Life has been proven omniperiodic. What next?

[Bullet51]

Synthesize the still life random.rle.

Random .Rle may be tricky due to the fact that, while being a pseudo-still life, is also bery unstable. it would have to be incrementally synthesized in layers so that it doesn't collapse, or synthesized all at once. It may be able to be synthesized but it's like tring to synthesize sir robin.

Code: Select all

x = 98, y = 98, rule = B3/S23
2obob2o3b2ob2o2bob2o3b2o3b2o2bo5bo8b2o2b2obob2ob2o3b2ob2o3b2o5b2ob2obo
3b2ob2obo$ob2obo5bobo2bob2o3bo2bobobo2b3o3b3o5bo2bo2bob2obobo4b2obobo
3bo2b2o2bobob2o2bobobob2o$6bo4bo2bobo4bo2bobobo7bo5bobo2bo2bobo5bobobo
6bo3bo3bob2o2bo3b3obobo$b6o5b2obobob2ob2obo2bo4b2obo2b4ob3ob3obob2ob2o
bob6obobo2b3o4b2ob2o4bobob3o$o12bo3b2obobo2bobob2o2bob2obo8bo3b2o2bobo
2bo6bobob2obo2b3o4bob2o2bobo3bo$b2ob2obobobobo2bo3bobo2bobo2bo7bob2ob
4o2bo3bobobobo2b3obo2bo4bo2bo2b4o4bobo2b2o$2bobob2ob2obo3bo3bobob2o2bo
2b6ob2obobo3b3ob2o2bobob3o2bob2obob3o4b2o3bob2obob2obo$2bobo7bobobob2o
3bo2b2o8bo7b3o3bo2b3obo4bobo4b2o3b4o2bo3bobobo4bo$b2obob6ob2o2bo6b2o2b
6o2bob6o4bo2bo5b4obobob2o4bo6bo2bobobobob3ob2obo$o3bobo4bo3bobo8bobo5b
obobo5b4ob2ob4o4bobobobob5ob4obob2o2bobobo4bob2o$b4o2b2o3bobo2bobo4b2o
2bobobobobo3bo2bo3bo2bo5b3o3bo2bo7bo3bobo3bobobo3b3o$5bobo3b2obobob2o
5bobob3obobob3obo2bo3bobob4o2b2o2b2obob4o2bob2o2bo3bobo2b3o3b4o$b5o2bo
5bobo7bo2bo5bobo2bo2bob2o2b2obobo3bo8bobo3bobo2bobob2obo2b2o2bobo4bo$o
5bobo2b4ob6o2bobo2b3obob2o3b2o2bobo2bobo2bobob6obobo2b2ob2obobo2bob3o
2bo3b3o$4o2bobobo11bobo2b2obo2bo3b3o2bobo2bo3bob2ob2o5bobob2o5bo2bob2o
5bob4o3bo$4bobobobo2b8obob3o5bob3o2bob2ob3o3bobo6b3obobo3b4obo3bo2b6o
5bob2o$2o2bobobobobo3bo3bobo4b2obob2o3bobo3bo3b4o3b5o2bobo2b3o3bo2b3o
2bo7b5obo$obobo2bobobob2o3bobo2b2obo2b2o4bobob4o2bo5b4o3bobo2bo5b2o2b
2o3b2ob7o6bo$2bo2bobobobobob4o2bobo3bo3b4obobo4b3ob2obo5bobobobo3b2obo
b2o2b2o2bobo7bob2ob2o$bobobobobobobobo3bobobob2ob3o5bo3b2o4bobob2o2b3o
bobobobo2bobo3bobob2o3b2ob6obo2bo$2bo2bo2bo2bobobo2b2obob2obo4b4ob4o2b
