Rules 1 transition from Life, 3-State INT edition

[Cyclotrons]

Now that there's a useable notation+script for 3-State INT rules, it's high time for this particular section of the rulespace to be explored.

Deciding on a canonical Life rule for this rulespace is difficult, as there are many rules that perfectly emulate Life in one state, so long as there are no cells of the other state in the universe. I decided to go with the strictest possible interpretation; that is, transitions only occur for the exact configuration of cells in the correct state, since this requires the least assumptions. It is most easily represented as such:

Code: Select all

BA;3;0/BB/BTA/ATB/SA;2;0.;3;0/SB

There are 954 neighborhood configurations * 3 starting states * 2 other possible end states per transition = 5724 rules to explore here. A lot, no? Thankfully, we can infer the behavior of large sections of this rulespace:

• Notice how toggling any transitions in BTA means that B cells can't exist in non-GoE patterns; the bulk behavior of the rule won't be affected. 5724 - 954 = 4770 rules left.
• The above is mostly true for BA, with the caveat that transitions that don't have any B cells can affect the rule's behavior, but those rules are equivalent to the ones in the 2-State INT version of this rulespace anyway, which is already explored. 4770 - 954 = 3816 rules left.
• Same goes for SA. 3816 - 954 = 2862 rules left.
• SB is a little more nuanced. Since B cells still have no way of replenishing themselves, the only objects they can form are still lives. Since, in this rulespace, B cells basically act like killer cells, so they can't be in still lives where A cells would be in their neighborhood, either, so 954 - 51 more down. In the remaining transitions, once a still life of B cells has formed (which is impossible in most of the remaining rules) they are immortal, meaning they basically act like LifeHistory gray cells they actually suppress births around them, so not quite. As these are well understood, they need not be investigated here. 2862 - 954 = 1908 rules left.

There is likely still significant pruning that can still be done, but I'll leave that to others. This leaves BB and ATB.

I decided to start with BB:

+BB1c;1c;0 - dies out quick due to clumps of life cells constantly producing cells that kill them on their edges
+BB1e;1e;0 - same as above

For constraints with only one cell state, you don't need to include the first set to indicate a unique configuration, so I stop doing so here.

+BB;2c;0 - looks like life this time, just very inactive (I haven't seen a soup of any size stabilize after 150 gens)
+BB;2e;0 - somewhere between the previous two
+BB;2k;0 - most active thus far. first one to have the glider. also has a 10c/20
+BB;2a;0 - dies out the quickest of any so far, which is impressive. dies harder too
+BB;2i;0 - most active thus far. first one that could potentially fool someone not paying attention. a relatively common object (.2A$A.A$A.A$2A!) produces 4 gliders
+BB;2n;0 - most active and lifelike thus far. has c/2 puffers and p72s

For BB;3;0s, you also have to subtract the constraint from the BA section, since that transition already occurs over there and takes precedence due to how rulefiles work.

+BB;3c;0 - similar to the last one but without the interesting stuff
+BB;3e;0 - less active than the last one. has a 10c/20
+BB;3k;0 - most active thus far. first one where the honey farm works
+BB;3a;0 - dies out quick. can't leave its bounding diamond
+BB;3i;0 - similar to above
+BB;3n;0 - not very active. boring
+BB;3y;0 - most active or nearly so. 16c/78d
+BB;3q;0 - not very active. has a WSS (though idk if it's the first)
+BB;3j;0 - dies out quick
+BB;3r;0 - not very active. the way bheps kinda fizzle out is kinda interesting i guess

Edit 1: the rest of the BB;;0 transitions
+BB;4c;0 - the most active and lifelike of the bunch by far. almost as active as actual life. BB occurs in the traffic light, but doesn't actually affect its evolution
+BB;4e;0 - similar to above, but a bit less so
+BB;4k;0 - less active. queen bee becomes a p30 oscillator, no stabilization needed
+BB;4a;0 - not very active at all. boring
+BB;4i;0 - slightly more active than the last one. has a funny c/9d (4.2A$3.2A$4A!)
+BB;4n;0 - simarly active to the last one. has a common pattern that gives rise to 4 evenly spaced traffic lights. 5c/17
+BB;4y;0 - a bit more active. pulsars seem a bit more common than normal
+BB;4q;0 - meh
+BB;4j;0 - pretty inactive
+BB;4r;0 - same as above. no gliders
+BB;4t;0 - inactive. self-stabilizing queen bee. honey farm is a more spread out traffic light
+BB;4w;0 - just boring
+BB;4z;0 - finally a bit more active again. otherwise boring

+BB;5c;0 - significantly less active than life... or at least it would be if the pi wasn't a 2D replicator
+BB;5e;0 - meh
+BB;5k;0 - meh
+BB;5a;0 - rpent is a very small rro with loopability 2, p60. bhep evolves into a LoM, which is a diehard that releases 2 gliders
+BB;5i;0 - meh
+BB;5n;0 - no glider. yes c/2 block puffer
+BB;5y;0 - most inactive in a bit
+BB;5q;0 - same as above
+BB;5j;0 - back to more typical levels of activity. otherwise boring
+BB;5r;0 - has a (5,3)c/21 (3.A$3.A$.2A$2A$A!)

