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Developing a more detailed classification of rule behaviors

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Developing a more detailed classification of rule behaviors

Postby Extrementhusiast » April 25th, 2018, 3:07 pm

Recently, as I've been sampling random rules, I've been finding that Wolfram's four classes of cellular automata don't seem to fully convey the rich variety of behaviors that are possible from random soups, so I'm trying to develop one myself in n-dimensional continuous parameter space.

Here are a few possible parameters to get started:
  • Speed of expansion
  • Shape of expansion (perhaps)
  • How quickly the center settles
  • Ratio of moving objects to stationary objects (if that can be determined)

Here are some locations of interest:
  • Active explosive: The vast majority of patterns fill space with chaos that never settles.
    • Examples: Seeds (B2/S)
  • Settling explosive: The vast majority of patterns fill space with chaos that soon decays into more recognizable objects.
    • Examples: Coagulations (B378/S235678), B3/S234
  • Lineland: Composed mainly of linear structures (puffers, backrakes, wickstretchers, 1D replicators); new lines form occasionally where old lines interact.
    • Examples: B2a3ikn4aj5aei6k/S
  • Brain: The vast majority of objects move, sometimes producing other moving objects.
    • Examples: Brian's Brain (/2/3), B2-ik3ny4y5r6i/S (partially, but it's the closest two-state example I can find)
  • Quickly settles: Pretty self-explanatory, although I am including the case of leaving nothing behind in this category.
    • Examples: B/S (extreme), B3/S2
  • Slowly fizzles: Also pretty self-explanatory, although some small debris is allowed to be left behind.
    • Examples: B2cik3-cikn4eiknrwy56-i78/S2c3cejy4jw5ej6cn8, B2n3-r4-eikqy5-ckqr6-ik7e/S01e2n3aejy4cwy5cijqy6-c7c8
  • Complex: Most portions settle fairly quickly into debris, but a few persistent areas of activity move, split, and/or rejoin, eventually dissipating.
    • Examples: Life (B3/S23)
(Obviously, some rules are a blend of two or more of these.)

Let me know what you guys think.
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Re: Developing a more detailed classification of rule behaviors

Postby KittyTac » April 25th, 2018, 9:26 pm

You beat me to it. Well done!
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Re: Developing a more detailed classification of rule behaviors

Postby Majestas32 » April 25th, 2018, 9:27 pm

I'll post my own soon
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Re: Developing a more detailed classification of rule behaviors

Postby KittyTac » April 25th, 2018, 9:29 pm

Though Seeds may stabilize eventually, if every cell except for the spaceships dies out suddenly, as an extreme form of the "bubbles".

Idea: Metacomplex, these rules display very interesting dynamics, but usually if run in a bounded grid, e.g: B2e3ain4-cjqtw5ceiry6-ac78/S2ac3ajknq4eiqwy5-ain6-e78:T1000,1000
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Re: Developing a more detailed classification of rule behaviors

Postby toroidalet » April 25th, 2018, 10:33 pm

KittyTac wrote:Idea: Metacomplex, these rules display very interesting dynamics, but usually if run in a bounded grid, e.g: B2e3ain4-cjqtw5ceiry6-ac78/S2ac3ajknq4eiqwy5-ain6-e78:T1000,1000

'interesting' is hard to define, so it's hard to see what you're referring to for this 'new' class of rules.
bounded grids can be approximated by sufficiently large infinite grids, though they mightn't experience the takeover of some agar as frequently as on bounded grids.


i'm confused as to how replicators would play into this definition. would they make a rule settling explosive?
have you considered exotic phenomena such as the 'snakes' which arise along crystallographic defects in certain rules?
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Re: Developing a more detailed classification of rule behaviors

Postby velcrorex » April 26th, 2018, 12:53 am

B34578/S0567 is explosive, but has two "phases," one more dense than the other. I'm not sure how that would be noted in the classification.
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Re: Developing a more detailed classification of rule behaviors

Postby Extrementhusiast » April 29th, 2018, 12:36 am

toroidalet wrote:i'm confused as to how replicators would play into this definition. would they make a rule settling explosive?
have you considered exotic phenomena such as the 'snakes' which arise along crystallographic defects in certain rules?

If there are replicators present, the rule tends to head toward lineland, depending on how explosive the rest of the pattern is. As for snakes, snakeland could be added as another location.

velcrorex wrote:B34578/S0567 is explosive, but has two "phases," one more dense than the other. I'm not sure how that would be noted in the classification.


I'd go by the innermost phase, which would be active explosive.
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Re: Developing a more detailed classification of rule behaviors

Postby LaundryPizza03 » April 30th, 2018, 11:55 pm

velcrorex wrote:B34578/S0567 is explosive, but has two "phases," one more dense than the other. I'm not sure how that would be noted in the classification.

