B2/S234 - Oscillators and Wickstretchers Galore!

[BlinkerSpawn]

Two-cell reduction of a p6:

Code: Select all

x = 10, y = 7, rule = B2/S234
bo2bo2bo$4ob4o$bo2bo3b2o$bo2bo$bo5b2o$8o$bo4bo!

[Alexey_Nigin]

Today I decided to search for periods that are multiples of 5.

p5:

Code: Select all

x = 23, y = 23, rule = B2/S234
3bobobo2bo2bo5bo2bo$3o2bobobobob5o2b2o$2bobobobo2bobo4b2obo$2bobobo2bo
bob2obo3bobo$obobobo2bobobob2obobobo$bobo2bo2b3ob2o2bobobo$bob2obobo6b
3obobo$obo3bob2obob2o2bobo2bo$ob3ob3ob2obobo2bob2o$o3bo8bo4bobobo$b3o
2b6o2b3ob2obo$obob3obo3bobobo4bo$o2bo4bo5bo2b6o$2bo2b2obo4b5o4bo$ob2o
2bob5o4bob2obo$bob4o8bobobob2o$bobo3b5ob3ob2obo$o3b2o5bo2bo3bobobo$obo
2b6obobobo3bobo$ob3o7bobob5obo$o3bo2bobob3o6bobo$2obobo9b5o2bo$o4b9obo
3bobo!

p10:

Code: Select all

x = 24, y = 25, rule = B2/S234
obobobobob2o4bo2b3o$obo2bobo4b2o2bobobo2bo$ob3obo2b3obob3o3b3o$obo2bob
obo2bo4bob2o2bo$o3bob2o2b2ob4obo4bo$o3bo3b2o7b2ob2o$o3b2obo2b7o3bobo$o
3bobobobo5bob2obobo$o2bobo2bo2b3obobobobobo$ob2ob2obobo3bo2bobobobo$ob
obobobobo3b3obob2obo$o3bo3bobobobo2bo3b2o$o3bo3bo3bo2b2obobo$o3bo3bobo
bobo4bo2b2o$obo2bo2bo3b2ob3obobo$ob2obob2o2bo5bobobobo$obo3bo2b2ob4obo
bobobo$obob2ob2obobo2bobobobobo$obobob2obobob2ob2obobobo$obo2bo3bo3bo
2bo2bobo$ob4ob4ob2o2b4ob2o$o6bo3bo2b2o$ob5ob2o2b2o2bob5o$obobobo3bo4bo
2bo3bo$obo3b2o2bob2ob2obo2bo!

p10 (a combination of the fourth p10 and the second p5 in the collection):

Code: Select all

x = 24, y = 23, rule = B2/S234
o2bob3o5bo3bobobobo$2obo4bob4obo4bobo$obob3obobo2b3obob2ob2o$obo4bo2bo
bo5bo$2ob5ob2ob6o2bob2o$3bo3b2o3bo6b2obo$3ob2o3bob2ob2ob2o3bo$2b2o2bob
3o3bobo2b4o$bo2b3obo3b3o2bo4bo$obobo4b3o3b2ob3o2bo$2bobob3obo2b2o2bo2b
2o$2o2bobo8b2o2bo2b2o$3bo2bob4o3bob3obobo$2obob4o6bobo3bobo$bobo6b5obo
bobobo$b2ob4ob2o3bobobobobo$7bo2bob3o2bobobobo$b5obobo2bo2bobobobobo$b
o4b5ob4ob3obobo$bob2o7bo3bo4bobo$bobob3ob2o5bob2o2bo$bobobob2o2b3o2bo
2b3o$bobo2bo2bo3bob3o4bo!

p10:

Code: Select all

x = 22, y = 28, rule = B2/S234
7bobobo2bo2b2ob2o$8obob2obobobobo$9bo4bobo3bo$7o2bobob2obo3bo$6b4ob2ob
obo2b2o$2o2bo8bob2o4bo$2b3o2b5obo4b2obo$obo2b2o5b3o2b2o2bo$ob4obob3o7b
2o$o5b2o2bob7o$b4o3bo10b3o$5b4o3b3ob2o$2bob2o2bo3bobobob4o$3o2bob2o3bo
bobobo$2bobobobo3bobob2obobo$2bobobo2b2obobo3bobo$2bobo2b2o3bob2ob2obo
$obobobobo3bo3bo4bo$2b2ob3o2bob2o2bob3o$obo5b3o5bobo2bo$2b6o2bob4o3b3o
$bo6bobobo3bo2bo$b7o2bobob4obobo$9b2o2bo4bob2o$2o2bob2obo2bobob2o$ob2o
bobobob2obobob4o$b2obo2bo2bobobo3bo$2bob3obobob2ob3o2bo!

[TheoSwartz]

Nico (glider_rider) just blew my mind with that new spaceship. What method did you use to find all those?

I will add the new oscs and the reduction to the collection later when I find a few more spare minutes.

EDIT: Here's Alexey's new oscillators stabilized

Code: Select all

x = 53, y = 14, rule = B2/S234
8bo10bo3bo7bo5bo10bo2bo$2bo3bob2o7bob6o5b3o3b2obo7b2ob3o$b5obo8b2obo3b
o7bob3o3b2o5b2obobo$6bobo8bobobobo8bobo2b2o8bo$5o2bo9bobobob2o7bo6bo7b
o3b2o$bo3bobo9bobobo9b5o3b2o6bo3bo$bo5bo9bo3bobo15bo7bo3bo$bo4bobo8bob
ob4o7b7o8bo3bo$6obo8b2o2bo12bo4b3o5bob2obo$bo4bob2o5b2ob2ob3o15bo7bo3b
o$8bo7bo2bo2bo24bo3bo$46b2obobo$47b2ob3o$48bo2bo!

