ChaosTrains

[Tropylium]

This is a rule that came up while exploring the space of rules where birth is determined on the Moore neighborhood, survival on the von Neumann neighborhood; B36/S23 there to be specific (nothing else of much interest has turn'd up so far).

Ruletable (save as ChaosTrains.table):

Code: Select all

# = BMoore36/SvonNeumann23

n_states:2
neighborhood:Moore
symmetries:rotate4reflect

var a = {0,1}
var b = {a}
var c = {a}
var d = {a}

#B3
0,1,1,1,0,0,0,0,0,1
0,1,1,0,1,0,0,0,0,1
0,1,1,0,0,1,0,0,0,1
0,1,0,1,0,1,0,0,0,1
0,1,0,1,0,0,1,0,0,1
0,0,1,1,1,0,0,0,0,1
0,0,1,1,0,1,0,0,0,1
0,0,1,1,0,0,1,0,0,1
0,0,1,0,1,0,1,0,0,1
0,0,1,0,1,0,0,1,0,1

#B6
0,1,1,1,1,1,1,0,0,1
0,1,1,1,0,1,1,1,0,1
0,1,1,1,1,0,1,1,0,1
0,1,1,1,1,1,0,1,0,1
0,0,1,1,1,1,1,1,0,1
0,0,1,1,1,0,1,1,1,1
0,0,1,1,1,1,0,1,1,1
0,0,1,1,1,1,1,0,1,1

#D0V
1,0,a,0,b,0,c,0,d,0
#D1V
1,1,a,0,b,0,c,0,d,0
#S2V
1,1,a,1,b,0,c,0,d,1
1,1,a,0,b,1,c,0,d,1
#S3V
1,1,a,1,b,1,c,0,d,1
#D4V
1,1,a,1,b,1,c,1,d,0

This is another of those rules with patterns that explode in one direction only, and only along a mirror axis, and here the chaos remains quite close to the axis — hence the name. Here are two small seeds that generate "trains":

Code: Select all

x = 4, y = 44, rule = ChaosTrains
3bo$2obo$2obo$3bo37$b2o$3o$3o$b2o!

These first interact around gen. 2070, and you can see how it quickly leads to large parts of the upper train dying out. If you keep running these, two surviving secondary trains are born at the right end around gens 8200 and 8500. The right end of the lower original train is killed around gen 9800 as the asymmetry created by one of the new trains catches up with it, the upper right one suffers the same fate around gen 14500. In the long term, more new trains would be born and old train-tracks keep decaying, eventually filling the plane with a sparse grid of ash. Pretty interesting cosmology IMO.

As for objects, I've found three marginally natural (switch-engine-ish, only seen each emerge once) glide-reflectiv spaceships — 4c/8 orthogonal, 6c/38 diagonal, and c/8 diagonal — plus a larger synthetic spaceship with huge sparks. "Blocky" still lifes and oscillators based on them are easy to construct; there's also a p24 shuttle.