A random field reaches an equilibrium of 64.6% after around 100 generations:
x = 554, y = 536, rule = B34578/S0567
248b3o3b3o3b3o2bo5b5ob4o8bo3bob4o9b3o2bo3bo2b3o8bo3bo2b3o$247bo3bobo3b
obo3bobo5bo5bo3bo7bo3bobo3bo7bo3bobo3bobo3bo7b2ob2obo3bo$247bo5bo5bo3b
obo5bo5bo3bo7bo3bobo3bo11bo2bobo6bo7bobobobo$248b3o2bo5b5obo5b3o3bo3bo
b5obo3bob4o11bo4bo6bo8bobobobo$251bobo5bo3bobo5bo5bo3bo7bo3bobo13bo4bo
bo4bo9bo3bobo$247bo3bobo3bobo3bobo5bo5bo3bo7bo3bobo12bo4bo3bo2bo10bo3b
obo3bo$248b3o3b3o2bo3bob5ob5ob4o9b3o2bo11b5obo3bob5o3bo3bo3bo2b3o8$b3o
3b3o4bo4b3o3b3o2b5o$o5bo3bo2b2o3bo3bobo3bo5bo$o5bo3bo3bo7bo5bo4bo$4o3b
3o4bo5b2o4b2o4bo12bo380bo$o3bobo3bo3bo7bo5bo2bo13bo380b2o2bo60bo$o3bob
o3bo3bo3bo3bobo3bobo14bo370bo8bobob2o50bo4bo3bobo19b2o$b3o3b3o3b3o3b3o
3b3o2bo14bo370b2o2b2o2bo3bo2bo46bo2b3o2b2obo2bob3o2b3o6bo2bo2b2o17bo$
45bo365b3o2b2obo2bobo6bo43bobob2o3b2o2bo4bo3b2o3bo2bobob2o4bo2b3o11b2o
$45bo345bo18bo3b2o2b2o3bo8bo41bobo25bobobo9b2o2bo8b2obobo$45bo345bo17b
o4b2o2bo13bo4b2o7bo24b3o29bo12b2o3bo2b5o2bo2bo$45bo302bo14bo12bo10b2ob
obo4b2o2bo6bo6bo17bo2bo2bo6b2o3bo19bo44bo4b3o10bo$45bo235bo54bo10b2o
10b2o2b3ob4o2bo2b2o8bo2b2obo3bo2b2obo4bo26bobo2bo6b2o3b3o4bo7bo3bo64bo
3b3o$45bo235b3o5b2o45b3o8bobo8bobobo3bo4b2ob2obo4b4o6bo3bo6b4o28bo4b2o
3bo2b3o3b2obobo3bo2bo3bo64bo2bo3b2o$45bo210bo4bo3bo5bo3bob2obo3b2o2bob
o12b3o7bo3b2o2bo14bo2b2o5bo2bo4b2o2bo2b2o8bo6bo2bo11b3o44bob4o10b2o2bo
2b3obo2bo65b2o6bo$45bo210b2o3b2obob5obobobo2b2o5b2o3bo10bo3bo2b2obob3o
2bob2o12bo5b3o2bo3bo2bobobo3bo16b3o12bo62bo3bobo4bobo66bo8bo$45bo172bo
32b3obobob2obobo8bo12bo4bo2b2o3b2obo4b2o2bo7b2o2b4o4b5o8b2o4bobo3b2o3b
o99b2o5b2o$45bo172bo23b4o4bo3b2o2bo4bo28b2obo2bo2bo18bo6bo3bo13bo5b2o
3bo104bo6bo$45bo171bobo3bo4bo2bo2b3o2b3o3bo3bo46b2o30b3o20bo$45bo167bo
3bobo2bobo3b3ob2o3b2o7b3o47bo$45bo150bo16b2obo3b2o3bobo18bo$45bo145bo
4b2o14bobobo3bo5b2o$45bo145b2ob2obo8bo5bo2bo10bo$45bo144bo2bo4bo2bo3bo
bo3bo$45bo143bo9bob2obo2bo2b2o$45bo143bo9b2o2bo4b2o$45bo139bo2bo11bo7b
o$45bo138bob2o$45bo134b4o2bo$45bo134bo$45bo133bo$45bo133bo$45bo132bo$
45bo125b5obo$45bo125bo4b2o$45bo125bo4bo$45bo124bo$45bo124bo$45bo120bo
2b2o$45bo120b3o$45bo115bo3bo$45bo115bo3bo$45bo115b2o2bo$45bo114bobobo$
45bo114bo2b2o$45bo109b2o3bo2bo$45bo108bo2bobo$45bo108bo3bo$45bo107bo$
45bo106bo$45bo100bo5bo$45bo100b2ob3o$45bo100bobo$45bo99bo$45bo99bo$45b
o98bo$45bo97bo$45bo97bo$45bo96bo$45bo96bo$45bo95bo$45bo95bo$45bo94bo$
45bo90bo2bo$45bo90b3o$45bo90bo$45bo89bo$45bo85bo3bo$45bo85b2obo$45bo
84bo2bo$45bo84bo$45bo83bo$45bo82bo$45bo81bo$45bo80bo$45bo80bo$45bo77b
3o$45bo76bo$45bo76bo$45bo75bo$45bo75bo$45bo74bo$45bo74bo$45bo74bo$45bo
73bo$45bo73bo$45bo71b2o$45bo70bo$45bo70bo$45bo69bo$45bo69bo$45bo68bo$
45bo68bo$45bo67bo$45bo67bo$45bo66bo$45bo66bo$45bo64b2o$45bo64bo$45bo
63bo$45bo63bo$45bo63bo$45bo62bo$45bo61b2o$45bo60bo$45bo60bo$45bo59bo$
45bo58b2o$45bo57bo$45bo57bo$45bo56bo$45bo56bo$45bo56bo$45bo56bo$45bo
54b2o$45bo54b2o$45bo53bo$45bo53bo$45bo53bo$45bo53bo$45bo52bo$45bo52bo$
45bo51bo$45bo50bo$45bo49bo$45bo49bo$45bo48bo$45bo48bo$45bo47bo$45bo47b
o$45bo46bo$45bo45bo$45bo45bo$45bo45bo$45bo45bo$45bo44bo$45bo44bo$45bo
44bo$45bo44bo$45bo43bo$45bo42bo$45bo42bo$45bo41bo$45bo41bo$45bo41bo$
45bo40bo$45bo40bo$45bo39bo$45bo39bo$45bo38bo$45bo38bo$45bo37bo$45bo37b
o$45bo36bo$45bo35bo$45bo35bo$45bo35bo$45bo34bo$45bo34bo$45bo34bo$45bo
33bo$45bo33bo$45bo33bo$45bo33bo$45bo32bo$45bo32bo$45bo32bo$45bo31bo$
45bo31bo$45bo31bo$45bo31bo$45bo30bo$45bo30bo$45bo30bo$45bo30bo$45bo30b
