## Rules with multiple chaotic phases

For discussion of other cellular automata.
Tropylium
Posts: 406
Joined: May 31st, 2011, 7:12 pm
Location: Finland

### Rules with multiple chaotic phases

A weird thing I noticed in B124/S34 recently. (Much of these effects will work in plain B12/S3 too.)

This is one of the 2×2 rules, where any pattern separated in 2×2 on/off segments will continue to evolve as such. And adding a small perturbation in a 2×2 area will quickly devolve into regular chaos. Fairly obvious stuff so far.

However, it seems that within 2×2 areas, there are all sorts of different types of chaos possible. E.g.
1. Complete chaos.
2. "Parallel chaos": Sort of p2. In every other generation, all 2×2 blocks in the pattern will align on every other line.
3. "Domino chaos": Similar to the previous, but all 2×2 blocks, and gaps between them, will be additionally an even number of units long. This ensures that the pattern will have a similar limitation on all phases (though with the "grain" rotated 90° every step).
4. "Weak dot chaos": Sort of p4, alternating between isolated dots/dominos on every 4th line; 4×4 and domino blots; pairs of lines of even length mixed with pairs of dots; and rectangles of width ≥ 6 interspersed with connecting lines.
6. "Strong dot chaos": Also sort of p4, except with the line-pair phase sorted so that every pair of lines is capped by a pair of dots, and that every rectangle phase produces rectangles of width = 6.

Try running a "large preblock" for an example:

Code: Select all

``````x = 4, y = 4, rule = B124/S34
2o\$2o\$4o\$4o!``````
Complete chaos will be forming in the center along the SW-NE diagonal; parallel chaos along the edges near these corners (mostly in the SW); domino chaos in the SE and NW corners.

A sample of domino chaos:

Code: Select all

``````x = 120, y = 106, rule = B124/S34
4b4o4b16o20b4o8b4o4b16o4b8o4b8o4b4o\$4b4o4b16o20b4o8b4o4b16o4b8o4b8o4b
4o3\$4o12b8o4b8o4b4o4b4o8b4o12b24o4b12o\$4o12b8o4b8o4b4o4b4o8b4o12b24o4b
12o3\$4o4b16o8b4o12b28o8b4o4b12o4b12o\$4o4b16o8b4o12b28o8b4o4b12o4b12o3\$
8o4b4o8b12o4b4o4b4o8b12o16b4o20b8o\$8o4b4o8b12o4b4o4b4o8b12o16b4o20b8o
3\$12b4o8b28o24b12o4b12o8b8o\$12b4o8b28o24b12o4b12o8b8o3\$20o8b8o8b4o12b
4o8b4o8b4o4b4o12b8o\$20o8b8o8b4o12b4o8b4o8b4o4b4o12b8o3\$4o8b40o4b4o8b4o
8b8o20b12o\$4o8b40o4b4o8b4o8b8o20b12o3\$12b4o4b4o8b4o4b8o8b8o28b4o4b4o\$
12b4o4b4o8b4o4b8o8b8o28b4o4b4o3\$4o4b4o4b8o4b8o8b12o4b4o12b20o20b4o\$4o
4b4o4b8o4b8o8b12o4b4o12b20o20b4o3\$4b12o8b12o12b4o4b4o12b24o12b4o4b4o\$
4b12o8b12o12b4o4b4o12b24o12b4o4b4o3\$4b20o4b4o12b4o4b8o4b8o32b4o4b4o\$4b
20o4b4o12b4o4b8o4b8o32b4o4b4o3\$12o4b4o8b8o20b4o20b4o16b8o8b4o\$12o4b4o
8b8o20b4o20b4o16b8o8b4o3\$4b4o4b16o4b8o8b4o8b4o4b8o4b12o4b12o8b4o\$4b4o
4b16o4b8o8b4o8b4o4b8o4b12o4b12o8b4o3\$4o4b8o4b8o12b8o8b4o4b4o12b8o24b4o
\$4o4b8o4b8o12b8o8b4o4b4o12b8o24b4o3\$4b4o4b4o8b4o4b4o4b8o8b8o8b4o4b4o
16b4o4b4o\$4b4o4b4o8b4o4b4o4b8o8b8o8b4o4b4o16b4o4b4o3\$8b4o8b8o4b4o4b8o
12b8o4b24o4b4o4b4o\$8b4o8b8o4b4o4b8o12b8o4b24o4b4o4b4o3\$4o4b4o4b4o4b16o
4b20o4b8o4b12o8b4o8b8o\$4o4b4o4b4o4b16o4b20o4b8o4b12o8b4o8b8o3\$40b8o8b
16o12b4o4b16o4b8o\$40b8o8b16o12b4o4b16o4b8o3\$4b8o8b4o12b4o20b4o4b16o12b
16o\$4b8o8b4o12b4o20b4o4b16o12b16o3\$4o16b12o4b4o4b12o8b4o4b8o4b8o20b8o\$
4o16b12o4b4o4b12o8b4o4b8o4b8o20b8o3\$12b4o4b4o32b4o4b12o8b4o8b12o4b8o\$
12b4o4b4o32b4o4b12o8b4o8b12o4b8o3\$8o4b8o4b4o16b16o4b8o4b4o8b8o4b4o4b
12o\$8o4b8o4b4o16b16o4b8o4b4o8b8o4b4o4b12o3\$4o12b24o4b12o8b8o4b4o8b12o
8b4o4b4o\$4o12b24o4b12o8b8o4b4o8b12o8b4o4b4o3\$4o16b8o4b4o4b4o8b8o20b32o
4b4o\$4o16b8o4b4o4b4o8b8o20b32o4b4o3\$4o4b4o4b4o4b4o4b8o4b8o12b8o8b4o4b
8o16b8o\$4o4b4o4b4o4b4o4b8o4b8o12b8o8b4o4b8o16b8o3\$4b4o4b40o20b4o4b8o8b
12o4b8o\$4b4o4b40o20b4o4b8o8b12o4b8o3\$12o4b8o4b8o8b4o8b4o4b4o4b4o8b4o4b
4o4b8o8b4o\$12o4b8o4b8o8b4o8b4o4b4o4b4o8b4o4b4o4b8o8b4o!``````
If you leave this to evolve, you'll find that this is actually a replicator pattern. Domino chaos appears to thus comprise deeply intertwined replicator strains, not of "real" chaos. So it's understandable that it would have a separate existence.