EDIT 2: Added to the collection!

[glider_rider]

Wow, thanks! I used JLS to find them.

I think other spaceships exist, but they seem very hard to find, as most patterns turn into uncleanable wickstretchers. (In particular, at c/2, there are TONS of wickstretchers, but I don't think there's a way to clean up the end, at least at period 2 or 4.)

[Sphenocorona]

Here's a space-filling wave that propagates at 7c/10:

Code: Select all

x = 31, y = 52, rule = B2/S234:T0,52
6bo2bobobo2bobobo2bo$2b3obo2bobobo2bobobo2bo$6bobo2bobobo2bobobo2bo$b
2o2b22o$o28bo$b30o$29bo$2b25o$bo23bo$2b2o2b17o$7bobo2bobobo2bobo$3b3ob
o2bobobo2bobobo$7bo2bobobo2bobobo$7bo2bobobo2bobobo$3b3obo2bobobo2bobo
bo$7bobo2bobobo2bobo$2b2o2b17o$bo23bo$2b25o$29bo$3b28o$2bo26bo$3b2o2b
20o$8bobo2bobobo2bobo2bo$4b3obo2bobobo2bobobo$8bo2bobobo2bobobo$8bo2bo
bobo2bobobo$4b3obo2bobobo2bobobo$8bobo2bobobo2bobo2bo$3b2o2b20o$2bo26b
o$3b28o$29bo$2b25o$bo23bo$2b2o2b17o$7bobo2bobobo2bobo$3b3obo2bobobo2bo
bobo$7bo2bobobo2bobobo$7bo2bobobo2bobobo$3b3obo2bobobo2bobobo$7bobo2bo
bobo2bobo$2b2o2b17o$bo23bo$2b25o$29bo$b30o$o28bo$b2o2b22o$6bobo2bobobo
2bobobo2bo$2b3obo2bobobo2bobobo2bo$6bo2bobobo2bobobo2bo!

It's based on a 5c/7 wickstretcher parasite:

Code: Select all

x = 39, y = 19, rule = B2/S234
7bo$5bo$5bo$7bo29bo$8b31o$37bo$9bo3b23obo$7bo4bo22bobo$2bo4bo5b2o9bo2b
2ob2ob3obo$o8bo9b2o6bo2bo4bobo$o14b3obob6ob2ob5obo$2bo34bo$3b36o$37bo$
4bo$2bo$2bo$4bo!

It would be really cool if either of the above speeds could be stabilized finitely without faster wickstrechers laying down a track...
EDIT: Here's an infinite wave moving at 5c/7 (or 10c14, since it's period 14):

Code: Select all

x = 11, y = 52, rule = B2/S234:T0,52
3bo$3bob3o$3bo$3bo4b2o$3bo6bo$2b8o2$b8o$2bo6bo$2bo4b2o$2bo$2bob3o$2bo$
2bo$2bob3o$2bo$2bo4b2o$2bo6bo$b8o2$8o$bo6bo$bo4b2o$bo$bob3o$bo$bo$bob
3o$bo$bo4b2o$bo6bo$8o2$b8o$2bo6bo$2bo4b2o$2bo$2bob3o$2bo$2bo$2bob3o$2b
o$2bo4b2o$2bo6bo$b8o2$2b8o$3bo6bo$3bo4b2o$3bo$3bob3o$3bo!

25c/39 parasite:

Code: Select all

x = 29, y = 25, rule = B2/S234
6b2o12b2o2$5bo2bo3b2o5bo2bo3b2o$9bo13bo$9bobo2bo8bobo2bo$9bo13bo$9bo
13bo$9bo13bo$9bo13bo$bo3bo3bo4bo3bo4bo$7o2bo3b7o3bo$bo3bo3bo4bo3bo4bo$
9bobobo2bo2bobobo$9bobobobobobobobo$9bobobobobobobobo$9bo2bo2bobo2bo2b
o$9bob2obobobob2obo$9bo2b2obobob2o2bo$9bobobobobobobobo$9bo2bo2bobo2bo
2bo$9bobobobobobobobo$9bo3b3ob3o3bo$9bo13bo$8b17o$9bo13bo!

EDIT 2: Weird p42 2c/3 parasite...

Code: Select all

x = 31, y = 26, rule = B2/S234
b2o25b2o2$o2bo23bo2bo$4bo21bo$4bob2o15b2obo$3b2ob3o13b3ob2o$4bobo17bob
o$6bo17bo$6bo3bo9bo3bo$6bob4o7b4obo$6bo3bo9bo3bo$6bo3bo9bo3bo$6bo3bo9b
o3bo$5b3o2b2o7b2o2b3o$6bo3bo9bo3bo$10bo9bo$10bobo5bobo$10b2o7b2o$10bob
2o3b2obo$10bobo5bobo$10bob7obo$10bo3bobo3bo$10bo3bobo3bo$10bo3bobo3bo$
9b13o$10bo9bo!

The fact that this thing is exactly 2c/3 is basically total serendipity, but it means that it's probably possible to de-parasitize it. (By this I mean to produce a finite support with maximum overall speed equal to or less than the speed of the parasite, thus making it a regular wickstretcher (or maybe even spaceship) component.

[TheoSwartz]

I like the term "parasite" for those growth patterns that require line stabilization! You've found some very interesting speeds too.