o$45bo29bo$45bo29bo$45bo29bo$45bo29bo$45bo28bo$45bo28bo$45bo27bo$45bo
27bo$45bo27bo$45bo26bo$45bo26bo$45bo25bo$45bo25bo$45bo25bo$45bo24bo$
45bo24bo$45bo24bo$45bo24bo$45bo24bo$45bo23bo$45bo23bo$45bo23bo$45bo23b
o$45bo22bo$45bo22bo$45bo22bo$45bo21bo$45bo21bo$45bo21bo$45bo21bo$45bo
20bo$45bo20bo$45bo20bo$45bo20bo$45bo20bo$45bo20bo$45bo19bo$45bo19bo$
45bo19bo$45bo19bo$45bo19bo$45bo19bo$45bo18bo$45bo18bo$45bo17bo$45bo17b
o$45bo17bo$45bo17bo$45bo16bo$28b7o10bo16bo$31bo13bo16bo$30bo14bo16bo$
29bo15bo16bo$28b7o10bo16bo$45bo15bo$29b5o11bo15bo$28bo5bo10bo15bo$28bo
5bo10bo15bo$28bo5bo10bo15bo$29b5o11bo15bo$45bo15bo$45bo14bo$28bo5bo10b
o14bo$28b7o10bo14bo$28bo5bo10bo14bo$45bo14bo$45bo14bo$28bo16bo14bo$28b
o16bo13bo$28b7o10bo13bo$28bo16bo13bo$28bo16bo13bo$45bo12bo$29b6o10bo
12bo$28bo2bo13bo12bo$28bo2bo13bo12bo$28bo2bo13bo12bo$29b6o10bo12bo$45b
o11bo$34bo10bo11bo$34bo10bo11bo$34bo10bo11bo$34bo10bo11bo$28b7o10bo11b
o$45bo10bo$28b6o11bo10bo$34bo10bo10bo$34bo10bo10bo$34bo10bo10bo$28b6o
11bo10bo$45bo10bo$29b2o14bo10bo$28bo2bo13bo9bo$28bo2bo13bo9bo$28bo2bo
13bo9bo$28b7o10bo9bo$45bo9bo$29b5o11bo9bo$28bo5bo10bo9bo$28bo5bo10bo9b
o$28bo5bo10bo8bo$29b5o11bo8bo$45bo8bo$29b2o14bo8bo$28bo2bo13bo8bo$28bo
2bo13bo8bo$28bo2bo13bo8bo$28b7o10bo7bo$45bo7bo$45bo7bo$45bo7bo$45bo7bo
$45bo7bo$45bo7bo$45bo6bo$45bo6bo$45bo6bo$45bo6bo$45bo6bo$45bo6bo$45bo
5bo$45bo5bo$45bo5bo$45bo5bo$45bo5bo$45bo5bo$45bo5bo$45bo5bo$45bo5bo$
45bo5bo$45bo5bo$45bo5bo$45bo5bo$45bo5bo$45bo4bo$45bo4bo$45bo4bo$45bo4b
o$45bo4bo$45bo4bo$45bo4bo$45bo4bo$45bo4bo$45bo4bo$45bo4bo$45bo4bo$45b
2o3bo$45b2o3bo$45b2o2bo$45b2o2bo$45b3obo$45b3obo$45b3obo$45b3obo$45b3o
bo$45b3obo$45b3obo$45b4o$45b2obo$45b2obo$45b2obo$45b2obo$45b2o$45b2o$
45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b
2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$
45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b
2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$
45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b
2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$
45b2o$45b2o$45b2o$45b2o$45b2o$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$
45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$
45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$
45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$
45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$
45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$
45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$5o2b3o3b3o5bo2b5o2b3o11bo$o5bo
3bobo3bo3b2o2bo5bo3bo10bo$o9bo5bo2bobo2bo9bo10bo$b3o5bo4b2o2bo2bo3b3o
4b2o11bo$4bo3bo7bob5o5bo5bo10b501o$o3bo2bo4bo3bo4bo2bo3bobo3bo$b3o2b5o
2b3o5bo3b3o3b3o8$43b3o185b3o2b5obo3bob5ob4o3b3o2b5o2b3o3b3o2bo3bo10bo
34bo4b3o4bo4b3o3bo180b3o3b3o3b3o$42bo3bo183bo3bobo5b2o2bobo5bo3bobo3bo
3bo5bo3bo3bob2o2bo9bo11bo22b2o3bo3bo2bobo2bo3bo3bo178bo3bobo3bobo3bo$
42bo2b2o183bo5bo5bobobobo5bo3bobo3bo3bo5bo3bo3bobobobo9bo4b4ob5o2b3o2b
4o2b5o3bo3bo2b2obo3bobo2b2o3bo182bobo2b2obo2b2o$42bobobo183bo2b2ob3o3b
o2b2ob3o3b4o2b5o3bo5bo3bo3bobo2b2o9bo3bo7bo3bo3bobo3bo9bo3bobobo7bobob
o3bo180b2o2bobobobobobo$42b2o2bo183bo3bobo5bo3bobo5bo2bo2bo3bo3bo5bo3b
o3bobo3bo9bo4b3o4bo3b5obo3bob5o3bo3b2o2bo7b2o2bo3bo182bob2o2bob2o2bo$
42bo3bo183bo3bobo5bo3bobo5bo3bobo3bo3bo5bo3bo3bobo3bo9bo7bo3bo3bo5bo3b
o9bo3bo3bo7bo3bo3bo178bo3bobo3bobo3bo$43b3o185b3o2b5obo3bob5obo3bobo3b
o3bo4b3o3b3o2bo3bo10bo2b4o5b2o2b4ob4o9b3o3b3o9b3o3bo180b3o3b3o3b3o$
320bo$320bo!

