
13bo47bo$23bo11bo49bo$24bo9bo51bo$25bo7bo53bo$26bo5bo55bo$27bo3bo57bo$
28bobo59bo$91bo!

Code: Select all

x = 147, y = 165, rule = marg7diag
77bobo$76bo3bo$75bo5bo$74bo7bo$73bo9bo$72bo11bo$71bo13bo$70bo15bo$69bo
17bo$68bo19bo$67bo21bo$66bo23bo$65bo25bo$64bo27bo$63bo29bo$62bo31bo$
61bo33bo$60bo35bo$59bo37bo$58bo39bo$57bo41bo$56bo43bo$55bo45bo$54bo$
103bo$52bo51bo$51bo53bo$50bo55bo$49bo57bo$48bo59bo$47bo61bo$46bo63bo$
45bo65bo$44bo67bo$43bo69bo$42bo71bo$41bo73bo$40bo75bo$39bo77bo$38bo79b
o$37bo81bo$36bo83bo$35bo85bo$34bo87bo$33bo89bo$32bo91bo$31bo$30bo35bob
o57bo$29bo35bo3bo21bobo33bo$28bo35bo5bo19bo3bo33bo$63bo7bo17bo5bo33bo$
26bo35bo9bo15bo7bo33bo$25bo35bo11bo13bo9bo33bo$24bo35bo13bo11bo11bo33b
o$23bo35bo15bo9bo13bo33bo$22bo35bo17bo7bo15bo33bo$21bo35bo19bo5bo17bo
33bo$20bo35bo21bo3bo19bo33bo$19bo35bo23bobo55bo$18bo35bo47bo35bo$17bo
83bo37bo$16bo37bo45bo39bo$15bo39bo43bo41bo$14bo41bo41bo43bo$13bo43bo
39bo45bo$12bo45bo37bo47bo$11bo47bo35bo49bo$10bo49bo33bo51bo$9bo51bo17b
obo$8bo53bo15bo3bo9bo53bo$7bo55bo13bo5bo7bo53bo$6bo57bo11bo13bo53bo$5b
o59bo17bo5bo53bo$4bo61bo7bo7bo5bo53bo$3bo63bo5bo13bo53bo$2bo69bo7bo5bo
53bo$bo65bo3bo13bo53bo$66bo3bo67bo$bo63bo17bo53bo$2bo61bo5bo11bo53bo$
3bo59bo7bo9bo53bo$4bo57bo9bo7bo53bo$5bo55bo11bo5bo53bo$6bo53bo13bo3bo
53bo$7bo51bo15bobo53bo$8bo49bo71bo$9bo47bo71bo$10bo45bo71bo$11bo43bo
71bo$12bo41bo$13bo39bo71bo$14bo71bobo35bo$15bo37bo31bo3bo33bo$16bo37bo
29bo5bo31bo$17bo37bo27bo7bo29bo$18bo37bo25bo9bo27bo$19bo37bo23bo11bo
25bo$20bo37bo21bo13bo23bo$21bo37bo19bo15bo21bo$22bo37bo17bo17bo19bo$
23bo37bo15bo19bo17bo$24bo37bo13bo21bo15bo$25bo37bo11bo23bo13bo$26bo37b
o9bo25bo11bo$27bo37bo7bo27bo9bo$66bo5bo29bo7bo$27bo39bo3bo31bo5bo$26bo
41bobo33bo3bo$25bo79bobo$24bo$23bo$22bo$21bo$20bo$19bo$18bo$17bo$16bo$
15bo$14bo$13bo$12bo$11bo$10bo$9bo$8bo$7bo$6bo$5bo$4bo$3bo$2bo$bo$o$59b
obo$o57bo3bo$bo55bo5bo$2bo53bo7bo$3bo51bo9bo$4bo49bo11bo$5bo47bo13bo$
6bo45bo15bo$7bo43bo17bo$8bo41bo19bo$9bo39bo21bo$10bo37bo23bo$11bo35bo
25bo$12bo33bo27bo$13bo31bo29bo$14bo29bo31bo$15bo27bo33bo$16bo25bo35bo$
17bo23bo37bo$18bo21bo39bo$19bo19bo41bo$20bo17bo43bo$21bo15bo45bo$22bo
13bo47bo$23bo11bo49bo$24bo9bo51bo$25bo7bo53bo$26bo5bo55bo$27bo3bo57bo$
28bobo59bo$91bo!
This is based on rule 206968711034748555365673889122449783979099.

Indeed, it breaks down aborting to 2*7^n-1 (A198480):

Code: Select all

x = 113, y = 97, rule = marg7diag
112.A$111.A$110.A$109.A$108.A$107.A$106.A$105.A$104.A$103.A$102.A$
101.A$100.A$99.A$98.A$97.A$96.A$95.A$94.A$93.A$92.A$91.A$90.A$89.A$
88.A$87.A$86.A$85.A$84.A$83.A$82.A$81.A$80.A$79.A$78.A$77.A$76.A$75.A
$74.A$73.A$72.A$71.A$70.A$69.A$68.A$67.A$66.A$65.A$64.A$63.A$62.A$61.
A$60.A$59.A$58.A$57.A$56.A$55.A$54.A$53.A$52.A$51.A$50.A$49.A$48.A$
47.A$46.A$45.A$44.A$43.A$42.A$41.A$40.A$39.A$38.A$37.A$36.A$35.A$34.A
$33.A$32.A$31.A$30.A$29.A$14.A13.A$13.A13.A$12.A13.A$11.A13.A$10.A13.
A$9.A13.A$8.A13.A$7.A13.A$6.A13.A$5.A13.A$4.A13.A$3.A13.A$A.A13.A!