A sample of parallel chaos:

Code: Select all

``````x = 64, y = 62, rule = B124/S34
8o4b4o6b2o2b10o8b4o2b2o6b4o\$8o4b4o6b2o2b10o8b4o2b2o6b4o3\$4b8o4b8o2b6o
4b4o2b2o18b2o\$4b8o4b8o2b6o4b4o2b2o18b2o3\$10b4o10b4o4b4o4b2o6b2o8b6o\$
10b4o10b4o4b4o4b2o6b2o8b6o3\$10b4o4b12o8b4o6b4o2b2o\$10b4o4b12o8b4o6b4o
2b2o3\$2o2b2o4b2o4b2o4b2o2b2o2b2o18b2o2b2o\$2o2b2o4b2o4b2o4b2o2b2o2b2o
18b2o2b2o3\$2o4b2o2b2o4b8o2b2o22b2o2b10o\$2o4b2o2b2o4b8o2b2o22b2o2b10o3\$
2b2o18b2o2b2o8b2o2b4o4b4o\$2b2o18b2o2b2o8b2o2b4o4b4o3\$4o8b2o12b2o2b8o6b
2o8b6o\$4o8b2o12b2o2b8o6b2o8b6o3\$24b2o4b8o\$24b2o4b8o3\$2o4b2o2b10o16b4o
4b2o12b2o2b2o\$2o4b2o2b10o16b4o4b2o12b2o2b2o3\$4b4o12b6o6b12o4b2o\$4b4o
12b6o6b12o4b2o3\$8o8b2o4b4o8b8o4b2o2b12o\$8o8b2o4b4o8b8o4b2o2b12o3\$2b4o
2b14o2b4o10b10o2b8o4b2o\$2b4o2b14o2b4o10b10o2b8o4b2o3\$2b2o4b14o2b4o2b4o
8b4o4b8o4b2o\$2b2o4b14o2b4o2b4o8b4o4b8o4b2o3\$4o12b2o2b6o16b2o2b8o4b2o\$
4o12b2o2b6o16b2o2b8o4b2o3\$2b2o6b2o4b2o2b6o6b2o8b2o10b2o4b4o\$2b2o6b2o4b
2o2b6o6b2o8b2o10b2o4b4o!``````
This time, no replicator effects appear. It is however noticable that the edges of the pattern will slowly evolve to domino chaos instead, leaving only a star-shaped center region. Here also an example area of dot chaos develops after a while. Watch the eastern edge.

A sample of weak dot chaos:

Code: Select all