3o3bo4bo4bobobob2obobo3bo2bo6bobo8bo$3b3o5bobobobo3bo4bob2o4bo6bo3b4ob
3ob5obo2bo3bob3obo3bobo3bo4b6o$6b5obo2bobo3bob2obobob3o2bob3obobo6bo2b
o6bo3b2obo4bo3b2ob3ob6o$b4o5bobob2obob3obo2bo6b2o3bobobob5o2bobo2b2obo
b3o2bo2b2o4bo6bo7bob2o$bo2bob2o4bobo3bo5bobo2b4o2b2o4bo2bo3bob2obobobo
bobo2bo2b2ob2o3bob4obob5ob2obo2b2o$2bobobo5bo2b2obo2b2obobobo3bobo2b3o
bobo2bobo2bobobobobobobo9bobobo3bobobo2bo7b2o$3b2o2bo5bobob2obo2b2obob
o2bo2bobo2bobobob2obobo2bobob2obo2b11obobobo3bo4bob2obo$o4b3o4b2obo4b
2o4bobobo3bo2bobobobo2bo2b2ob2obo4bobo4bo7bobob5o2bobobob6o$5o10bob2o
3b4obobob3ob2obobobobobo4bo3bob2o2bo2bo4b2ob4o2bo5b3obobo6bo$4bob2o4b
4obob3o3bobobo5bo2bobobobob2o3bo3bobo4b7ob2o4bobo2b3o3bobob4o$3obo2bo
3bo5bo4b3o2bobob3obob2obobobobo2bob2ob2o2b4o11b3o2bobo3b3o2bo5bo$o2bob
2o4bob5ob2o3bobo2bobo2b2obo2bobobo2b3obo4b2o4bob2o2b5o3b2o2b3o4b2ob5o$
bobo5b2obo6bob3o2bobo3bo5b2o2bobo6bob2o3b2o2bobo2bo2bo2bobo2b2o3b4o3bo
$2obob2o2bo2bo2b3o8bob3ob6o2b3o2b4ob2obob3o2bobo2b3o5bob3o2b3o3bob2o2b
o$3bobobobob2obo3b9o4bo5bobo3bobo2bobo8b2ob3o9bo3bobo2b2obo2bob2o2bo$
3bobobobo4b4o9b3obobobobo2bo2bo2bobo2b8o6b5o6b3o2bobobobobo3b3o$b2obo
2bobob2o5bo2b2o2bo3bobob2obobobo3b2obobobo7bob4o5bob4o3bobo3bobo2bobo$
bo2bob2ob2ob2ob2obo2bo2bob3o2bo4bobob2o3bobobo2b8obo3b2o2b2obo3bobo2bo
3bob2obobob2o$2bobobo9bob2obob2o4b2ob4obobo2bo2bobobo12b2o3bo4bo2b2ob
2ob2ob2o4bobobo$b2obo2b5ob2obo2bobo4b2o2bobo4bobobo2b2obob4ob4ob2obob
2ob5o3bo2bo2bo5b3o2bobo$2bobo7b2o2b3o2b4obo3bobo2b3obob3o3bo4bobo2bobo
2bo2bo10b2o2bo2b5o2b3ob2o$2bobobobobo4bo3b2o3bobo2b2obobo3bobo3b2o2b4o
3bobo2bobobo2b7o7b3o5bo4bo$b2o2bob2ob4obo2bo2b2obobobo2bobob2obo3bobo
7b4ob4o2bob2obo4b8o5b2obo2b2o2bo$o2bobo8b2obobobo2bobobobo2bobo2b5o2b
6obo8bobo2bo3bo9bob2o2bo2bobo2b2obo$b2obobob5o4bobobo2bobobo2b3obobo5b
obo4bo3b2ob2o2bob2obo2b10obobobobo2bob2obo2bo$4bobobo4b4o2bob2obobob3o
5bobob2obo2b2o3b3obobobobo2bobobo10b2obobob2obo2bobobo$b2obobo2b3o5b2o
5bobo4bob2obob2obobo4bo6bo3bobobo2bobo2b3ob3o4bobo4bobo2bob2o$o2bo2b3o