Code: Select all

x = 117, y = 82, rule = ChaosTrains
33b2o$32b3o$31b2obo$33bobo$34b2o$34b2o2$4o3b4o5b4o6bo$4o3b4o5b4o4bob2o
$b2o5b2o7b2o4b5o$17b2o4bob2o$16bo2bo4b3o$16b2obo$19bo20b2o$36b2o2b4o$
24b2o4b2o4b5o2bo$24b2o4b2o6bobo2b2o$23b2o3b2o8b7o$23b2o3b2o3b2ob3o2b2o
$33b2ob3o$34b3o$23b2o8b2o$23b2o8b2o2$62bo$24bo4bo3bo6bo6bo6bo5b2o$24bo
3b2o3b2o2b4o3b5o2b4o4bobo26b2o10b2o$24bo3bo3bo7bo4bo6bo2bo3b2o27b2o10b
2o8b2o3b2o$58bo28b4o8b4o7b2o3b2o$85b3o2b3o4b3o2b3o6b3obo$35bobo47b3o2b
3o4b3o2b3o6b3obo$23b2o3b2o2b2obobob2o2b2ob2o2b2o35b4o8b4o7b2ob4o$23b7o
2b9o2b2ob2o2b2o36b3o9b2o8b2ob2o$44b3ob3o38bo23b2o$25b2ob2o4b2ob2o4b2o
2b2ob2o36b3o9b2o8b2ob2o$25b2ob2o4b2ob2o4b2o2b2ob2o35b4o8b4o7b2ob2o$85b
3o2b3o4b3o2b3o3b9o$17b2o59b2o5b3o2b3o4b3o2b3o3b2o2bo2bo$17b2o19bo5b2o
8b2o12b2obo4b4o4b2o6b2o2b2o6b2o6b5o$16b4o4b3ob3o4b6o3b5o5b5ob2o6b5ob3o
2b2o3b2o6b2o2b2o6b2o7b2o$15b2o2b2o2b2ob3ob2o2b2ob4o7b3o5bob4o4b2o4bobo
4b2o32b2o$16b4o4b3ob3o4b3o2b2o4b5o5b3o2b2o3b2o2b3ob5o$17b2o21b2o4b2o2b
2o3b2o4b2o4b4o4bob2o5b2o6b2o2b2o6b2o$17b2o31b2o3b2o10b2o15b2o6b2o2b2o
6b2o$85b3o2b3o4b3o2b3o$85b3o2b3o4b3o2b3o$26bo7b2o25b3o23b4o8b4o$24b3o
3bob5o4b3o5b2o11b2o24b3o9b2o$25b2o3b4o5bob2o6b2o6b3o2bo26bo$23b2o5b2o
7b2o5b3o6bo2b2o29bo$23b3o5bo7b2o6b3o3b3o2bo29b3o9b2o$23bo30b3o30b4o8b
4o$54bo30b3o2b3o4b3o2b3o$27b2o56b3o2b3o4b3o2b3o$25bob2o58b4o8b4o$23b2o
bo61b2o10b2o$23b2o63b2o10b2o3$23bo$23b2o3b3o$23b2o4b2obo$30b2o11bo$22b
3o5b4o7b2ob3o$23b2o7b2o7b2ob3o$33bo9bo3$23b2o$23b2o$25b2o$25b2obo$27b
2o$27b2o$27bob2o$29b2obo$31bob2o$33b2o$35b2o$35b2o$37b2o$37b2o!

A couple puffers mostly based on the 2-train spaceship:

Code: Select all

x = 277, y = 12, rule = ChaosTrains
50b4o3b4o$50b4o3b4o$4o3b4o40b2o5b2o$4o3b4o85b4o3b4o$b2o5b2o86b4o3b4o$b
2o4bo2bo21b4o3b4o54b2o5b2o$b2o29b4o3b4o100b4o3b4o40b4o3b4o69b2o$b2o30b
2o5b2o34b4o3b4o56b4o3b4o40b4o3b4o34b4o3b4o15b4o4b4o$76b4o3b4o57b2o5b2o
21b4o3b4o10b2o5b2o35b4o3b4o15b4o4bo2bo$77b2o5b2o39b4o3b4o38b4o3b4o37b
4o3b4o7b2o5b2o17b2o6b2o$125b4o3b4o39b2o5b2o38b4o3b4o$126b2o5b2o88b2o5b
2o!

And here's a "breeder" demonstrating the chaoticness of the trains' growth:

Code: Select all

x = 31, y = 4, rule = ChaosTrains
20b4o3b4o$4o3b4o9b4o3b4o$4o3b4o10b2o5b2o$b2o5b2o!

[EricG]

Ha!

You keep posting better and better rules that "explode along one axis" -- this one is great!

Each time you post one of these rules, I think to myself that I really ought to organize my patterns in the B3/S2456 family of rules. I may never get them organized, so I'll just mention this: If you didn't already know, you may be amused to see that the same "chaos train" behavior exists in some life-like rules, such as B3/S02456, B3/S024568 (even more so!), and other related rules, such as B38/S024568. Nice name too - I've been calling them lavalamps, but they really are more like trains.