``````x = 94, y = 94, rule = B124/S34
2o16b2o12b2o6b4o4b4o4b4o4b4o14b2o4b2o\$2o16b2o12b2o6b4o4b4o4b4o4b4o14b
2o4b2o7\$4o6b2o4b4o20b4o4b4o4b4o4b4o\$4o6b2o4b4o20b4o4b4o4b4o4b4o7\$4o36b
2o22b4o4b4o4b2o8b2o\$4o36b2o22b4o4b4o4b2o8b2o7\$50b2o22b2o4b2o8b2o\$50b2o
22b2o4b2o8b2o7\$4o4b2o8b2o20b4o6b2o12b4o12b2o8b2o\$4o4b2o8b2o20b4o6b2o
12b4o12b2o8b2o7\$10b2o6b2o4b4o4b4o22b2o4b2o8b2o4b4o4b4o\$10b2o6b2o4b4o4b
4o22b2o4b2o8b2o4b4o4b4o7\$2o8b2o12b2o6b4o6b2o6b2o4b2o16b2o4b4o4b2o\$2o8b
2o12b2o6b4o6b2o6b2o4b2o16b2o4b4o4b2o7\$2b2o4b4o4b2o6b4o4b4o4b2o14b2o8b
2o12b2o\$2b2o4b4o4b2o6b4o4b4o4b2o14b2o8b2o12b2o7\$2b2o4b2o8b2o4b2o24b2o
6b2o6b2o4b4o\$2b2o4b2o8b2o4b2o24b2o6b2o6b2o4b4o7\$2b2o4b2o40b2o6b2o4b4o
4b2o\$2b2o4b2o40b2o6b2o4b4o4b2o7\$4o6b2o4b4o4b4o12b2o6b4o4b4o14b2o4b4o4b
2o\$4o6b2o4b4o4b4o12b2o6b4o4b4o14b2o4b4o4b2o7\$4o4b4o12b4o4b4o4b2o6b4o4b
4o14b2o6b2o4b4o\$4o4b4o12b4o4b4o4b2o6b4o4b4o14b2o6b2o4b4o!``````
(Here an even more ordered type of domino chaos will evolve near the edges — I guess equal to replicator mess with some further parity constraints.)

A sample of strong dot chaos:

Code: Select all

``````x = 108, y = 102, rule = B124/S34
32b2o2b4o2b2o20b2o2b20o2b2o\$32b2o2b4o2b2o20b2o2b20o2b2o3\$32b2o2b4o2b2o
20b2o2b20o2b2o\$32b2o2b4o2b2o20b2o2b20o2b2o3\$8b2o2b4o2b2o4b2o2b4o2b2o4b
2o2b4o2b2o36b2o2b12o2b2o\$8b2o2b4o2b2o4b2o2b4o2b2o4b2o2b4o2b2o36b2o2b
12o2b2o3\$8b2o2b4o2b2o4b2o2b4o2b2o4b2o2b4o2b2o36b2o2b12o2b2o\$8b2o2b4o2b
2o4b2o2b4o2b2o4b2o2b4o2b2o36b2o2b12o2b2o3\$2o2b12o2b2o4b2o2b4o2b2o12b2o
2b4o2b2o12b2o2b12o2b2o\$2o2b12o2b2o4b2o2b4o2b2o12b2o2b4o2b2o12b2o2b12o
2b2o3\$2o2b12o2b2o4b2o2b4o2b2o12b2o2b4o2b2o12b2o2b12o2b2o\$2o2b12o2b2o4b
2o2b4o2b2o12b2o2b4o2b2o12b2o2b12o2b2o3\$8b2o2b4o2b2o12b2o2b4o2b2o4b2o2b
4o2b2o4b2o2b4o2b2o12b2o2b4o2b2o\$8b2o2b4o2b2o12b2o2b4o2b2o4b2o2b4o2b2o
4b2o2b4o2b2o12b2o2b4o2b2o3\$8b2o2b4o2b2o12b2o2b4o2b2o4b2o2b4o2b2o4b2o2b
4o2b2o12b2o2b4o2b2o\$8b2o2b4o2b2o12b2o2b4o2b2o4b2o2b4o2b2o4b2o2b4o2b2o
12b2o2b4o2b2o3\$2o2b44o2b2o20b2o2b12o2b2o4b2o2b4o2b2o\$2o2b44o2b2o20b2o
2b12o2b2o4b2o2b4o2b2o3\$2o2b44o2b2o20b2o2b12o2b2o4b2o2b4o2b2o\$2o2b44o2b
2o20b2o2b12o2b2o4b2o2b4o2b2o3\$16b2o2b4o2b2o4b2o2b4o2b2o\$16b2o2b4o2b2o
4b2o2b4o2b2o3\$16b2o2b4o2b2o4b2o2b4o2b2o\$16b2o2b4o2b2o4b2o2b4o2b2o3\$2o
2b20o2b2o12b2o2b20o2b2o20b2o2b12o2b2o\$2o2b20o2b2o12b2o2b20o2b2o20b2o2b
12o2b2o3\$2o2b20o2b2o12b2o2b20o2b2o20b2o2b12o2b2o\$2o2b20o2b2o12b2o2b20o
2b2o20b2o2b12o2b2o3\$16b2o2b20o2b2o36b2o2b20o2b2o\$16b2o2b20o2b2o36b2o2b
20o2b2o3\$16b2o2b20o2b2o36b2o2b20o2b2o\$16b2o2b20o2b2o36b2o2b20o2b2o3\$2o
2b20o2b2o36b2o2b20o2b2o\$2o2b20o2b2o36b2o2b20o2b2o3\$2o2b20o2b2o36b2o2b
20o2b2o\$2o2b20o2b2o36b2o2b20o2b2o3\$24b2o2b12o2b2o44b2o2b12o2b2o\$24b2o
2b12o2b2o44b2o2b12o2b2o3\$24b2o2b12o2b2o44b2o2b12o2b2o\$24b2o2b12o2b2o
44b2o2b12o2b2o3\$8b2o2b12o2b2o44b2o2b12o2b2o\$8b2o2b12o2b2o44b2o2b12o2b
2o3\$8b2o2b12o2b2o44b2o2b12o2b2o\$8b2o2b12o2b2o44b2o2b12o2b2o3\$2o2b4o2b
2o12b2o2b4o2b2o28b2o2b4o2b2o12b2o2b4o2b2o\$2o2b4o2b2o12b2o2b4o2b2o28b2o
2b4o2b2o12b2o2b4o2b2o3\$2o2b4o2b2o12b2o2b4o2b2o28b2o2b4o2b2o12b2o2b4o2b
2o\$2o2b4o2b2o12b2o2b4o2b2o28b2o2b4o2b2o12b2o2b4o2b2o3\$8b2o2b12o2b2o4b
2o2b4o2b2o28b2o2b12o2b2o4b2o2b4o2b2o\$8b2o2b12o2b2o4b2o2b4o2b2o28b2o2b
12o2b2o4b2o2b4o2b2o3\$8b2o2b12o2b2o4b2o2b4o2b2o28b2o2b12o2b2o4b2o2b4o2b
2o\$8b2o2b12o2b2o4b2o2b4o2b2o28b2o2b12o2b2o4b2o2b4o2b2o!``````
This is again a replicator, seemingly to be the dot replicator analogue of domino chaos with some further parity constraints.

I could document many further types of "chaotic replicator mixtures", but that's not my main point. What I find impressive here is particularly the distinction between "full" and "parallel" chaos — the existence of these as distinct from each other does not seem to be immediately predicted at all.

Also, does anything like this happen in other rules? Do parity restrictions exist in e.g. rules like LongLife (B345/S5)?

Extrementhusiast
Posts: 1858
Joined: June 16th, 2009, 11:24 pm
Location: USA

### Re: Rules with multiple chaotic phases

Tropylium wrote:Also, does anything like this happen in other rules? Do parity restrictions exist in e.g. rules like LongLife (B345/S5)?
In random three-state rules, there is sometimes the situation where state 1 cells expand indefinitely, but an interior area where there are state 2 cells persists and grows, usually to the expense of the state 1 cells. (Or vice versa, obviously.) But that might not be what you're looking for, as there are two states and two types of chaos, thus making one for each state.
I Like My Heisenburps! (and others)

towerator
Posts: 328
Joined: September 2nd, 2013, 3:03 pm

### Re: Rules with multiple chaotic phases

It looks like a new specie
Diagonal lines chaos:

Code: Select all