3b4obo6bobob4obo2bo5bob4o2bob2obobo2bo2bobo2bobo2bobo2b3obo2b4obo3bo$b
o2b2o3b3o3bobobob2obobobo5b3ob3obobo3b4obobob3o3bobobo2b2o3bobo2bob2ob
o3bo3b2ob2o$2b2o3b2o4bobobob2obobobo2b5o3bo2bobo2b3o5bobo4b4obobobo5bo
b2obo2bobobo6bob2o$5b2o2b6obobo3bobob2obo4b2obobo2b3o3b6obob2obo4bobob
5obo2bob2obobob2o5bo$2b3o2bobo6bo2bob2obo4bob2o3b2obobo3b2o9bobo2b4o2b
2o4bob3o5bobo3bo3b2o$bo3bobobob4ob3o3bobob2obobob2o3b2obob2o2b5ob3o3b
2o3bobo3b2obo4b5obob3obo3bob2o$bobo2bo2bobo2b2o3b2o3bob2ob2o2bob2o4b2o
bobo4bobo2b3o2bobo2bob2obobob2obo3bobo3bo2bo2bob2o$2ob2obobo3bo4bo3b4o
8bobob4o3bo2b2o2bobobo3bobobobobo4bo2bo2bobo4b2obo3bobo$6bob5ob2ob4o4b
9obobo2bob2obobobobobo2bobo2bobobobob2obobo2b2ob4obobob3o2bo$2ob2o2bo
6bobo5b3o4bo4bo3bobobo2bo3bobob4obobobo2b2obobo2bob2o6bobobo4b2ob2o$bo
bo4b6o2bob4o4bo4b2obob3obo2b3obobobo5bo2bobobo3bo2bobo2bob4obobob5o2bo
2bo$o2bobo7bobobo5bob2o5bo2bo4b3o3bobo3b5o3bobo2bobob3o2bobobo2bobobo
5bo2bobo$2obob7o3bo3b5obo6bo3b4o3b2obobob2o5b3o2b4obo4b2o2bo2bobobobob
2o2bob2ob2o$bob2o7b3ob3obo5bo3bob4o3bobo2bobobobo2b3o4b2o6b4o4b2obobob
obobobobobo$o5bob2o2bo3bo5b4obobobo4b2obob3o2bobo3b2o2b3obo2bob3o4b4o
2bobob2obo3bobobo$4ob2obo7bob4obo3bobo3b2obobo5b2obobo6bo2bo2b2obo2b3o
bo3bobobo4b4o3bob2o$3bobo2bo2bo3b2obo8bob4obobobob4o3bob4obobobo4bobob
o2bobo2b2obo2b4o4b2obobo$2obo2bobobobobo6b2o2b2obo3bobobobobo3bob2o5b
2obob2o3bo2bob2o2bobo2bobobo4bo2bob2obo$obobobobobobob2ob5o4bobob2o3bo
2bo2bob2obo2b3o3bobo3b2obobobo3bobo2bobobob3obobo4b2o$2bobobobobobo2bo
bo5bo2bo2bo2b3o3b3o3bo3b2o2b2obobob2obobobobo2b2o2b3obo2bo2bobob4obo2b
o$2bobobobobob2obo2b6o3bobobo9b2obo6bo2bobobobobobobobobo2b2o4b2obobo
2bo4bobob2o$b2ob2obo2bobo2b3o2bo7bo2b4o2bobo2bobob4obobo2bobobobobob2o
bobo4bobo3bobobo2b2o3bobo$bo5bobo2bobo3bo3b2o2bobobo3b4ob3o2bobo2bobob
3o2bo2bo2bo4bob6obob2obobob2o2b4o2bo$2b6ob2obo2bobo3b2o2bobobob2o5bo5b
obobo2b2o3b2obobobo2b3obo7bobo2bobo3b2o4b3o$11bob3ob2o5b2obo2bo2b4obob
obobo2bob2o3bo4bobo2b2o2bobob5obo2bobo2bobo3bobo$4ob5obo13bob2obobo4bo