This is unusually slow for a Class 3 rule. For comparison, the same field in B2/S stabilizes in just 30 generations:
x = 554, y = 536, rule = B2/S
248b3o3b3o3b3o2bo5b5ob4o8bo3bob4o9b3o2bo3bo2b3o8bo3bo2b3o$247bo3bobo3b
obo3bobo5bo5bo3bo7bo3bobo3bo7bo3bobo3bobo3bo7b2ob2obo3bo$247bo5bo5bo3b
obo5bo5bo3bo7bo3bobo3bo11bo2bobo6bo7bobobobo$248b3o2bo5b5obo5b3o3bo3bo
b5obo3bob4o11bo4bo6bo8bobobobo$251bobo5bo3bobo5bo5bo3bo7bo3bobo13bo4bo
bo4bo9bo3bobo$247bo3bobo3bobo3bobo5bo5bo3bo7bo3bobo12bo4bo3bo2bo10bo3b
obo3bo$248b3o3b3o2bo3bob5ob5ob4o9b3o2bo11b5obo3bob5o3bo3bo3bo2b3o8$5o
2b3o3b3o5bo2b5o2b3o$o5bo3bobo3bo3b2o2bo5bo3bo$o9bo5bo2bobo2bo9bo$b3o5b
o4b2o2bo2bo3b3o4b2o11bo$4bo3bo7bob5o5bo5bo10bo$o3bo2bo4bo3bo4bo2bo3bob
o3bo10bo$b3o2b5o2b3o5bo3b3o3b3o11bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo
$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo
$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo
$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo
$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo
$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo
$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo
$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo
$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo
$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo
$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo
$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo
$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo
$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo
$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo
$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo
$28b7o10bo$31bo13bo$30bo14bo$29bo15bo$28b7o10bo$45bo$29b5o11bo$28bo5bo
10bo$28bo5bo10bo$28bo5bo10bo$29b5o11bo$45bo$45bo$28bo5bo10bo$28b7o10bo
$28bo5bo10bo$45bo$45bo$28bo16bo$28bo16bo$28b7o10bo$28bo16bo$28bo16bo$
45bo$29b6o10bo$28bo2bo13bo$28bo2bo13bo$28bo2bo13bo$29b6o10bo$45b2o$34b
o10b2o$34bo10b2o$34bo10b2o$34bo10b2o$28b7o10b2o$45b2o$28b6o11b2o$34bo
10b2o$34bo10b2o$34bo10b2o$28b6o11b2o$45b2o$29b2o14b2o$28bo2bo13b2o$28b
o2bo13b2o$28bo2bo13b2o$28b7o10b2o$45b2o$29b5o11b2o$28bo5bo10b2o$28bo5b
o10b2o$28bo5bo10b2o$29b5o11b2o$45b2o$29b2o14b2o$28bo2bo13b2o$28bo2bo
13b2o$28bo2bo13b2o$28b7o10b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b
2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$
45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b
2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$
45b2o$45b2o$45b2o244bo$45b2o70b2o24b3o11b2o22bo10b2o32bo8bo28b2o24bob
4o9bo5bo4bo5b2o63b2o60b2o36b4o28b2o$45b2o41b3o3b13o4bo2b3o2bob6o4bo2b
3o2b2obo3bo2b2o3b3o2b3o2b5o2b8o2b6o2b3o2b5o2b3o2bo2b5o2b3o3b4ob5o2bobo
2b5o2b18o2b11o2b7o3bo6bo4bo2bob5ob4ob5o2b5o2bo2b5o3b4ob2o5b3o2b2ob4o8b
8o4bo2b2ob2o8b15o2b3o2b5o3b4o3b2ob7o2b11o2b10o2bo4bo2b3o4b3o5b2ob2o3b
4ob7o2b3o5b3o4b6o2b2o$45b2o40bo3b3o13b2o2b3o6bo6b4ob2o3b2o2bo5b2o2b3o