``````x = 138, y = 134, rule = B124/S34
2o2b2o2b2o18b2o2b2o2b2o74b2o2b2o2b2o\$2o2b2o2b2o18b2o2b2o2b2o74b2o2b2o
2b2o\$22b2o2b2o10b2o2b2o22b2o2b2o6b2o2b2o22b2o2b2o10b2o2b2o\$22b2o2b2o
10b2o2b2o22b2o2b2o6b2o2b2o22b2o2b2o10b2o2b2o\$4b2o26b2o6b2o22b2o18b2o
22b2o6b2o\$4b2o26b2o6b2o22b2o18b2o22b2o6b2o\$2b2o2b2o10b2o30b2o46b2o30b
2o\$2b2o2b2o10b2o30b2o46b2o30b2o\$32b2o6b2o2b2o2b2o2b2o2b2o34b2o2b2o2b2o
2b2o2b2o6b2o\$32b2o6b2o2b2o2b2o2b2o2b2o34b2o2b2o2b2o2b2o2b2o6b2o\$18b2o
2b2o6b2o10b2o18b2o6b2o6b2o6b2o18b2o10b2o6b2o2b2o\$18b2o2b2o6b2o10b2o18b
2o6b2o6b2o6b2o18b2o10b2o6b2o2b2o\$4b2o2b2o30b2o6b2o14b2o18b2o14b2o6b2o\$
4b2o2b2o30b2o6b2o14b2o18b2o14b2o6b2o\$2b2o14b2o26b2o18b2o2b2o6b2o2b2o
18b2o26b2o\$2b2o14b2o26b2o18b2o2b2o6b2o2b2o18b2o26b2o\$2o46b2o18b2o10b2o
18b2o\$2o46b2o18b2o10b2o18b2o\$2b2o14b2o10b2o2b2o10b2o14b2o6b2o6b2o6b2o
14b2o10b2o2b2o10b2o\$2b2o14b2o10b2o2b2o10b2o14b2o6b2o6b2o6b2o14b2o10b2o
2b2o10b2o\$12b2o34b2o50b2o34b2o\$12b2o34b2o50b2o34b2o\$2b2o14b2o2b2o6b2o
6b2o70b2o6b2o6b2o2b2o\$2b2o14b2o2b2o6b2o6b2o70b2o6b2o6b2o2b2o\$2o10b2o6b
2o6b2o30b2o26b2o30b2o6b2o6b2o\$2o10b2o6b2o6b2o30b2o26b2o30b2o6b2o6b2o\$
14b2o10b2o2b2o86b2o2b2o10b2o\$14b2o10b2o2b2o86b2o2b2o10b2o\$2o2b2o10b2o
2b2o2b2o14b2o2b2o6b2o42b2o6b2o2b2o14b2o2b2o2b2o\$2o2b2o10b2o2b2o2b2o14b
2o2b2o6b2o42b2o6b2o2b2o14b2o2b2o2b2o\$2b2o22b2o2b2o2b2o10b2o2b2o2b2o38b
2o2b2o2b2o10b2o2b2o2b2o\$2b2o22b2o2b2o2b2o10b2o2b2o2b2o38b2o2b2o2b2o10b
2o2b2o2b2o\$12b2o2b2o2b2o2b2o2b2o38b2o10b2o38b2o2b2o2b2o2b2o2b2o\$12b2o
2b2o2b2o2b2o2b2o38b2o10b2o38b2o2b2o2b2o2b2o2b2o\$2b2o30b2o2b2o6b2o6b2o
14b2o6b2o14b2o6b2o6b2o2b2o\$2b2o30b2o2b2o6b2o6b2o14b2o6b2o14b2o6b2o6b2o
2b2o\$4b2o2b2o2b2o2b2o2b2o2b2o10b2o22b2o26b2o22b2o10b2o2b2o2b2o2b2o\$4b
2o2b2o2b2o2b2o2b2o2b2o10b2o22b2o26b2o22b2o10b2o2b2o2b2o2b2o\$6b2o2b2o
10b2o22b2o10b2o10b2o6b2o10b2o10b2o22b2o\$6b2o2b2o10b2o22b2o10b2o10b2o6b
2o10b2o10b2o22b2o\$8b2o34b2o10b2o6b2o18b2o6b2o10b2o\$8b2o34b2o10b2o6b2o
18b2o6b2o10b2o\$6b2o54b2o2b2o14b2o2b2o\$6b2o54b2o2b2o14b2o2b2o\$4b2o34b2o
2b2o10b2o2b2o6b2o10b2o6b2o2b2o10b2o2b2o\$4b2o34b2o2b2o10b2o2b2o6b2o10b