b2ob2obobo2bob2ob4obob2o2b2o2bobo3bo2bobobob2ob4ob2ob2o$o2bobo3bo2b4ob
2o6bo2bobob4obo7bob2obo2bo6bo2bobo2b2o2bobo2bobobobo7bo3bobo$5bobo2b2o
3bobo2bo2bob2obo2bo4bo2b2ob4obo2bobo2b3obobobo2bo5bob4obobobob5o3b2o$
4bobob2o2bo2bo2bob4o2bo2bobob2o5bobo4bobobob2o2bobobob2obob5o5bo2bobob
o4b3o2b2o$3bo2bobo2bobob2obo5bo3b2ob2o2b5o2bob2obobobo3bobobob2o3bobo
5b3obobo2bo3b2obo2bo2bo$3b4obob2obo4b5o2b3o6bo4bobobo2bobobo2b3obo2bo
3b3obo2b3o3b2obobob4o2bobob2o$o7bo2bobob3o5b2o4b6ob2obobobobo2bo2b2o3b
ob2o2b2o4bobo4bo3b2obo6bo2bo$4ob4o2bobobo2b5o3b3obo5b2obo2b2obobobobo
2bo2bo2b2o2b4o2b5ob2o3bobob3ob2obo$3bobo3b2o2bo2bo6b3o6b3o4bo4bobo2bo
2bob2obobo2bo5b2o6bob3o2bobo2bo3b2o$2obo3bo2bobob2ob4obo2bob5o2bob2ob
5o2bobobobo2bobobobob5o3bob2obo3bob2o2bobob2o2bo$obo2bob2o3bo3bo3bobo
3bo5bo2bobo5bobobobobobo4bob2obo4b4obo2bo3bo3b3o2bobobobo$3b3o3b3ob2ob
o2bo3b3o2b3o2b2o2bob3obobobobo2bob3obo5b4o5bo2b2o3b3o3bobobobo2bo$6bob
o4bo2bobob3o3b2o3b2o2b2obo2bobobobo2bobo4bobob2obo3bob3ob2o3bobo3b2o2b
obob2obo$b4obob4obob2obobo2bobo2b2o4bo3bobo2bobob2obob4o3b2obo4b2obo2b
o2b4o3b2obob2obobo2b2o$o4bo5bobobo2bobo2bobobo2b5ob2obob3obo3bo6b3o3bo
bo3bobobo2bo4b3obobo2bobobobo$4obob4o2bobob2o2b3ob2o2bo5bobo2bo4b3o2b
4obo3bobo2b4o2bob2obob2o3bobob2obobobo2b2o$3bobobo2bob2o2bo2b2o9b4obob
o4b3o3b2o3bob5obobo6bo4bobob2obobo3bo2bo2bobo$2obobo2bo2bo2bobobo2bob
7o3bob2ob4o2bobo3bo2bo7bo2bob5ob4obo3bobobobo3bob2o2bo$o2bo2bob2obo2bo
bob2obobo6b2obo4bo3bo3b3o2bob6obo2b2obo4bo5b3obo3bobobobo2bob2o$bob4o
4b4obo4bobob4obobob3obob2ob3o3b3o6bob2obo2bob2obob4o3bob4obob2obo3bo$
2o5b4o5bob3obo2bo2bo3bo4bobo3bo2b3o3b5obo4bob2obo2bobo4bobo5b2o4b2o2bo
$2b4obo2bob2obo2bo3bobo3bobo2b3obo2b2obobo3b2o6b2ob2obo4bobo3b4obobob
2o4b3o2bob2o$2bo2bo2bobobo3b2o4bo2b4ob3o3bob2o2bo2b2o2bob5o4bo2b6ob4o
3bobobobob4o3bobo$6bobobobob2o4b2obobo7bo2bo3bobobo2bobobo2bo5bobo6bo
4bo4bobobobo3bobo2bob2o$5b2obobo2bo2bobo2bobobob2ob3o2b2o3bobob2o2bobo
5bobobobobob2obob3o5bobobo2bo2bobobo2b2o$9b2o4b2ob2o4b2ob2obo10bo7bo5b
2ob2o3b2obob2obo6b2ob2o2b2o3b2ob2o!