8b2o5b2o8b2o6b2o10b2o3b2ob2o5b2o3b3o10b2o3b2o5b2o20bo10b2o7b3o7b5ob2o
25b2ob2o5b3o4bo2b5o3b2o2bo4b8o8b4o5bo2b8o15b2o3b2o5b3o4b3o2bo9bo10b2o
10b2ob4ob2o10b5o2bo2b3o4bo9bo2b5o3b4o6b2o$45b2o35b5o22b2o$45b2o34bo$
45b2o32b2o$45b2o30b2o$45b2o29bo$45b2o29bo$45b2o28bo$45b2o28bo$45b2o27b
o$45b2o27bo$45b2o26bo$45b2o26bo$45b2o25bo$45b2o25bo$45b2o24bo$45b2o24b
o$45b2o24bo$45b2o23bo$45b2o23bo$45b2o23bo$45b2o22bo$45b2o22bo$45b2o21b
o$45b2o21bo$45b2o21bo$45b2o20bo$45b2o20bo$45b2o20bo$45b2o19bo$45b2o19b
o$45b2o19bo$45b2o19bo$45b2o19bo$45b2o18bo$45b2o18bo$45b2o18bo$45b2o18b
o$45b2o18bo$45b2o17bo$45b2o17bo$45b2o17bo$45b2o17bo$45b2o16bo$45b2o16b
o$45b2o16bo$45b2o16bo$45b2o16bo$45b2o15bo$45b2o15bo$45b2o15bo$45b2o15b
o$45b2o15bo$45b2o14bo$45b2o14bo$45b2o14bo$45b2o14bo$45b2o14bo$45b2o14b
o$45b2o14bo$45b2o13bo$45b2o13bo$45b2o13bo$45b2o13bo$45b2o13bo$45b2o13b
o$45b2o13bo$45b2o12bo$45b2o12bo$45b2o12bo$45b2o12bo$45b2o12bo$45b2o12b
o$45b2o12bo$45b2o12bo$45b2o11bo$45b2o11bo$45b2o11bo$45b2o11bo$45b2o11b
o$45b2o10bo$45b2o10bo$45b2o9bo$45b2o9bo$45b2o9bo$45b2o9bo$45b2o9bo$45b
2o9bo$45b2o9bo$45b2o8bo$45b2o8bo$45b2o8bo$45b2o8bo$45b2o8bo$45b2o8bo$
45b2o8bo$45b2o7bo$45b2o7bo$45b2o6bo$45b2o6bo$45b2o6bo$45b2o6bo$45b2o6b
o$45b2o6bo$45b2o6bo$45b2o6bo$45b2o5bo$45b2o5bo$45b2o5bo$45b2o5bo$45b2o
5bo$45b2o5bo$45b2o5bo$45b2o5bo$45b2o5bo$45b2o5bo$45b2o5bo$45b2o5bo$45b
2o4bo$45b2o4bo$45b2o4bo$45b2o4bo$45b2o4bo$45b2o4bo$45b2o4bo$45b2o4bo$
45b2o4bo$45b2o4bo$45b2o4bo$45b2o4bo$45b2o4bo$45b2o4bo$45b2o4bo$45b2o4b
o$45b2o3bo$45b2o3bo$45b2o3bo$45b2o3bo$45b2o3bo$45b2o3bo$45b2o3bo$45b2o
3bo$45b2o3bo$45b2o3bo$45b2o3bo$45b2o3bo$45b2o3bo$45b2o3bo$45b2o3bo$45b
2o3bo$45b2o2bo$45b2o2bo$45b2o2bo$45b2o2bo$45b2o2bo$45b2o2bo$45b2o2bo$
45b2o2bo$45b2o2bo$45b2o2bo$45b2o2bo$45b2o2bo$45b2obo$45b2obo$45b2obo$
45b2obo$45b2obo$45b2obo$45b2obo$45b2obo$6b5ob5o2b3o3b3o3b3o11b3o$6bo9b
obo3bobo3bobo3bo10b3o$6bo8bo2bo3bobo3bobo2b2o10b3o$7b3o4bo4b3o3b4obobo
bo10b2o$10bo2bo4bo3bo5bob2o2bo10b501o$6bo3bobo5bo3bo5bobo3bo$7b3o2bo6b
3o3b3o3b3o8$43b3o185b3o2b5obo3bob5ob4o3b3o2b5o2b3o3b3o2bo3bo10bo34bo4b
3o4bo4b3o3bo180b3o3b3o3b3o$42bo3bo183bo3bobo5b2o2bobo5bo3bobo3bo3bo5bo
3bo3bob2o2bo9bo11bo22b2o3bo3bo2bobo2bo3bo3bo178bo3bobo3bobo3bo$42bo2b
2o183bo5bo5bobobobo5bo3bobo3bo3bo5bo3bo3bobobobo9bo4b4ob5o2b3o2b4o2b5o
3bo3bo2b2obo3bobo2b2o3bo182bobo2b2obo2b2o$42bobobo183bo2b2ob3o3bo2b2ob
3o3b4o2b5o3bo5bo3bo3bobo2b2o9bo3bo7bo3bo3bobo3bo9bo3bobobo7bobobo3bo
180b2o2bobobobobobo$42b2o2bo183bo3bobo5bo3bobo5bo2bo2bo3bo3bo5bo3bo3bo
bo3bo9bo4b3o4bo3b5obo3bob5o3bo3b2o2bo7b2o2bo3bo182bob2o2bob2o2bo$42bo
3bo183bo3bobo5bo3bobo5bo3bobo3bo3bo5bo3bo3bobo3bo9bo7bo3bo3bo5bo3bo9bo
3bo3bo7bo3bo3bo178bo3bobo3bobo3bo$43b3o185b3o2b5obo3bob5obo3bobo3bo3bo
4b3o3b3o2bo3bo10bo2b4o5b2o2b4ob4o9b3o3b3o9b3o3bo180b3o3b3o3b3o$320bo$
320bo!
x = 4, y = 3, rule = B3-q4z5y/S234k5j
2b2o$b2o$2o!