2o6b2o2b2o10b2o2b2o\$2b2o2b2o22b2o6b2o2b2o10b2o6b2o6b2o6b2o6b2o6b2o10b
2o2b2o6b2o\$2b2o2b2o22b2o6b2o2b2o10b2o6b2o6b2o6b2o6b2o6b2o10b2o2b2o6b2o
\$28b2o2b2o30b2o2b2o10b2o2b2o30b2o2b2o\$28b2o2b2o30b2o2b2o10b2o2b2o30b2o
2b2o\$2b2o22b2o10b2o2b2o10b2o6b2o6b2o6b2o6b2o6b2o10b2o2b2o10b2o\$2b2o22b
2o10b2o2b2o10b2o6b2o6b2o6b2o6b2o6b2o10b2o2b2o10b2o\$28b2o2b2o22b2o2b2o
2b2o18b2o2b2o2b2o22b2o2b2o\$28b2o2b2o22b2o2b2o2b2o18b2o2b2o2b2o22b2o2b
2o\$2b2o10b2o6b2o10b2o2b2o18b2o6b2o2b2o6b2o2b2o6b2o18b2o2b2o10b2o6b2o\$
2b2o10b2o6b2o10b2o2b2o18b2o6b2o2b2o6b2o2b2o6b2o18b2o2b2o10b2o6b2o\$28b
2o2b2o6b2o14b2o10b2o10b2o10b2o14b2o6b2o2b2o\$28b2o2b2o6b2o14b2o10b2o10b
2o10b2o14b2o6b2o2b2o\$26b2o6b2o6b2o22b2o14b2o22b2o6b2o6b2o\$26b2o6b2o6b
2o22b2o14b2o22b2o6b2o6b2o\$32b2o2b2o2b2o18b2o2b2o2b2o2b2o2b2o2b2o2b2o2b
2o18b2o2b2o2b2o\$32b2o2b2o2b2o18b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o18b2o2b
2o2b2o\$26b2o2b2o6b2o2b2o14b2o6b2o14b2o6b2o14b2o2b2o6b2o2b2o\$26b2o2b2o
6b2o2b2o14b2o6b2o14b2o6b2o14b2o2b2o6b2o2b2o\$28b2o2b2o2b2o10b2o50b2o10b
2o2b2o2b2o\$28b2o2b2o2b2o10b2o50b2o10b2o2b2o2b2o\$38b2o2b2o2b2o54b2o2b2o
2b2o\$38b2o2b2o2b2o54b2o2b2o2b2o\$24b2o2b2o18b2o18b2o10b2o18b2o18b2o2b2o
\$24b2o2b2o18b2o18b2o10b2o18b2o18b2o2b2o\$30b2o38b2o6b2o38b2o\$30b2o38b2o
6b2o38b2o\$20b2o18b2o6b2o6b2o34b2o6b2o6b2o18b2o\$20b2o18b2o6b2o6b2o34b2o
6b2o6b2o18b2o\$2b2o14b2o6b2o14b2o2b2o18b2o2b2o6b2o2b2o18b2o2b2o14b2o6b
2o\$2b2o14b2o6b2o14b2o2b2o18b2o2b2o6b2o2b2o18b2o2b2o14b2o6b2o\$16b2o22b
2o6b2o6b2o6b2o18b2o6b2o6b2o6b2o22b2o\$16b2o22b2o6b2o6b2o6b2o18b2o6b2o6b
2o6b2o22b2o\$10b2o6b2o2b2o18b2o62b2o18b2o2b2o\$10b2o6b2o2b2o18b2o62b2o
18b2o2b2o\$32b2o30b2o18b2o30b2o\$32b2o30b2o18b2o30b2o\$2b2o22b2o2b2o2b2o
18b2o10b2o14b2o10b2o18b2o2b2o2b2o\$2b2o22b2o2b2o2b2o18b2o10b2o14b2o10b
2o18b2o2b2o2b2o\$12b2o34b2o6b2o2b2o26b2o2b2o6b2o34b2o\$12b2o34b2o6b2o2b
2o26b2o2b2o6b2o34b2o\$6b2o2b2o2b2o10b2o6b2o6b2o6b2o14b2o14b2o14b2o6b2o
6b2o6b2o10b2o\$6b2o2b2o2b2o10b2o6b2o6b2o6b2o14b2o14b2o14b2o6b2o6b2o6b2o
