Natural puffer in B34j5k/S23:

`x = 63, y = 14, rule = B34j5k/S23`

22bo$20b2ob2o$20b2ob2o$33b2o$2bo18bobo8bo2bo9b2o14b2o$b2o4b2o5bo4b4o

10b2o10b2o14b2o$2o5b3o3bobo2bobo$bobo5bo3bo2bo8b2o23bo$2b2o3b3o3bobo2b

3o2b2o2bo19bob2o$8bo3b2o9b3ob2o16bo5bo$12b2o7b3o2b2o6bo11bo3bo$20bo3b

3o6bobo5bobo3b3o$20bo3b2o7bobo12bo$21b3o10bo6bobo!

(As a side note, the same pattern run in just B34j/S23 produces a MMS breeder.)

EDIT: Another, messier puffer:

`x = 23, y = 99, rule = B34j5k/S23`

9b3o$9bo2bo$8bo2b2o$8b2o4$7b2ob2o$7bo$7b2ob2o$9bo2$5bo2bo$9bo$9bo$5b2o

b2o$7bo4$8bo$6b2ob2o$9bobo$9b2ob2o$8b3o3bo$7b2o2b2o$11bo3bo$9bo2bo2bo$

14bo$13bo$11b3o8$6b2o$6b2o4b2o$3bo7bobo$3bo2b2o4bo$6bo3$6bo$bo4bo$bo$o

4bo$2ob2o3$19bo$18bobo$18bobo$19bo$15bo$15bo$15bobo$15b3o2$13b2obo$5b

3o5b2ob2o2$3bo5bo$3bo5bo$3bo5bo2$5b3o8b2o$13bo2bo$13bo2bo$12b4o$13b4o

2b2o$14b2o2bo2bo$19b2o5$4bo$4bo$4bo2$6b3o13$20b2o$19bo2bo$20b2o!

And a symmetrical one:

`x = 33, y = 24, rule = B34j5k/S23`

2b2o$2b2o6b3o$9b4o$bo7bo2bo2b2o$2o21bo$5b2o14b2obo4bo$o15bo7bo3bob2o$

6o9b4o9bo3bo$2b4o9bo7bo4b2o2bo$5bo8bob3o9b2ob2o$9bo7bo2bo8b2o$8bobob3o

4b3o$8bobob3o4b3o$9bo7bo2bo8b2o$5bo8bob3o9b2ob2o$2b4o9bo7bo4b2o2bo$6o

9b4o9bo3bo$o15bo7bo3bob2o$5b2o14b2obo4bo$2o21bo$bo7bo2bo2b2o$9b4o$2b2o

6b3o$2b2o!

EDIT 2: A specific combination of the two basic blockpuffers gives a bonus beehive:

`x = 41, y = 98, rule = B34j5k/S23`

23b2o$6b2o15b2o$6b2o2$24bo$23bobo$23bobo$7bobo14bo$4bo3bo3bo2$4bo3bo3b

o$6bobo$7b5o$7b2obo2$28b6o2bo2bo$12b2o9b2o2bo6b3o3bo$6b2ob2ob2o9b2o2bo

7b2o$7b6o15b3ob2o$8b4o22b2obo$24bo10b5o$23bobo10b3o$23bobo$11b3o10bo$

10b2o2bo$8b2o4bo$8b2ob2o2bo$8bo3b4o$9bobo2b2o$10bo2$32b3o$20b3o7b2ob2o

$19bo2bo6bo2bo2bo$19bo9bo2b3o$20b2o8b5o$24bo$6b3o14bobo$6bobo14bobo$6b

o2bo14bo$8b2o6$25bo$24b3o$24b2obo$8bo7b2o9b2o$7bo7bo2bo7b2o$10b3ob2o2b

o$11bob2ob2o$9bo4bo8b2o$7b2obo$6bo6bo12b2o$2o4b2obobo14b3o$2o3bo5bo10b

o4bobo$5bob4o13b2o2b2o$6b4o10bo$7b2o11bo$18bo2bo$2bo2bo11bo2b2o$5bo9b

2o3b2o$15b2obob4o$2bo12bo2bo2bob2o$7bo8bo4b3o$4bo11bo2bo2bo$5bo13b2o$

7bo10bo$19b2o4$6bo$6b3o$6bo2bo8bob2o$8b2o7b2o3bo$15bo5b2o$15bobo3b2o$

15b3o2b3o$5b3o11bob2o$4b2o2bo10bo2b2o$2b2obo14bo$2b2obo$3bo4bo$3bo2bo$

4b3o$18b3o$17b2ob2o$17b2obo4$19b2o$16b2o2bo$17b3o$18bo!

The puffers can also crawl on each other's trails:

`x = 38, y = 276, rule = B34j5k/S23`

11b3o$11bo2bo$9bo4bo$12bob2o$12bob2o$9bo2b2o$10b3o4$8b2o$7bo$7bo3bo$8b

o3bo$8b3o$9bo4bo$8b2o5bo$9b2obobo$10b4o$11bo7$14bo$6b2o5bobo$5bo2bo4bo

bo$6b2o6bo3$15bo$15bo$7b2o$6b2obo$bobo3bob2o$o2bo3bob2o$o2bo3bo2bo$b2o

5bob2o$10bobo$10bo3bo$10bo3bo$11bo2b2o$14b2o$14bo10$13b2o$13b2o15$13b

2o$13b2o15$13b2o$13b2o15$13b2o$13b2o14$19b3o$13b2o3bo2bo$13b2o3b2o2bo$

21b2o4$19b2ob2o$23bo$19b2ob2o$21bo5$21bo2b2o$18bob2o$13b2o2bob2o4bo$

13b2ob2obo5bo$19b2o4bo$19b4obo$19b3obo10$18b3o$17bo3bo$16bo5bo$22bo$

17b3o2bo$19b2o2$21b3o$20bo3bo$20bo3bo$20bo3bo$21b3o5$23b2o$23bobo$23b

3o$17b2o6b2o$17bobo2bob2o$17b3o3b2o$18b2o3bo2$25bo$18b3o4bo$19bo5bo8$

27b2o$25bobobo$25b3obo$25b4o2$22b2o$21b2obo$24bo$23b3o8$28b2o$25bo2b2o

$21b2o2bo$20bo5bo$19b2o2bobo$20b2o3bo$21b3o10$25b3o$24b2obo$22b2obo$

25bobo$20b2obobo2bo$21bo$21bo4bo$22b2o2bo$27b3o5$21b3ob2o$18b2ob6o$18b

2o3b2o4b3o$24b2o2bo3bo$28bo3bo$20b4o4bo3bo$20b4o5b3o$22bo5$24b3o$24bob

o$18bobo9bobo$18b2o11b2o3$24bobo$24b3o7$35bo$32b5o$34bo2bo$35b2o$34b2o

$33bo7$30b2o$30b2o7$18b2o11b2o$18b2o11b2o!

EDIT 3: A natural MMS breeder (sufficiently rare that, while it slows apgsearch down, it does not make the rule unapgsearchable):

`x = 16, y = 16, rule = B34j5k/S23`

7obobobobo$6bob2o2b2o$obo2b2obob4o$3b4o2b5o$ob2o3b5o2bo$2o2b3o2bobo$3b

o2b4obobo$2b2o2bob2o2b3o$b3o2b2o5bobo$o3bo7bo$bo2bob5o2bobo$4bo2bobo2b

4o$bo3bob5ob3o$ob5o2bo3b2o$b8obo3b2o$o4b4obo3bo!

