User:HotdogPi/Block factory LCM gun

Unlike User:hotdogPi/3o2$o!, this is intended to go to mainspace.

Some least common multiple guns use a reaction where a block factory with a specific predecessor (highlighted below) is sparked by a dot. If the dot appears in the generation that that specific predecessor appears, it gets turned into a glider, while if it is sparked after that generation, the block dies cleanly.

Gallery

x = 42, y = 32, rule = LifeSuper 25.2A4.2A$25.A.A2.A.A$27.A2.A$26.A4.A$26.2A2.2A$28.2A$36.A2$34.A.3A$ 36.2A.A$12.2A10.A.A9.A.2A$13.A10.A.A10.3A.A$13.A.2A$14.A11.3A10.A$3.A 5.A8.C5.A2.A$2.A.A4.3A15.A$2.A.A7.A3.C.C7.A.2A$2A2.2A5.A5.2C3.A2.3A. 2A$.A.A3.A3.A3.E7.A4.A$A2.3A.A$A.A8.A4.A$.A.2A.A4.A4.A15.2A$3.A2.A2.A .A3.A16.A$3.A2.A2.A2.A2.A17.3A$.A.2A.A6.A4.A16.A$A.A14.A2.A$A2.3A.A5. A3.A2.A$.A.A3.A4.A.A4.A$2A2.2A7.A$2.A.A$2.A.A$3.A! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ GPS 30 THUMBSIZE 2 ]] On the left is a p18 century shuttle that provides a corner dot spark in yellow, while on the right is a p80 R-pentomino hassler that provides the block, with the specific predecessor needed highlighted in light pink. The LCM of 18 and 80 is 720, so this is a period-720 glider gun. The p166 R-pentomino hassler can also turn an R-pentomino into a block in the same way. (click above to open LifeViewer)

x = 36, y = 34, rule = LifeSuper 28.A2.A$27.A$26.A5.A$25.2A.A.A.3A$26.A3.2A3.A$26.A2.A.A.A.A2$25.A.A.A .A2.A$25.A3.2A3.A$26.3A.A.A.2A$28.A5.A$33.A$29.E2.A$25.C.C$25.C2.C$ 11.2A14.2C$.2A8.2A6.2A$2.A15.A.A$.A$.2A17.A3.A$3.A5.3A6.3A.A.A$.3A16. 2A.2A$A20.2A$2A2$15.3A10.2A$17.A11.A$10.A4.3A8.3A$8.A.A15.A$4.2A.2A 18.2A$4.2A2.2A18.A$27.A$17.2A8.2A$17.2A! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ GPS 30 THUMBSIZE 2 ]] The dot spark is provided by a period-7 meatball, while the block is provided by a p192 version of 51P384. The block predecessor is slightly different; both versions work. LCM(7,192)=1344, so this is a period-1344 glider gun. (click above to open LifeViewer)