Here is a variant of the p3 bouncer mechanism above that extends downward by the minimum length:
Code: Select all
x = 39, y = 34, rule = B3/S23
obo$b2o33b3o$bo36bo$37bo3$6bobo$7b2o21b3o$7bo24bo$31bo3$12bobo$13b2o9b
3o$13bo12bo$25bo$29b2o$28bo2bo$12bo5bobo6bobobo$11bobo5b2o6bo2bo$11bob
o5bo$9b2o2bob2o10bobo$10bobo2b2o2b2o3b2obo$4bo5bob2o5bobobo3bob3o$4b3o
2b2obo7bo3bo2b3o2bo$2b2o3bo4b2o12bo2bob2o$3bo2bo5bob2o2bo5bo2b2obo$3bo
bob3obo5b2o3b2o3bobob2o$2b2obo3bobobo6bo3b2obobobo$3bobob2o2b4o3bobobo
bobob2o2bo$3bo4bo3b3ob3o5bobo4b2o$4bob5o4bo6bobobo$2bobob4o6bob3o3bob
2o$2b2o12bo5b2o!
I thought perhaps that this variant
might be useful in shrinking some guns slightly, but I'm not really sure. After minimizing for downward extension length, I then minimized the length the pattern extends both left and right (luckily simultaneously). After that I minimized the overall height and the minimum population (again simultaneously).
I tried a few generous LLS searches for different boat restoration reactions that extend downward by fewer cells, but all returned unsatisfiable. I'm running one more extremely generous search, but it will probably take several more hours to complete.
Edit: here is a single-"spark" p4 that is almost certainly larger than necessary:
Code: Select all
x = 48, y = 31, rule = B3/S23
obo$b2o33b3o$bo36bo3b2o$37bo4bo$44bo2bo$43b5o$6bobo$7b2o21b3o5bo2b3obo
$7bo24bo4bobo3b2obo$31bo6bo2b2o3bo$35b4o4b2ob2o$34bo3b2ob2o2bo$12bobo
19bo2b3o3bobo$13b2o9b3o6b2obo7bo$13bo12bo4bo4b2ob5o$25bo5bobo$28b2o2bo
2bob5o$28b2ob2o2bobo3bo$18bobo6b2obobo2bo4bo$19b2o7bo7bo3b2o$19bo7b3ob
5o5bo$15b2o9bo2bo10bo$15b2o2b2o3bo4b9o2b2o$19bobo2b2ob4o6bo4bo$20bo4bo
2bobo3b3o2b2obo$25b2ob2ob2obob4o2b2o$17b2o9b2o9b2o$18bo12b5o3bo2b2obo$
15b3o9bob2o5b2o3bo4bo$15bo11bobo3b4o2bobo3b2o$26b2o5bobo2b2ob2o!
The p4 oscillator extends two rows lower than the tail of the fishhook eater in the bouncer mechanism (when considered over its full period). There may be a solution that extends only one row lower than the eater tail, but a fairly generous search for a solution that does not extend below the eater tail returned unsatisfiable.
Edit 2: I tried an even more generous LLS search for a p4 oscillator that extends only one row lower than the tail of the fishhook eater, but it returned unsatisfiable after 2 days. I think it's quite unlikely that a solution with downward extension length less than the example shown above exists.
I also tried a very generous search for a p2 bouncer that allowed a completely alternate catalyst in place of the boat, but it returned unsatisfiable. I'm now running an even more generous search that also allows the block to be replaced with a p2 catalyst. I expect this search will also return unsatisfiable.