User avatar
wwei47
Posts: 577
Joined: February 18th, 2021, 11:18 am

Re: Margolus Media

Post by wwei47 » April 21st, 2021, 11:41 pm

How do you construct these rules? How do you decide what happens when 3 or more cells meet?

Code: Select all

x = 19, y = 17, rule = Symbiosis
11.A$9.2A.A$3.A$2.3A3.A6.A$.A2.A3.2A5.A$A7.A.3A2.2A$A.3A4.A.4A.3A$.2A
2.B3.A4.A$B.B8.2A$13.A$12.2A$7.B3.2A4.2B$8.2A.A5.A$10.A3.A$9.2AB.B$8.
A2.2B4.B$8.B9.A!

User avatar
muzik
Posts: 4155
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

Re: Margolus Media

Post by muzik » April 22nd, 2021, 2:00 pm

wwei47 wrote:
April 21st, 2021, 11:41 pm
How do you construct these rules?
Notepad++ and a lot of trial and error.
wwei47 wrote:
April 21st, 2021, 11:41 pm
How do you decide what happens when 3 or more cells meet?
Most of that is pretty much undefined since I'm currently only interested in simulating single diagonal line oscillators, and I only define those which are integral to the functioning of those.

User avatar
wwei47
Posts: 577
Joined: February 18th, 2021, 11:18 am

Re: Margolus Media

Post by wwei47 » April 22nd, 2021, 3:48 pm

muzik wrote:
April 22nd, 2021, 2:00 pm
Most of that is pretty much undefined since I'm currently only interested in simulating single diagonal line oscillators, and I only define those which are integral to the functioning of those.
Okay then. How do you decide the important ones?

Code: Select all

x = 19, y = 17, rule = Symbiosis
11.A$9.2A.A$3.A$2.3A3.A6.A$.A2.A3.2A5.A$A7.A.3A2.2A$A.3A4.A.4A.3A$.2A
2.B3.A4.A$B.B8.2A$13.A$12.2A$7.B3.2A4.2B$8.2A.A5.A$10.A3.A$9.2AB.B$8.
A2.2B4.B$8.B9.A!

User avatar
muzik
Posts: 4155
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

Re: Margolus Media

Post by muzik » April 22nd, 2021, 3:49 pm

wwei47 wrote:
April 22nd, 2021, 3:48 pm
muzik wrote:
April 22nd, 2021, 2:00 pm
Most of that is pretty much undefined since I'm currently only interested in simulating single diagonal line oscillators, and I only define those which are integral to the functioning of those.
Okay then. How do you decide the important ones?
If the absence of the transition would result in diagonal line oscillators not working, then it has to be added (and follow the expected rules).

User avatar
wwei47
Posts: 577
Joined: February 18th, 2021, 11:18 am

Re: Margolus Media

Post by wwei47 » April 22nd, 2021, 4:12 pm

muzik wrote:
April 22nd, 2021, 3:49 pm
If the absence of the transition would result in diagonal line oscillators not working, then it has to be added (and follow the expected rules).
Which state do you pick for it to transition to though?

Code: Select all

x = 19, y = 17, rule = Symbiosis
11.A$9.2A.A$3.A$2.3A3.A6.A$.A2.A3.2A5.A$A7.A.3A2.2A$A.3A4.A.4A.3A$.2A
2.B3.A4.A$B.B8.2A$13.A$12.2A$7.B3.2A4.2B$8.2A.A5.A$10.A3.A$9.2AB.B$8.
A2.2B4.B$8.B9.A!

User avatar
muzik
Posts: 4155
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

Re: Margolus Media

Post by muzik » April 22nd, 2021, 4:29 pm

wwei47 wrote:
April 22nd, 2021, 4:12 pm
muzik wrote:
April 22nd, 2021, 3:49 pm
If the absence of the transition would result in diagonal line oscillators not working, then it has to be added (and follow the expected rules).
Which state do you pick for it to transition to though?
By checking what the next generation should look like, as each generation of such an oscillator should look like a set of overlapping rectangles. For 2 states the rectangles XOR each other, for 3 and up the XOR is generalised as being modulo n.

For example (using the 2x2 blocks for clarity), for the 2 state case, generation 0 of a 2x12 rectangle is, via an arbitrary convention called the "identity property", a 2x12 rectangle:

Code: Select all

x = 2, y = 12, rule = B3/S5
2o$2o$2o$2o$2o$2o$2o$2o$2o$2o$2o$2o!
The second generation is a 4x10 rectangle:

Code: Select all

x = 4, y = 10, rule = B3/S5
4o$4o$4o$4o$4o$4o$4o$4o$4o$4o!
The third generation is the XOR of a 2x12 rectangle and a 6x8 rectangle (1+1=2, 2 mod 2=0):

Code: Select all

x = 6, y = 12, rule = B3/S5
2b2o$2b2o$2o2b2o$2o2b2o$2o2b2o$2o2b2o$2o2b2o$2o2b2o$2o2b2o$2o2b2o$2b2o
$2b2o!
For our 3 state case, we start out again with a 2x12 rectangle:

Code: Select all

x = 2, y = 12, rule = marg3
2o$2o$2o$2o$2o$2o$2o$2o$2o$2o$2o$2o!
This again evolves into a 4x10:

Code: Select all

x = 4, y = 10, rule = marg3
4A$4A$4A$4A$4A$4A$4A$4A$4A$4A!
In the next generation, since we use modulo 3 instead of modulo 2, 1+1 no longer equals 0, but equals 2. As a result, the cells in the middle no longer die, and instead transition to state 2:

Code: Select all

x = 6, y = 12, rule = marg3
2.2A$2.2A$2A2B2A$2A2B2A$2A2B2A$2A2B2A$2A2B2A$2A2B2A$2A2B2A$2A2B2A$2.
2A$2.2A!

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