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Re: Developing a more detailed classification of rule behaviors

Postby LaundryPizza03 » May 1st, 2018, 12:28 am

Anti-Coagulations (B478/S234678) settles to a density of 7.2% after about 1,500 generations. It forms chaotic blobs that gradually decay into closely packed still lifes and low-period oscillators. Below is the population plot of a 1024*1024 random field over 3000 generations:
x = 557, y = 536, rule = B478/S234678
248b3o3b3o3b3o2bo5b5ob4o8bo3bob4o9b3o2bo3bo2b3o8bo3bo2b3o$247bo3bobo3b
obo3bobo5bo5bo3bo7bo3bobo3bo7bo3bobo3bobo3bo7b2ob2obo3bo$247bo5bo5bo3b
obo5bo5bo3bo7bo3bobo3bo11bo2bobo6bo7bobobobo$248b3o2bo5b5obo5b3o3bo3bo
b5obo3bob4o11bo4bo6bo8bobobobo$251bobo5bo3bobo5bo5bo3bo7bo3bobo13bo4bo
bo4bo9bo3bobo$247bo3bobo3bobo3bobo5bo5bo3bo7bo3bobo12bo4bo3bo2bo10bo3b
obo3bo$248b3o3b3o2bo3bob5ob5ob4o9b3o2bo11b5obo3bob5o3bo3bo3bo2b3o8$5ob
5o2b3o3b3o4bo4b3o$o5bo5bo3bobo6b2o3bo$o5bo9bobo7bo3bo$b3o3b3o5bo2b4o4b
o3b4o11bo$4bo5bo3bo3bo3bo3bo3bo3bo10bo$o3bobo3bo2bo4bo3bo3bo3bo3bo10bo
$b3o3b3o2b5o2b3o3b3o3b3o11b2o$45b2o$45b2o$45b2o$45b2o$45bobo$45bobo$
45bobo$45bobo$45bo2bo$45bo2bo$45bo2bo$45bo2bo$45bo3bo$45bo3bo$45bo3bo$
45bo4bo$45bo4bo$45bo4bo$45bo5bo$45bo5bo$45bo5bo$45bo6bo$45bo6bo$45bo6b
o$45bo7bo$45bo7bo$45bo7b2o$45bo8bo$45bo9bo$45bo9b2o$45bo9b2o$45bo10b2o
$45bo10b2o$45bo11bo$45bo12bo$45bo12b2o$45bo13bo$45bo13b2o$45bo14b2o$
45bo14b2o$45bo15bo$45bo15b2o$45bo16b2o$45bo17bo$45bo18b2o$45bo18b2o$
45bo18b2o$45bo19b2o$45bo20bo$45bo20b2o$45bo20b2o$45bo21b2o$45bo22b2o$
45bo23bo$45bo23bo$45bo23b2o$45bo24bo$45bo24b2o$45bo25b2o$45bo26b2o$45b
o26b2o$45bo27b2o$45bo28bo$45bo28b2o$45bo29b2o$45bo30bo$45bo30bo$45bo
30b2o$45bo31b2o$45bo32bo$45bo32b2o$45bo32b3o$45bo34bo$45bo34b2o$45bo
35bo$45bo35bo$45bo36bo$45bo36b2o$45bo37bo$45bo37b2o$45bo37b2o$45bo38bo
$45bo38b2o$45bo39bo$45bo39b2o$45bo40b2o$45bo41bo$45bo41b2o$45bo42bo$
45bo42bo$45bo43bo$45bo43b2o$45bo44bo$45bo45bo$45bo45bo$45bo45bo$45bo
46bo$45bo46bo$45bo47bo$45bo47bo$45bo47b2o$45bo47b2o$45bo48bo$45bo49bo$
45bo49bo$45bo49b2o$45bo50bo$45bo50b2o$45bo51bo$45bo51b2o$45bo52bo$45bo
52bo$45bo52b2o$45bo53bo$45bo53bo$45bo53b2o$45bo54bo$45bo54bo$45bo54b2o
$45bo55bo$45bo55b2o$45bo56bo$45bo56bo$45bo56b2o$45bo56b2o$45bo57b2o$
45bo58bo$45bo58bo$45bo58bo$45bo59bo$45bo59bo$45bo60bo$45bo60bo$45bo60b
2o$45bo60b2o$45bo61bo$45bo62bo$45bo62bo$45bo62bo$45bo62b2o$45bo63bo$
45bo63bo$45bo64bo$45bo64bo$45bo65bo$45bo65bo$45bo65bo$45bo66bo$45bo66b
o$45bo66bo$45bo66b2o$45bo67bo$45bo67bo$45bo67b2o$45bo68bo$45bo68bo$45b
o68bo$45bo69bo$45bo69bo$45bo69bo$45bo69bo$45bo70bo$45bo70bo$45bo70b2o$
45bo71bo$45bo71bo$45bo71bo$45bo72bo$45bo72bo$45bo72bo$45bo72bo$45bo73b
o$45bo73bo$45bo73b2o$45bo74bo$45bo74b2o$45bo75bo$45bo75bo$45bo75bo$45b
o76bo$45bo76bo$45bo77bo$45bo77bo$45bo77bo$45bo78bo$45bo78bo$45bo78bo$
45bo79bo$45bo79bo$45bo79b2o$45bo80bo$45bo80bo$45bo80b2o$45bo81bo$45bo
81bo$45bo81bo$45bo81b2o$45bo82bo$45bo82bo$45bo82b2o$45bo83bo$45bo83bo$
45bo83b2o$45bo84bo$45bo84bo$45bo84b2o$45bo85bo$45bo85bo$45bo85bo$45bo
85bo$45bo86bo$45bo86bo$45bo86bo$45bo86bo$45bo87bo$45bo87bo$45bo87bo$
28b7o10bo88bo$31bo13bo88bo$30bo14bo88bo$29bo15bo89bo$28b7o10bo89bo$45b
o89bo$29b5o11bo90bo$28bo5bo10bo90bo$28bo5bo10bo90bo$28bo5bo10bo90b2o$
29b5o11bo91bo$45bo91bo$45bo92bo$28bo5bo10bo92bo$28b7o10bo92bo$28bo5bo
10bo92b2o$45bo93bo$45bo93bo$28bo16bo93b2o$28bo16bo94bo$28b7o10bo94bo$
28bo16bo94bo$28bo16bo95bo$45bo95bo$29b6o10bo95bo$28bo2bo13bo95b2o$28bo
2bo13bo96bo$28bo2bo13bo96bo$29b6o10bo96b2o$45bo97bo$34bo10bo97b2o$34bo
10bo98bo$34bo10bo98bo$34bo10bo98bo$28b7o10bo99bo$45bo99bo$28b6o11bo99b