Here's the first one I noticed... B3/02456 has a puffer engine, and two of them can interact to make the 13c/30 spaceship referenced here: http://fano.ics.uci.edu/ca/rules/b3s02456/g8.html
I was trying to build a rake by putting puffers side by side in various configurations when I noticed the following:

Code: Select all

x = 16, y = 46, rule = B3/S02456
3b2o6b2o$2b4o4b4o$3b2o6b2o$3b2o6b2o$2bo2bo4bo2bo$b2o2b2o2b2o2b2o$b6o2b
6o$2bo2bo4bo2bo5$3b2o6b2o$2bo2bo4bo2bo$3b2o6b2o3$2bo2bo4bo2bo$bob2obo
2bob2obo$bo4bo2bo4bo$b2o2b2o2b2o2b2o$bob2obo2bob2obo$b6o2b6o$3b2o6b2o$
2bo2bo4bo2bo$3b2o6b2o$2bo2bo4bo2bo$3b2o6b2o2$3b2o6b2o$3b2o6b2o2$3b2o6b
2o$2bo2bo4bo2bo$2b4o4b4o$2bo2bo4bo2bo$3b2o6b2o$3b2o6b2o2$o2b2o2b2o2b2o
2bo$3o2b6o2b3o$b6o2b6o$obo2bob2obo2bobo$b6o2b6o$2b4o4b4o$2b4o4b4o!

The central active area persists for at least 5 million generations, and after spawning North and South puffers early on,it spawns East and West puffers at around 2.5 million generations. It reminds me of the replicator in B36/S245, but I'm not sure if there is really any relationship.

Here's another:
Two tiny c/2 spaceships which work in B3/S2456 collide in B3/S02456 to make a chaos train:

Code: Select all

x = 4, y = 23, rule = B3/S02456
4o$o2bo$o2bo$o2bo$4o$b2o$b2o$4o8$4o$o2bo$o2bo$o2bo$4o$b2o$b2o$4o!

Two 2c/5 spaceships found by Skowe for the B3/S2456 rule collide together and make a chaos train in B3/S02456:

Code: Select all

x = 22, y = 87, rule = B3/S02456
6bo8bo$4bo12bo$4b4o6b4o$5bo10bo$2bobobobo4bobobobo$3bo3bo6bo3bo$3b2o
12b2o$2b5o8b5o$4bobo8bobo$7bo6bo$7b2o4b2o$4bo2b2o4b2o2bo$3bo14bo$4bo2b
o6bo2bo$bob4o8b4obo$2bobo2bo6bo2bobo$bob5o6b5obo$2bobo2bobo2bobo2bobo$
2bob5ob2ob5obo$4b2ob2ob2ob2ob2o$4o3bo6bo3b4o$2b2obobo6bobob2o$b2ob4o6b
4ob2o$b2o2bob8obo2b2o$b2o3bo2bo2bo2bo3b2o$b5o4b2o4b5o$3b4ob2o2b2ob4o$
5bob2o4b2obo$4b2o2b6o2b2o$8bo4bo$5bo2b2o2b2o2bo$4bobob6obobo$2b2o2bobo
b2obobo2b2o$6bobo4bobo$3b2obo8bob2o$4b2obobo2bobob2o$3b3o4b2o4b3o$5b2o
b2o2b2ob2o$8b6o$10b2o8$6bo8bo$4bo12bo$4b4o6b4o$5bo10bo$2bobobobo4bobob
obo$3bo3bo6bo3bo$3b2o12b2o$2b5o8b5o$4bobo8bobo$7bo6bo$7b2o4b2o$4bo2b2o
4b2o2bo$3bo14bo$4bo2bo6bo2bo$bob4o8b4obo$2bobo2bo6bo2bobo$bob5o6b5obo$
2bobo2bobo2bobo2bobo$2bob5ob2ob5obo$4b2ob2ob2ob2ob2o$4o3bo6bo3b4o$2b2o
bobo6bobob2o$b2ob4o6b4ob2o$b2o2bob8obo2b2o$b2o3bo2bo2bo2bo3b2o$b5o4b2o
4b5o$3b4ob2o2b2ob4o$5bob2o4b2obo$4b2o2b6o2b2o$8bo4bo$5bo2b2o2b2o2bo$4b
obob6obobo$2b2o2bobob2obobo2b2o$6bobo4bobo$3b2obo8bob2o$4b2obobo2bobob
2o$3b3o4b2o4b3o$5b2ob2o2b2ob2o$8b6o$10b2o!

