Close variants of Life
Probably the most-studied minor variant of Conway Life is High Life, B36/S23, which I mentioned earlier (3 or 6 neighbors cause birth, 2 or 3 cause survival). It appears very much like Life, but has a simple replicator that copies itself in an XOR-ish way along a diagonal line. Conway once said he thought maybe it was the CA he should have discovered, but apart from the replicator and various nifty things derived from it, it actually seems slightly less rich; its random soups are slightly quieter.
These other variants I've been messing with don't seem to have been studied all that much:
B37/S23: This initially seems similar to Life on small scales, but it's ultimately a chaotic rule: sufficiently large random soups never seem to settle down, and they keep slowly growing and evaporating standard Life gliders around their edges. There's a naturally occurring puffer that shoots out from the edges of finite soups (update: just found a second one, which makes a nice double row of ponds). Static debris looks Life-like but there's a sort of flattened rosette of four buns and four boats that shows up a lot (at least until the chaos eats it).
B37/S238: Like the above, only more so. The first puffer from the above rule still exists (though its debris is less impressive-looking), and there's an asymmetrically perturbed variant that is a naturally occurring breeder, shooting more puffers sideways from its contrail. If the endless swarms of gliders don't kill it first, it will expand to fill a quarter-plane. Even if they do kill it, there's a fair chance that one of the child puffers will get perturbed into another breeder.
B3/S238: This one's nice: it's not a chaotic rule, but soups seem a little hotter than in Conway Life and take longer to settle down. The debris looks just like Life leftovers except that pulsars are much more common, as is still life 12.121, a sort of big beehive that exists in standard Life but is not at all common. A surprising number of well-known engineered objects (like the Gosper glider gun) still work, though the bigger ones generally don't. Many could probably be modified to work.
These other variants I've been messing with don't seem to have been studied all that much:
B37/S23: This initially seems similar to Life on small scales, but it's ultimately a chaotic rule: sufficiently large random soups never seem to settle down, and they keep slowly growing and evaporating standard Life gliders around their edges. There's a naturally occurring puffer that shoots out from the edges of finite soups (update: just found a second one, which makes a nice double row of ponds). Static debris looks Life-like but there's a sort of flattened rosette of four buns and four boats that shows up a lot (at least until the chaos eats it).
B37/S238: Like the above, only more so. The first puffer from the above rule still exists (though its debris is less impressive-looking), and there's an asymmetrically perturbed variant that is a naturally occurring breeder, shooting more puffers sideways from its contrail. If the endless swarms of gliders don't kill it first, it will expand to fill a quarter-plane. Even if they do kill it, there's a fair chance that one of the child puffers will get perturbed into another breeder.
B3/S238: This one's nice: it's not a chaotic rule, but soups seem a little hotter than in Conway Life and take longer to settle down. The debris looks just like Life leftovers except that pulsars are much more common, as is still life 12.121, a sort of big beehive that exists in standard Life but is not at all common. A surprising number of well-known engineered objects (like the Gosper glider gun) still work, though the bigger ones generally don't. Many could probably be modified to work.