o$34bo10bo100bo$34bo10bo100bo$34bo10bo100bo$28b6o11bo100bo$45bo100b2o$
29b2o14bo101bo$28bo2bo13bo101bo$28bo2bo13bo101bo$28bo2bo13bo101b2o$28b
7o10bo102bo$45bo102bo$29b5o11bo102bo$28bo5bo10bo102bo$28bo5bo10bo103bo
$28bo5bo10bo103bo$29b5o11bo104bo$45bo104bo$29b2o14bo104bo$28bo2bo13bo
104bo$28bo2bo13bo105bo$28bo2bo13bo105bo$28b7o10bo105bo$45bo106bo$45bo
106bo$45bo106bo$45bo106b2o$45bo107bo$45bo107bo$45bo107b2o$45bo108bo$
45bo108bo$45bo108bo$45bo109bo$45bo109bo$45bo109bo$45bo110bo$45bo110bo$
45bo110bo$45bo110b2o$45bo111bo$45bo111bo$45bo111bo$45bo111b2o$45bo112b
o$45bo112bo$45bo113bo$45bo113bo$45bo113bo$45bo113b2o$45bo114bo$45bo
114bo$45bo114b2o$45bo115bo$45bo115bo$45bo115bo$45bo116bo$45bo116bo$45b
o116bo$45bo117bo$45bo117bo$45bo117b2o$45bo118bo$45bo118bo$45bo118bo$
45bo119bo$45bo119bo$45bo119bo$45bo120bo$45bo120bo$45bo120bo$45bo121bo$
45bo121bo$45bo121bo$45bo122bo$45bo122bo$45bo122bo$45bo123bo$45bo123bo$
45bo123bo$45bo124bo$45bo124bo$45bo124bo$45bo124b2o$45bo125bo$45bo125bo
$45bo125b2o$45bo126bo$45bo126bo$45bo126b2o$45bo127bo$45bo127bo$45bo
127bo$45bo127b2o$45bo128bo$45bo128bo$45bo129bo$45bo129bo$45bo129bo$45b
o129b2o$45bo130bo$45bo130bo$45bo131bo$45bo131bo$45bo131bo$45bo132bo$
45bo132bo$45bo132bo$45bo133bo$45bo133bo$45bo133b2o$45bo134bo$45bo134bo
$45bo134b2o$45bo135bo$45bo135bo$45bo135b2o$45bo136bo$45bo136b2o$45bo
137bo$45bo137bo$45bo138bo$45bo138bo$45bo138b2o$45bo139bo$45bo139bo$45b
o139bo$45bo140bo$45bo140bo$45bo140bo$45bo141bo$45bo141bo$45bo142bo$45b
o142bo$45bo142b2o$45bo143bo$45bo143bo$45bo144bo$45bo144bo$45bo145bo$
45bo145bo$45bo145b2o$45bo146bo$45bo146bo$45bo146b2o$45bo147bo$45bo147b
2o$45bo148bo$45bo148b2o$45bo149bo$45bo149bo$45bo149bo$45bo150bo$45bo
150b2o$45bo151bo$45bo151b2o$45bo152bo$45bo152bo$45bo153bo$45bo153bo$
45bo154bo$45bo154bo$45bo154b2o$45bo155bo$45bo155b2o$45bo156bo$45bo156b
o$45bo157bo$45bo157bo$45bo158bo$45bo158bo$45bo159bo$45bo159bo$45bo160b
o$45bo160bo$45bo161bo$45bo161b2o$45bo162bo$45bo162bo$45bo163bo$45bo
163b2o$45bo164bo$45bo164b2o$45bo165b2o$45bo166bo$45bo166b2o$45bo167bo$
45bo167b2o$45bo168bo$45bo169bo$45bo169b2o$45bo170b2o$45bo171bo$45bo
171b2o$45bo172b2o$45bo173bo$45bo173b2o$45bo174bo$45bo175bo$45bo175b2o$
45bo176b2o$45bo176b2o$45bo177b2o$45bo178b2o$45bo179bo$45bo180bo$45bo
180b2o$45bo181b2o$45bo182b2o$45bo183b2o$45bo184b2o$45bo185bo$45bo186bo
$45bo186b2o$45bo187b2o$45bo188b2o$45bo189b2o$45bo191bo$45bo192b2o$45bo
193bo$45bo194b2o$45bo195b2o$45bo196b2o$45bo197b2o$45bo198b3o$45bo200b
2o$45bo201b3o$45bo203b2o$45bo205b2o$45bo206b2o$45bo207b3o$45bo209b3o$
45bo211b4o$45bo214b3o$45bo216b3o$45bo219b3o$45bo221b4o$45bo224b4o$45bo
227b5o$6b5ob5ob5ob5o2b3o11bo230b5o$10bobo5bo5bo5bo3bo10bo234b7o$9bo2bo
5bo5bo5bo2b2o10bo240b9o$8bo4b3o3b3o3b3o2bobobo10bo248b15o$7bo8bo5bo5bo
b2o2bo10b501o$6bo5bo3bobo3bobo3bobo3bo$6bo6b3o3b3o3b3o3b3o8$43b3o185b
3o2b5obo3bob5ob4o3b3o2b5o2b3o3b3o2bo3bo10bo34bo4b3o4bo4b3o3bo177b3o3b
3o3b3o3b3o$42bo3bo183bo3bobo5b2o2bobo5bo3bobo3bo3bo5bo3bo3bob2o2bo9bo
11bo22b2o3bo3bo2bobo2bo3bo3bo175bo3bobo3bobo3bobo3bo$42bo2b2o183bo5bo
5bobobobo5bo3bobo3bo3bo5bo3bo3bobobobo9bo4b4ob5o2b3o2b4o2b5o3bo3bo2b2o
bo3bobo2b2o3bo179bobo2b2obo2b2obo2b2o$42bobobo183bo2b2ob3o3bo2b2ob3o3b
4o2b5o3bo5bo3bo3bobo2b2o9bo3bo7bo3bo3bobo3bo9bo3bobobo7bobobo3bo177b2o
2bobobobobobobobobo$42b2o2bo183bo3bobo5bo3bobo5bo2bo2bo3bo3bo5bo3bo3bo
bo3bo9bo4b3o4bo3b5obo3bob5o3bo3b2o2bo7b2o2bo3bo179bob2o2bob2o2bob2o2bo
$42bo3bo183bo3bobo5bo3bobo5bo3bobo3bo3bo5bo3bo3bobo3bo9bo7bo3bo3bo5bo
3bo9bo3bo3bo7bo3bo3bo175bo3bobo3bobo3bobo3bo$43b3o185b3o2b5obo3bob5obo
3bobo3bo3bo4b3o3b3o2bo3bo10bo2b4o5b2o2b4ob4o9b3o3b3o9b3o3bo177b3o3b3o
3b3o3b3o$320bo$320bo!