There are various other interesting patterns in the B3/S2456 family but chaos trains are the relevant reason to bring up the B3 rules.

And I certainly don't meant to, ahem, derail this thread or get this discussion off track -- I just needed to blow off steam. ChaosTrains.table is a really cool rule, so keep chugging along, full steam ahead!

[EricG]

So, ChaosTrains is B36/S2ei3aejky4aijkqtwyz5aijkqrvy6aeik7e

MCell Weighted Life rules PuttPutt and Ben's-Rule-9 also explode along one axis.
I was hoping maybe comparing their rules would be instructive.

In Alan Hensel's notation

Code: Select all

ChaosTrains is  B36/                S2ei3aejky4aijkqtwyz5aijkqrvy6aeik7e  
PuttPutt is     B2ceiv3aijkqrvy4ce8/S12ceiv3ce4ce8
Ben's-Rule-9 is B2ceiv3eiqrv4e     /S1c2ak3ciqrv4ejy

I draw no immediate conclusions!

On a different note, I tried out Paul Tooke's modified gfind on ChaosTrains.
Here are the results up to /l80:

Code: Select all

x = 387, y = 66, rule = ChaosTrains
299bo7bo21b2o$297b2o9b2o14b2ob6ob2o$298b2o7b2o15b3ob4ob3o$300b2o3b2o
18bobob2obobo$323bob2ob4ob2obo$297bo3bo3bo3bo14b2ob6ob2o$298b2o7b2o14b
2obo6bob2o$298b2o7b2o15b2obob2obob2o$303bo21b4o2b4o$296b4ob5ob4o16bob
2obo$303bo25b2o$297b2o2b2ob2o2b2o$297b13o16bob4obo$296b5obobob5o15b2o
4b2o$299bobobobobo17b2ob4ob2o$298b5ob5o17bob4obo$299b2ob3ob2o21b2o$
298bo2bo3bo2bo19bo2bo$298b3ob3ob3o19b4o51bo$298b2o7b2o20b2o52b3o$329b
2o51b3o$299b3o3b3o20b4o52b3o$299b9o20bo2bo49b5o$299bo2b3o2bo21b2o54bo$
299bobobobobo$302b3o24b2o$296bo6bo6bo18b2o$297b2obo5bob2o17bo4bo$297bo
3b5o3bo18bo2bo$257b2o37b2o3b5o3b2o17bo2bo$257bo2bo37bo9bo14b3o3b2o3b3o
$257b3o37b2o9b2o13b3o2b4o2b3o$259bo38bobo5bobo15bobo2b2o2bobo$258b3o
36b2o9b2o13b2o3bo2bo3b2o$256b2ob2o36b4obobob4o14bo10bo$192b2o9b2o21b2o
