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.
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x = 201, y = 117, rule = B3/S23
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.
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x = 160, y = 21, rule = B3/S23