Also, several other distinct natural, high-period puffers:

`x = 29, y = 111, rule = B34j5k/S23`

14b2ob2o$13bobob2o$14bo4$14bo$13bobo$14b2o$3b2o$3b2o5bo$9bobo8b2o$9bob

o8b2o$10bo$3bo12bo$3bo11bobo$3bo11bobo$16bo8$24b2o$23bo2bo$24b2o8$15b

3o$15b3o$14bo3bo$9bo4b2ob2o$8bobo$8bobo$9bo14b2o$23bo2bo$24b2o$4b3o8b

2o$4b3o7bobo$2b2o9b2o2bo2bo5b2o$2b2o10b2o5bo3bo2bo$2b2o11bo4bo5b2o$10b

2o4b4o$10b2o5bo$10b2o$7b3o$7b3o4bo$14bo$14bo2$10b3o3b3o2$14bo$14bo$14b

o$2b2o$2b2o4$10bo$2b3o4b3o$2bobo3b5o$2o2bo2b2o$o5b3o2b2o$3o5b4o$9b2o3$

5b2o$4b2o$5bo$2bob2obo$bo4bobo$6bobo$2bob2obo3$17b2o$17b2o$2o8b3o$2o8b

3o2$5bo12bo$4bobo11bo$4bobo4b2o5bo$5bo5b2o$11b3o$9b2obo$8bo3bo$8bo3bo$

9b3o4b2o$3b2o12b2o$3b3o10b3o$4bo12bo3$6b2o6b2o$5b2o2bo2bo2b2o$4b2o3bo

2bo3b2o$4b4obo2bob4o$5bo2b2o2b2o2bo$6b3o4b3o$7bo6bo!