3b2o23b2obo39b3o3b3o16b2o8b2o$193bo9bo22bo5bo23b2o40b11o15b2o3b2o3b2o$
193bo9bo22bo5bo26bo63bobob2o2b2obobo$192b3o7b3o20b3o3b3o23bo2bobo36b2o
5b2o17b3ob2ob3o$193b2o7b2o21b2o5b2o23b3o2b2o35bob2ob2obo17bob2o2b2obo$
64bobo127b2o5b2o19b4o7b4o21bob3o35bo2bo3bo2bo$63bo2bo127bob2ob2obo21b
2o7b2o23b3o65bo2b2o2bo$63b2o2b2obo123b3obob3o21bo2b2ob2o2bo23bobo37b2o
7b2o$62bo2bobo2bo126bobo28bobo29bo38b2obobob2o18bo6bo$62b4ob4o122bo3bo
bo3bo20bo3bobo3bo23b4o36b2o7b2o18b6o$63b2o3b2o85bo37b2ob2ob2ob2o20b2ob
2ob2ob2o22bob2o40b5o19b4o2b4o$156b2o35b2o3bo3b2o20b2o3bo3b2o21b5o21b2o
14b5ob5o17b2ob2ob2o$154bo2bo36b2obobob2o22b2obobob2o24bo21b6o12b3o5b3o
16b4o2b4o$154bobo40b3o28b3o26b2o20bob4obo11b3o5b3o16b3ob2ob3o$154bobo
39b5o26b5o26b2ob2o15b3o4b3o11bo7bo21b2o$130b2o21bo2bo39bobobo26bobobo
24bob7o15b2o2b2o42b4o$83bo44b6o20bo23bobo13bobobobobo22bobobobobo22bob
3ob2o15b8o$82b2o21bobo19bo2b2o2bo19b2o20b2ob3o12b2obobob2o22b2obobob2o
22b2o2bob2o16b2o2b2o$83bobo2bo15b3o20b2ob2ob2o19b2o17bo5b2o12b3o5b3o
20b3o5b3o22bobo21b4o$83b2ob4o14b2o2bo17bo2bo2bo2bo20bo18bo18b2ob3ob2o
22b2ob3ob2o23b3o21bo2bo$67b2obo12bobob2o15b4o18b4o2b4o17bo2bo16b4o20bo
bo28bobo27bo23b2o$67bo2bo13bo20b2o20b2o4b2o18b2ob2o124b2o$4bo57bob2ob
4o11b4o18bo2bo44bo2bo$5b2o3bo51bo2bo2b2o34b4o46bob2o$o3bo3b2o52b4o39b
2o47b3o$b2o5b2o53b2o87bobo$b2o33bob2obo111b2o$33bobob4obobo108b2o$31b
5ob4ob5o$32b4o6b4o$32b4o6b4o!

[EricG]

I do notice that many (or maybe even most) of the trains which get started in ChaosTrains will continue in B3/S024568, and you can usually switch back and forth between those two rules without derailing the train. In many cases, you can also switch between ChaosTrain and the less explosive B3/S02456 (no S8). In contrast, switching from ChaosTrains to PuttPutt or Ben's-Rule-9 throws the train off its track.

[chineseman]