10b2o\$12b2o2b2o2b2o6b2o14b2o10b2o10b2o10b2o10b2o10b2o14b2o6b2o2b2o2b2o
\$12b2o2b2o2b2o6b2o14b2o10b2o10b2o10b2o10b2o10b2o14b2o6b2o2b2o2b2o\$6b2o
2b2o6b2o2b2o2b2o18b2o2b2o2b2o2b2o30b2o2b2o2b2o2b2o18b2o2b2o2b2o\$6b2o2b
2o6b2o2b2o2b2o18b2o2b2o2b2o2b2o30b2o2b2o2b2o2b2o18b2o2b2o2b2o\$12b2o14b
2o6b2o22b2o6b2o10b2o6b2o22b2o6b2o14b2o\$12b2o14b2o6b2o22b2o6b2o10b2o6b
2o22b2o6b2o14b2o\$22b2o2b2o2b2o6b2o10b2o2b2o38b2o2b2o10b2o6b2o2b2o2b2o\$
22b2o2b2o2b2o6b2o10b2o2b2o38b2o2b2o10b2o6b2o2b2o2b2o\$52b2o2b2o34b2o2b
2o\$52b2o2b2o34b2o2b2o\$2b2o2b2o2b2o34b2o10b2o10b2o6b2o10b2o10b2o\$2b2o2b
2o2b2o34b2o10b2o10b2o6b2o10b2o10b2o\$20b2o26b2o10b2o26b2o10b2o26b2o\$20b
2o26b2o10b2o26b2o10b2o26b2o\$10b2o14b2o34b2o6b2o6b2o6b2o34b2o\$10b2o14b
2o34b2o6b2o6b2o6b2o34b2o\$4b2o22b2o6b2o10b2o10b2o26b2o10b2o10b2o6b2o\$4b
2o22b2o6b2o10b2o10b2o26b2o10b2o10b2o6b2o\$2b2o34b2o2b2o2b2o2b2o6b2o30b
2o6b2o2b2o2b2o2b2o\$2b2o34b2o2b2o2b2o2b2o6b2o30b2o6b2o2b2o2b2o2b2o\$20b
2o6b2o10b2o2b2o6b2o2b2o34b2o2b2o6b2o2b2o10b2o6b2o\$20b2o6b2o10b2o2b2o6b
2o2b2o34b2o2b2o6b2o2b2o10b2o6b2o\$34b2o22b2o30b2o22b2o\$34b2o22b2o30b2o
22b2o\$4b2o2b2o22b2o6b2o10b2o10b2o18b2o10b2o10b2o6b2o\$4b2o2b2o22b2o6b2o
10b2o10b2o18b2o10b2o10b2o6b2o\$2b2o26b2o10b2o6b2o46b2o6b2o10b2o\$2b2o26b
2o10b2o6b2o46b2o6b2o10b2o\$4b2o22b2o22b2o2b2o6b2o18b2o6b2o2b2o22b2o\$4b
2o22b2o22b2o2b2o6b2o18b2o6b2o2b2o22b2o\$6b2o10b2o2b2o26b2o14b2o14b2o14b
2o26b2o2b2o\$6b2o10b2o2b2o26b2o14b2o14b2o14b2o26b2o2b2o\$2o14b2o6b2o2b2o
14b2o6b2o2b2o2b2o2b2o18b2o2b2o2b2o2b2o6b2o14b2o2b2o6b2o\$2o14b2o6b2o2b
2o14b2o6b2o2b2o2b2o2b2o18b2o2b2o2b2o2b2o6b2o14b2o2b2o6b2o\$2b2o2b2o10b
2o14b2o2b2o6b2o2b2o14b2o14b2o14b2o2b2o6b2o2b2o14b2o\$2b2o2b2o10b2o14b2o
2b2o6b2o2b2o14b2o14b2o14b2o2b2o6b2o2b2o14b2o\$4b2o2b2o18b2o10b2o6b2o2b
2o6b2o26b2o6b2o2b2o6b2o10b2o\$4b2o2b2o18b2o10b2o6b2o2b2o6b2o26b2o6b2o2b
2o6b2o10b2o\$18b2o6b2o6b2o18b2o38b2o18b2o6b2o6b2o\$18b2o6b2o6b2o18b2o38b
2o18b2o6b2o6b2o\$4b2o6b2o18b2o2b2o2b2o2b2o2b2o10b2o6b2o10b2o6b2o10b2o2b
2o2b2o2b2o2b2o18b2o\$4b2o6b2o18b2o2b2o2b2o2b2o2b2o10b2o6b2o10b2o6b2o10b