Unless the "quickly settles" category includes higher densities as well, this would be something new, but not unusual:
x = 554, y = 536, rule = B2c3aeny4a5i6i7e/S12a3ejry4etz5y6c8
248b3o3b3o3b3o2bo5b5ob4o8bo3bob4o9b3o2bo3bo2b3o8bo3bo2b3o$247bo3bobo3b
obo3bobo5bo5bo3bo7bo3bobo3bo7bo3bobo3bobo3bo7b2ob2obo3bo$247bo5bo5bo3b
obo5bo5bo3bo7bo3bobo3bo11bo2bobo6bo7bobobobo$248b3o2bo5b5obo5b3o3bo3bo
b5obo3bob4o11bo4bo6bo8bobobobo$251bobo5bo3bobo5bo5bo3bo7bo3bobo13bo4bo
bo4bo9bo3bobo$247bo3bobo3bobo3bobo5bo5bo3bo7bo3bobo12bo4bo3bo2bo10bo3b
obo3bo$248b3o3b3o2bo3bob5ob5ob4o9b3o2bo11b5obo3bob5o3bo3bo3bo2b3o8$5o
2b3o3b3o5bo2b5o2b3o$o5bo3bobo3bo3b2o2bo5bo3bo$o9bo5bo2bobo2bo9bo$b3o5b
o4b2o2bo2bo3b3o4b2o11bo$4bo3bo7bob5o5bo5bo10bo$o3bo2bo4bo3bo4bo2bo3bob
o3bo10bo$b3o2b5o2b3o5bo3b3o3b3o11bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo
$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo
$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo
$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo
$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo
$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo$45bo
$45bo$45bo$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o
$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b
2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$
45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b
2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$
45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b
2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$
45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b
2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$
45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b
2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$
45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b2o$45b
2o$45b2o$28b7o10b2o$31bo13b2o$30bo14b2o$29bo15b2o$28b7o10b2o$45b2o$29b
5o11b2o$28bo5bo10b2o$28bo5bo10b2o$28bo5bo10b2o$29b5o11b2o$45b2o$45b2o$
28bo5bo10b2o$28b7o10b2o$28bo5bo10b2o$45b2o$45b2o$28bo16b2o$28bo16b2o$
28b7o10b2o$28bo16b2o$28bo16b2o$45b2o$29b6o10b2o$28bo2bo13b2o$28bo2bo
13b2o$28bo2bo13bobo$29b6o10bobo$45bobo$34bo10bobo$34bo10bobo$34bo10bob
o$34bo10bobo$28b7o10bobo$45bobo$28b6o11bobo$34bo10bobo$34bo10bobo$34bo
10bobo$28b6o11bobo$45bobo$29b2o14bobo$28bo2bo13bobo$28bo2bo13bobo$28bo
2bo13bobo$28b7o10bobo$45bobo$29b5o11bobo$28bo5bo10bobo$28bo5bo10bobo$
28bo5bo10bobo$29b5o11bobo$45bobo$29b2o14bobo$28bo2bo13bobo$28bo2bo13bo
bo$28bo2bo13bobo$28b7o10bobo$45bobo$45bobo$45bobo$45bobo$45bobo$45bobo
$45bobo$45bobo$45bobo$45bobo$45bobo$45bobo$45bobo$45bobo$45bobo$45bobo
$45bobo$45bobo$45bobo$45bobo$45bobo$45bobo$45bobo$45bobo$45bobo$45bobo
$45bobo$45bobo$45bobo$45bobo$45bobo$45bobo$45bobo$45bobo$45bobo$45bobo
$45bobo$45bobo$45bobo$45bobo$45bobo$45bobo$45bobo$45bobo$45bobo$45bobo
$45bobo$45bobo$45bobo$45bobo$45bobo$45bobo$45bobo$45bobo$45bobo$45bobo
$45bobo$45bobo$45bo2bo$45bo2bo$45bo2bo$45bo2bo$45bo2bo$45bo2bo$45bo2bo
$45bo2bo$45bo2bo$45bo2bo$45bo2bo$45bo2bo$45bo2bo$45bo2bo$45bo3bo$45bo
3bo$45bo3bo$45bo3bo$45bo3bo$45bo3bo$45bo3bo$45bo3bo$45bo3bo$45bo3bo$
45bo3bo$45bo3bo$45bo3bo$45bo3bo$45bo3bo$45bo4bo$45bo4bo$45bo4bo$45bo4b
o$45bo4bo$45bo4bo$45bo4bo$45bo4bo$45bo4bo$45bo4bo$45bo4bo$45bo4bo$45bo
4bo$45bo4bo$45bo4bo$45bo4bo$45bo5bo$45bo5bo$45bo5bo$45bo5bo$45bo5bo$
45bo5bo$45bo5bo$45bo5bo$45bo5bo$45bo5bo$45bo5bo$45bo5bo$45bo6bo$45bo6b
o$45bo6bo$45bo6bo$45bo6bo$45bo6bo$45bo6bo$45bo6bo$45bo6bo$45bo6bo$45bo
7bo$45bo7bo$45bo7bo$45bo7bo$45bo7bo$45bo7bo$45bo7bo$45bo7bo$45bo8bo$
45bo8bo$45bo8bo$45bo8bo$45bo8bo$45bo8bo$45bo8bo$45bo8bo$45bo9bo$45bo9b
o$45bo9bo$45bo9bo$45bo9bo$45bo9bo$45bo10bo$45bo10bo$45bo10bo$45bo10bo$
45bo10bo$45bo10bo$45bo11bo$45bo11bo$45bo11bo$45bo11bo$45bo11bo$45bo11b
o$45bo12bo$45bo12bo$45bo12bo$45bo12bo$45bo12bo$45bo12bo$45bo13bo$45bo
13bo$45bo13bo$45bo13bo$45bo14bo$45bo14bo$45bo14bo$45bo14bo$45bo15bo$
45bo15bo$45bo15bo$45bo15bo$45bo16bo$45bo16bo$45bo16bo$45bo16bo$45bo17b
o$45bo17bo$45bo17bo$45bo18bo$45bo18bo$45bo18bo$45bo19bo$45bo19bo$45bo
20bo$45bo20bo$45bo21bo$45bo21bo$45bo22bo$45bo22bo$45bo23bo$45bo24bo$
45bo24bo$45bo25bo$45bo26bo$45bo27bo$45bo28bo$45bo29bo$45bo30bo$45bo31b
o$45bo32bo$45bo33bo$45bo34b2o$45bo36b2o$45bo38bo$45bo39b3o$45bo42b2o$
45bo44b2o$45bo46b4o$45bo50b4o$45bo54b4o$9bo3b3o3b3o3b3o2b5o10bo58b6o$
8b2o2bo3bobo3bobo3bobo14bo64b8o$7bobo2bo2b2o5bobo2b2obo14bo72b12o$6bo
2bo2bobobo3b2o2bobobo2b3o11bo84b20o$6b5ob2o2bo5bob2o2bo5bo10b501o$9bo
2bo3bobo3bobo3bobo3bo$9bo3b3o3b3o3b3o3b3o8$43b3o185b3o2b5obo3bob5ob4o
3b3o2b5o2b3o3b3o2bo3bo10bo34bo4b3o4bo4b3o3bo180b3o2b5o2b3o$42bo3bo183b
o3bobo5b2o2bobo5bo3bobo3bo3bo5bo3bo3bob2o2bo9bo11bo22b2o3bo3bo2bobo2bo
3bo3bo178bo3bobo5bo3bo$42bo2b2o183bo5bo5bobobobo5bo3bobo3bo3bo5bo3bo3b
obobobo9bo4b4ob5o2b3o2b4o2b5o3bo3bo2b2obo3bobo2b2o3bo182bobo5bo2b2o$
42bobobo183bo2b2ob3o3bo2b2ob3o3b4o2b5o3bo5bo3bo3bobo2b2o9bo3bo7bo3bo3b
obo3bo9bo3bobobo7bobobo3bo181bo3b3o2bobobo$42b2o2bo183bo3bobo5bo3bobo
5bo2bo2bo3bo3bo5bo3bo3bobo3bo9bo4b3o4bo3b5obo3bob5o3bo3b2o2bo7b2o2bo3b
o180bo7bob2o2bo$42bo3bo183bo3bobo5bo3bobo5bo3bobo3bo3bo5bo3bo3bobo3bo
9bo7bo3bo3bo5bo3bo9bo3bo3bo7bo3bo3bo179bo4bo3bobo3bo$43b3o185b3o2b5obo
3bob5obo3bobo3bo3bo4b3o3b3o2bo3bo10bo2b4o5b2o2b4ob4o9b3o3b3o9b3o3bo
179b5o2b3o3b3o$320bo$320bo!
x = 4, y = 3, rule = B3-q4z5y/S234k5j
2b2o$b2o$2o!

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