Code: Select all

x = 87, y = 130, rule = chaostrains
24b2o5b2o$4b2o5b2o10b4o3b4o$3b4o3b4o9bo2bo3bo2bo$3bo2bo3bo2bo9b4o3b4o$
3b4o3b4o3$24b2o5b2o$4b2o5b2o10bo2bo3bo2bo36b2o5b2o$3bo2bo3bo2bo10b4ob
4o17b2o5b2o10b4o3b4o$4b4ob4o11b2o2bo2b2o16b4o3b4o9bo2bo3bo2bo$4b2o2bo
2b2o10bo3bobo3bo15bo2bo3bo2bo9b4o3b4o$3bo3bobo3bo9b3obobob3o15b4o3b4o$
3b3obobob3o9bo2b2ob2o2bo$3bo2b2ob2o2bo$22b6ob6o35b2o5b2o$2b6ob6o9b2o5b
2o17b2o5b2o10bo2bo3bo2bo$4b2o5b2o10b5ob5o15bo2bo3bo2bo10b4ob4o$3b5ob5o
8b2o2bo3bo2b2o15b4ob4o11b2o2bo2b2o$2b2o2bo3bo2b2o7b5obob5o15b2o2bo2b2o
10bo3bobo3bo$2b5obob5o6bobo4bo4bobo13bo3bobo3bo9b3obobob3o$bobo4bo4bob
o4bobob2o5b2obobo12b3obobob3o9bo2b2ob2o2bo$obob2o5b2obobo7b3o3b3o16bo
2b2ob2o2bo$4b3o3b3o10bo2b2ob2o2bo34b6ob6o$3bo2b2ob2o2bo8b2o2b2ob2o2b2o
13b6ob6o9b2o5b2o$2b2o2b2ob2o2b2o8b4o3b4o16b2o5b2o10b5ob5o$3b4o3b4o35b
5ob5o8b2o2bo3bo2b2o$48b2o2bo3bo2b2o7b5obob5o$48b5obob5o6bobo4bo4bobo$
12bobo20bo11bobo4bo4bobo4bobob2o5b2obobo$9b2o2b2o2bo17bobo8bobob2o5b2o
bobo7b3o3b3o$7b4obob2obo12bob2ob2o13b3o3b3o10bo2b2ob2o2bo$6b8o2bo2b4o
6b5o3bo11bo2b2ob2o2bo8b2o2b2ob2o2b2o$5bob3o5b3ob5o6b2obo14b2o2b2ob2o2b
2o8b4o3b4o$5b2ob2ob7o4b3o3b2ob2o16b4o3b4o$12b3o2b2obo2b2ob5obo$7bo2bob
7o4b7obo$9bo2b6o2bo6b2obo27bobo20bo$10bob3o5b2o2b2o33b2o2bo17bobo$6b4o
3bo6bo3b3o5b3o20b2obob2obo12bob2ob2o$5bobobo3bo6b2o9b2ob2o15b3ob5o2bo
2b4o6b5o3bo$6b3o22b2obobo13b2o9b3ob5o6b2obo$6bob3o21b6o13bob2o4b5o4b3o
3b3o$33bob5o10bo3bo4b2o2b2obo2b2ob4o$34bo2b2o13bob3o2bo2b3o4b8obo$37b
2o7b6ob2o4bo2b2o2bo6b7o$38bo7bo3b3ob2o2b3o5b2o2b2o5b3o$45b4ob2ob2o2b2o
bo5bo3b3o3b4o$10bobobo7b2o21bo2bob2ob2o3b2o6b2o12bo$10b2o2bo5bob2o6bob
o10b2o4bo3bo4bo18b4o$9b2o2b2o4b5o6b2o6bo3b2o35bobo$bo8b3o5bob2obo5b4o
5b2o2b2obo35bo$b2o13b2obo9b3o6b5ob2o34b2o$o15b2o2b2o5bo11bo4b2o33b4o$
7b2o6b2ob2obo5bobo13bo36b3o$7b2o7b4o7b3o$17bo38bobobo7b2o$56b2o2bo5bob
2o3bo3bo$55b2o2b2o4b5o4b2ob2o$47bo8b3o5bob2obo3bo3b3o3b3o$47b2o13b2obo
13bo3bob2o$46bo15b2o2b2o8b2o5b3o$53b2o6b2ob2obo8b3o5bo$53b2o7b4o8b5o$b
2o6bobo13b2o36bo9b2obo$bo6b2obo13b2o47b4o$4bo3b4obo60bobo$10b4o$7b2ob
4o$7bob5o$bobo2bobo2bo$6b4obo$4bob7o34b2o6bobo13b2o$o2bo3bo39bo6b2obo
13b2o$3obob3obo39bo3b4obo$2bo53b4o$10b3o40b2ob4o$53bob5o$47bobo2bobo2b
o$52b4obo$50bob7o$46bo2bo3bo$46b3obob3obo$48bo$56b3o12$18b2o$18b4o$20b
4o$19b2o$20b3o4$64b2o$64b4o$66b4o$65b2o$66b3o15$13b2o$13b2o36bo$50b3o$
46b5ob2o$46b5ob2o$50b3o$51bo!