2o2b2o2b2o2b2o2b2o18b2o\$2b2o2b2o18b2o14b2o18b2o6b2o6b2o6b2o18b2o14b2o\$
2b2o2b2o18b2o14b2o18b2o6b2o6b2o6b2o18b2o14b2o\$8b2o2b2o22b2o26b2o2b2o
10b2o2b2o26b2o22b2o\$8b2o2b2o22b2o26b2o2b2o10b2o2b2o26b2o22b2o!
``````
It generates a lot of diagonal lines, they go up to 10 blocks long. Also, at the "sparse" generations, one can notice a checkerboard pattern is always empty.
This is game of life, this is game of life!
Loafin' ships eaten with a knife!

Kazyan
Posts: 1028
Joined: February 6th, 2014, 11:02 pm

### Re: Rules with multiple chaotic phases

Tropylium wrote:Also, does anything like this happen in other rules? Do parity restrictions exist in e.g. rules like LongLife (B345/S5)?
B1/S1's edges seem to split into different densities and patterns of ON cells as the pattern expands.

Code: Select all

``````x = 3, y = 2, rule = B1/S1
b2o\$o!``````
At generation 5,000, there's an ordered phase that works like relplication, a second phase at the upper right that consists of jumbled replicators that are all aligned in what "stage" of replication they're in, and the bulk of the expanding square is just chaos.
Tanner Jacobi
Coldlander, a novel, available in paperback and as an ebook.

Extrementhusiast
Posts: 1858
Joined: June 16th, 2009, 11:24 pm
Location: USA

### Re: Rules with multiple chaotic phases

Kazyan wrote:
Tropylium wrote:Also, does anything like this happen in other rules? Do parity restrictions exist in e.g. rules like LongLife (B345/S5)?
B1/S1's edges seem to split into different densities and patterns of ON cells as the pattern expands.

Code: Select all

``````x = 3, y = 2, rule = B1/S1
b2o\$o!``````
At generation 5,000, there's an ordered phase that works like relplication, a second phase at the upper right that consists of jumbled replicators that are all aligned in what "stage" of replication they're in, and the bulk of the expanding square is just chaos.
This seems to show a fourth phase:

Code: Select all

``````x = 4, y = 2, rule = B1/S1
o2bo\$2bo!
``````
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