pcallahan wrote:This *should* be a complete set of collisions with still life constellations of that size that produce a single, clean HWSS. Corrections welcome. ...

Two of the above collisions provide slightly cheaper ways to edge-shoot a HWSS, which reduce the incremental cost of adding an HWSS to one existing flotilla from 12 gliders to 11 or 10. My original 12-glider block+tub construction also works for the two other difficult cases (one of which is the opposite side of the same flotilla); unfortunately, these two new collisions don't work in the other two cases. All other cases that involve edge-shooting an additional HWSS can be accomplished by one of the basic 4-glider methods, or a 9-glider one using a carrier. Unfortunately, the carrier one makes a spaceship that goes through two complete cycles with different backs before forming an true HWSS, making it unsuitable in many cases where the backs of two spaceships rub each other closely.

The 12 could be reduced to 11 if there exists a 3-glider way to make the tub+block constellation; the 10 could be reduced if there is a cheaper way to make the down boat on carrier, or if that plus the loaf or five other similar still-lifes that invoke the same mechanism could be made more cheaply. The 11 could be reduced to 9 if the barge could be made from 3 gliders.

Code: Select all

```
x = 201, y = 117, rule = B3/S23
43bobb3o$44bobo$42b3obbo14boo18boo18boo18boo18boo18boo$63bo19bo19bo19b
o19bo19bo$61bo19bo19bo19bo19bo19bo$37bobb3o18boo18boo18boo18boo18boo
18boo$38bobo110bo$36b3obbo35bo23boo10bo7boo13bo4boo9boobbo4boo$78boo
20bobo11bo5bobo12bobobbobo8boobbobobbobo$77boo22bo10b3oboo3bo13bobbobb
o13bobbobbo$82boo32bobo17boo18boo$81bobobo30bo51bo22b3o4bo$83bobobo79b
3o21bobbobb3o$85boo79boobo21bo4boobo$166b3o22bo3b4o$166b3o22bo3b4o$
166b3o22bo4b3o$167boo23bobobboo$$40bo$35bo3bo15boo18boo$36boob3o12bobb
o16bobbo78bo$35boo17bobbo16bobbo3bo75boo$55boo18boobboo38bobo34boo$80b
oo38boo$120bo$122bo15bo19bo$97bo19bo3bo15bobo17bobo$96bobo17bobobb3o
12bobo17bobo$bbo94bo19bo19bo19bo$bo$b3o52bo19bo19bo19bo19bo19bo$22boo
9bo8boo11bobo4boo11bobo4boo11bobo4boo11bobo4boo11bobo4boo11bobo4boo$bo
19bobo7bobo7bobo12bobobbobo12bobobbobo12bobobbobo12bobobbobo12bobobbob
o12bobobbobo$boo19bo9boo8bo14boo3bo14boo3bo14boo3bo14boo3bo14boo3bo14b
oo3bo$obo32b3o$37bo$30bo5bo$30boo$29bobo$$168bo22b3o4bo$167b3o21bobbo
bb3o$166boobo21bo4boobo$166b3o22bo3b4o$166b3o22bo3b4o$166b3o22bo4b3o$
167boo23bobobboo9$37bobo57bobo57bobo$38boo58boo58boo$38bo59bo59bo$$42b
o59bo59bo$42bobo57bobo57bobo$37boo3boo53boo3boo53boo3boo$37boo58boo58b
oo$32bobo57bobo57bobo$33boo58boo58boo$33bo8bo50bo8bo50bo8bo$41bobo57bo
bo57bobo$35bo6bo52bo6bo52bo6bo$36boo9b3o27b3o16boo58boo$35boo9bobbo26b
obbo15boo11bo29bo16boo$49bo21b3o5bo27b3o21b3o3b3o28bo22b3o4bo$32bo6bo
5bo3bo21bobbo4bo12bo6bo7boboo20bobbobboboo11bo6bo7b3o21bobbobb3o$32boo
5boo8bo21bo7bo12boo5boo7b3o20bo6b3o11boo5boo5boobo21bo4boobo$31bobo4bo
bo5bobo22bo4bobo12bobo4bobo7b3o20bo6b3o10bobo4bobo5b3o22bo3b4o$71bo3bo
32b3o20bo6b3o25b3o22bo3b4o$71bo36boo21bo6boo26b3o22bo4b3o$34b3o35bobo
19b3o35bobo19b3o10boo23bobobboo$36bo59bo59bo$35bo59bo59bo20$160bobo$
161boo5bo29bo$161bo5b3o21b3o3b3o$167boboo20bobbobboboo$155bo5boo5b3o
20bo6b3o$153bobo6bo5b3o20bo3bobb3o$154boo4bo7boo21bo6boo$160boo29bo3bo
$192bobo$157boo$156bobo3boo$158bobbobo$163bo3$151b3o$153bo$152bo!
```

There are a lot of other LWSS and MWSS syntheses.

Edge-shooting a LWSS or MWSS is usually easy (3-4 gliders), but there are a few cases where adding a MWSS to an existing collision is more complicated, requiring an 8-glider mechanism, so it's possible that some natural methods might be cheaper.

Code: Select all

```
x = 160, y = 21, rule = B3/S23
9bo49bo$9bobo47bobo$9boo48boo$119bo$119bobo$3o11bobo13b3o31bobo52boo$o
bbo3boo5boo9bo4bobbo23boo5boo9bo$o6bobo5bo7boo5bo6bo19bobo5bo7boo12bo$
o3bo3bobo13boo4bo5b3o11b3o5bobo13boo4b3o3b3o16bo4b3o11bobo18bo4b3o$o3b
o4bo20bo5boboo10bobbo5bo20bobbobboboo14b3o3bobbo3boo5boo9bo8b3o3bobbo$
o15bo13bo6b3o10bo15bo13bo6b3o13boobo3bo6bobo5bo7boo8boobo3bo6bo$bobo
11bo15bo5b3o10bo3bo10bo14bo3bobb3o13b3o4bo3bo3bobo13boo7b3o4bo5b3o$11b
oobb3o19boo11bo3bo6boobb3o12bo6boo15boo4bo3bo4bo24boo4bo5boboo$11bobo
36bo10bobo16bo3bo24boo15bo22boo6b3o$11bo39bobo7bo19bobo25boo14bo23boo
6b3o$110bobo8boobb3o22boo5boo$121bobo$110boo9bo$$149bo$149bo!
```