+BB;6c;0 - very common large diagonal puffers
+BB;6e;0 - decent jump in activity from the past few
+BB;6k;0 - aaand we're back (activity wise)
+BB;6a;0 - meh
+BB;6i;0 - one of the most active ones
+BB;6n;0 - meh

+BB;7c;0 - meh
+BB;7e;0 - common diagonal puffer, pulsars a bit more common than normal

+BB;8;0 - the most active of the bunch (besides the one that exploded anyway). still not as active as life proper


Note that I've been using a soup of all A cells to test these rules, since that more accurately reflects the behavior of interest of at least this subset of the BB rules.

[MEisSCAMMER]

The block eats gliders handily (eater 1 fails though):

Code: Select all

x = 7, y = 6, rule = BA;3;0/BB;2n;0/BTA/ATB/SA;2;0.;3;0/SB
2A$2A2$4.2A$4.A.A$4.A!

Edit: RRO (if I have the terminology correct):

Code: Select all

x = 12, y = 10, rule = BA;3;0/BB;2n;0/BTA/ATB/SA;2;0.;3;0/SB
$7.3A4$2.2A$2.A2.A$3.3A!

[Cyclotrons]

BB;0;0 - BB;0;8 is interesting. This space basically acts like two 2SINT rules that act as mutual killer cells for each other. However, since only one transition is allowed, the only transitions where B can escape the bounding diamond are BB ;0;1c, ;0;1e, and ;0;2a. BB;0;2c also has margolus oscillators that could allow for interesting interactions.

+BB;0;0 - Flickering B cells throughout the universe. Life activity is snuffed out no matter what.
+BB;0;1c - B cells spread uncontrollably and quickly kill any A activity. SLs and blinkers are preserved. Can be held back by SL walls like such:
(boy native lifeviewer support sure would be nice)
+BB;0;1e - Similar to above. Kills life activity even faster.
+BB;0;2a - Pretty balanced; neither one completely overtakes the other. A lot of interesting stuff is probably possible.

As for BB in configurations with both states, there probably is nontrivial behavior, but it will be few and far between and hard to find.

[Cyclotrons]

+ATB;0;0 - less active than life, but still has some activity

+ATB;1c;0 - dies out quick
+ATB;1e;0 - dies even quicker. has a 2c/4o

For ATB;2;0 and ATB;3;0 transitions, you should subtract them from the SA transition too.

+ATB;2c;0 - most SLs are gone. little activity. 10c/20o
+ATB;2e;0 - block is much rarer. small decently common p12
+ATB;2k;0 - meh
+ATB;2a;0 - meh
+ATB;2i;0 - slighly more active now. has c/3 (2.A$.A.A$A3.A$.3A!)
+ATB;2n;0 - similar to above

+ATB;3c;0 - notable jump in activity here; most active (in ATB) thus far. pi is a failed puffer
+ATB;3e;0 - right back to less activity
+ATB;3k;0 - meh
+ATB;3a;0 - dies quick. no blocks. 10c/20
+ATB;3i;0 - boring
+ATB;3n;0 - meh
+ATB;3y;0 - meh
+ATB;3q;0 - has a common p24
+ATB;3j;0 - boring
+ATB;3r;0 - boring

+ATB;4c;0 - another big jump in activity; almost as active as life. the pi in particular is a lot more active
+ATB;4e;0 - not nearly as active, but still more active than most before
+ATB;4k;0 - similar to above
+ATB;4a;0 - boring
+ATB;4i;0 - boring
+ATB;4n;0 - has a (3,1)c/10
+ATB;4y;0 - the pi is kinda interesting i guess
+ATB;4q;0 - fizzles out quick
+ATB;4j;0 - meh
+ATB;4r;0 - pi is a failed spaceship
+ATB;4t;0 - meh
+ATB;4w;0 - meh
+ATB;4z;0 - pi debris is all loaves

+ATB;5c;0 - meh
+ATB;5e;0 - common diagonal rakepuffers
+ATB;5k;0 - decently active, otherwise boring
+ATB;5a;0 -less active. pulsars are common
+ATB;5i;0 - meh
+ATB;5n;0 - meh
+ATB;5y;0 - boring
+ATB;5q;0 - common quadratic puffers
+ATB;5j;0 - diagonal puffers
+ATB;5r;0 - pi is a clean orthogonal puffer

+ATB;6c;0 - common 17c/152d
+ATB;6e;0 - pretty active, but boring
+ATB;6k;0 - has a more spread out traffic light in addition to the normal one
+ATB;6a;0 - 4c/48o (.3A$A3.A$A4.A$.2A2.A$3.2A!)
+ATB;6i;0 - more active than life is for some ungodly reason
+ATB;6n;0 - orthogonal traffic light puffer

+ATB;7c;0 - weirdly inactive
+ATB;7e;0 - meh

+ATB;8;0 - also meh

Same thing goes as BB in terms of configurations with both cells.

-

Something interesting to note: the state of this rulespace will be basically be the same for higher-state INT, too: there would be no way to have sustained interactions with multiple types of cells in just one transition.