`x = 57, y = 216, rule = B34j5k/S23`

4b3o28bo$35bo$35bo2$31b3o3b3o2$21b2o12bo$21bobo11bo$22bo12bo2$39b2o$

35bo3b2o$35bo$35bo2$31b3o3b3o$18b2o$17bo2bo14bo13b2o$18b2o15bo12bo2bo$

7bo2bo24bo13b2o$7bo2bo$3o7bo$9b2o24bo$4b2o3b2o12b2o9bobo$3bo4bobo12b2o

10bo$4b5obo$4b4ob3ob3o$6b2ob2o$7b3o$8bo2$26b3o2$24bo$24bo$24bo3$9bo$9b

o$9bo$4b3o2$8b2o18b2o$8b2o18b2o2$b2o$b2o$35bo$35bo$35bo2$4b2o25b3o3b3o

$3bo2bo$3bo2bo14b2o12bo$4b2o15bobo11bo$22bo12bo8$4b3o5$32b2o$32b2o5$9b

o44b2o$8bobo42bo2bo$9b2o43b2o$22b2o$22b2o2$35b2o9b2o$34bo2bo7bobo$12b

2o9bo11b2o3b2o4bo$4b2o6b2o9bo16b2o$3bo2bo16bo$3bo2bo$4b2o11bo$13b2obob

o$13b2obobo$17bo$28b2o$28b2o4$4b3o28bo$35bo$35bo2$31b3o3b3o2$21b2o12bo

$21bobo11bo$22bo12bo7$20b2o$20b2o4$4b2o$3bo2bo16bo2b2o$3bo2bo11bob2ob

2o$4b2o11bo3bo2bo18b3o$21bo2b2o16bo$17bo3bob2o7b2o7bo$20bo12bo7bo2b2o$

34b2o5b2o2b3o$35b2o8b3o$36b2o7b2o2$24b3o6bo$11b3o11b3o5b2o3b2o$10bo3bo

11bobo3b2o3b3o$10bo4bo11b2o3bo5b2o$11b2o2bo$13b2o3$30b2o$30b2o$2b2o$2b

o$13b3o12b2o$28b2o2$b2o$b2o$35bo$35bo$35bo2$4b2o25b3o3b3o$3bo2bo$3bo2b

o14b2o12bo$4b2o15bobo11bo$22bo12bo8$8bo$7b3o15b2o$7bo2bo13bo2bo$10b2o

13b2o$9b2o$23bo$21bo2bo$5b3o13bobo9bo$4bo3bo13b2o7bo2bo$4bo3bo21b2ob2o

$4bo3bo14b3o5bo$5b3o24b2o2$20b2o7bo$19b3o6bobo$15b2o2b2o7bo2bo$15b2o2b

ob2o$8b2o10bobo$8b3o8bo$2b2o4b3o9b2ob3o$b2o5b2o13bo2bo$2b3obob2o12b2o$

3b4o5bo11b3o$5bo4bo2bo$10bo2bo$10b2ob2o$9bobo12b3o$9b2ob2obo8bo2bo$9b

4o11bob2o$5b2o4b2o4b3o8b2o$5b2o6bo3b2obo6b3o$5b2o6bo4bob2obo4bo$12bo6b

ob2obo$22bobo$23bo3$23bo$23b3o$23bo2bo$25b2o$9b3o$10b2o$7bo2b2o$7b2o

13b3o$21b2o2bo$19b2obo$9b2o8b2obo$9bob2o7bo4bo$9bo3bo6bo2bo$10bo10b3o

3$9b2o2bo$9bo2bo$10b3o!

`x = 47, y = 147, rule = B34j5k/S23`

17b3o$17bo2bo7bo$16bo3bo6b3o$16b3o2bo4bo2b2o$17b4o5b3obo$29b2o3$21bo$

22bo7b2o$18bo2bo10bo$18bo2bo6b4o$19bo8b3o3$19b2ob2o$19b2o3bo6b3o$17bo

4bobo5b4o$15b3o5bo5b3o$27b2ob4o$21bo5bo2bo3bo$19b2o6bob3obo$19bo8b3o2b

o$29b3o$30b2o$17b2o$17b2o9bo$27bobo$21bo5bobo$20b3o5bo$19b2o2bo$18b2ob

3o$18bo2b2o2$21bo$20b2ob2o$21bob2o$21bo3bo$23b2o$20b2ob2o$21b2o$21bo$

21bo9$37b3o$35bobo$34bob2o$33bo2bo$33b2o$16bo17b2o$15bobo15bo$14bo3bo

12b2o5bo$15bobo8b3obo6b2ob2o3b2o$16bo9bo2b2o6bo4bo2b2o$27b3o10bobo2bo$

28bo12bo$15b3o$15b4o14b2o$15b5o12bobo$12b3o4bo12b2o$13b2ob3o11b3o2b2o$

14bo15b4o2b2o$30b2ob2obob2o$36bo$35b2ob2o$35b3o2$22bo$21bobo$20bo3bo$

20bo2bo4b2o$20b3o5b2o$7b3o10$4b2o$4b2o3$10b2o$9bo2bo$3o7b2o2$29bo5bo$

29bo5bo$3o26bo5bo$9b3o$9bo2bo18b3o$8bo3bo$8bo3bo9bo$8bobob2o7bobo10bo$

13bo6bo3bo9bo$20bo3bo9bo$8bo11bobo2bo$9bo15b2o3b3o3b3o$10bo9b2obob2o$

23b3o8bo$11b2o7b3obo9bo$11b3o20bo$4b3o5bo$5b2o4bo3$27bo$19b2o5bo2bo$

16b2ob2o$16bo2bo6bo3bo$15bo2bo11bo$16bobo10b2o$17bo7b3o$21bo$20b3obo2b

o$19b2obo3bo$18bo2bo$18bo19b2o$25bo3bo7bo2bo$19bo4bo3bobo7b2o$21b3o4bo

bo$29bo5$15bo$14bobo$14b2o5$20b3o$25b2o$25b2o!

EDIT 4: Six-cell (hexomino!) infinite growth:

`x = 4, y = 3, rule = B34j5k/S23`

3bo$4o$o!