[GUYTU6J]

Synthesize the still life random.rle.

In my opinion that is quite a large leap. A more manageable step would be synthesizing the maximum density 10x10 still lives as I proposed in this post.

What is the largest bounding box height (no larger than width) inside which every possible (strict or pseudo, dense or not) still life has a glider synthesis, again?

EDIT: refined question

[confocaloid]

If I understand correctly, an upper bound is 25 (due to the 26x32 unconstructible still life, Unique father problem). A simple lower bound is 2 (blocks and snakes, xs18_bdzbdzbd, xs18_drzrmz65). It should be possible to improve the lower bound by a few cells with some more thinking.

[HerscheltheHerschel]

Synthesize the still life random.rle.

Random .Rle may be tricky due to the fact that, while being a pseudo-still life, is also bery unstable. it would have to be incrementally synthesized in layers so that it doesn't collapse, or synthesized all at once. It may be able to be synthesized but it's like tring to synthesize sir robin.

Code: Select all

x = 98, y = 98, rule = B3/S23
2obob2o3b2ob2o2bob2o3b2o3b2o2bo5bo8b2o2b2obob2ob2o3b2ob2o3b2o5b2ob2obo
3b2ob2obo$ob2obo5bobo2bob2o3bo2bobobo2b3o3b3o5bo2bo2bob2obobo4b2obobo
3bo2b2o2bobob2o2bobobob2o$6bo4bo2bobo4bo2bobobo7bo5bobo2bo2bobo5bobobo
6bo3bo3bob2o2bo3b3obobo$b6o5b2obobob2ob2obo2bo4b2obo2b4ob3ob3obob2ob2o
bob6obobo2b3o4b2ob2o4bobob3o$o12bo3b2obobo2bobob2o2bob2obo8bo3b2o2bobo
2bo6bobob2obo2b3o4bob2o2bobo3bo$b2ob2obobobobo2bo3bobo2bobo2bo7bob2ob
4o2bo3bobobobo2b3obo2bo4bo2bo2b4o4bobo2b2o$2bobob2ob2obo3bo3bobob2o2bo
2b6ob2obobo3b3ob2o2bobob3o2bob2obob3o4b2o3bob2obob2obo$2bobo7bobobob2o
3bo2b2o8bo7b3o3bo2b3obo4bobo4b2o3b4o2bo3bobobo4bo$b2obob6ob2o2bo6b2o2b
6o2bob6o4bo2bo5b4obobob2o4bo6bo2bobobobob3ob2obo$o3bobo4bo3bobo8bobo5b
obobo5b4ob2ob4o4bobobobob5ob4obob2o2bobobo4bob2o$b4o2b2o3bobo2bobo4b2o
2bobobobobo3bo2bo3bo2bo5b3o3bo2bo7bo3bobo3bobobo3b3o$5bobo3b2obobob2o
5bobob3obobob3obo2bo3bobob4o2b2o2b2obob4o2bob2o2bo3bobo2b3o3b4o$b5o2bo
5bobo7bo2bo5bobo2bo2bob2o2b2obobo3bo8bobo3bobo2bobob2obo2b2o2bobo4bo$o
5bobo2b4ob6o2bobo2b3obob2o3b2o2bobo2bobo2bobob6obobo2b2ob2obobo2bob3o
2bo3b3o$4o2bobobo11bobo2b2obo2bo3b3o2bobo2bo3bob2ob2o5bobob2o5bo2bob2o
5bob4o3bo$4bobobobo2b8obob3o5bob3o2bob2ob3o3bobo6b3obobo3b4obo3bo2b6o
5bob2o$2o2bobobobobo3bo3bobo4b2obob2o3bobo3bo3b4o3b5o2bobo2b3o3bo2b3o
2bo7b5obo$obobo2bobobob2o3bobo2b2obo2b2o4bobob4o2bo5b4o3bobo2bo5b2o2b
2o3b2ob7o6bo$2bo2bobobobobob4o2bobo3bo3b4obobo4b3ob2obo5bobobobo3b2obo
b2o2b2o2bobo7bob2ob2o$bobobobobobobobo3bobobob2ob3o5bo3b2o4bobob2o2b3o
bobobobo2bobo3bobob2o3b2ob6obo2bo$2bo2bo2bo2bobobo2b2obob2obo4b4ob4o2b
3o3bo4bo4bobobob2obobo3bo2bo6bobo8bo$3b3o5bobobobo3bo4bob2o4bo6bo3b4ob
3ob5obo2bo3bob3obo3bobo3bo4b6o$6b5obo2bobo3bob2obobob3o2bob3obobo6bo2b
o6bo3b2obo4bo3b2ob3ob6o$b4o5bobob2obob3obo2bo6b2o3bobobob5o2bobo2b2obo
b3o2bo2b2o4bo6bo7bob2o$bo2bob2o4bobo3bo5bobo2b4o2b2o4bo2bo3bob2obobobo
bobo2bo2b2ob2o3bob4obob5ob2obo2b2o$2bobobo5bo2b2obo2b2obobobo3bobo2b3o
bobo2bobo2bobobobobobobo9bobobo3bobobo2bo7b2o$3b2o2bo5bobob2obo2b2obob
o2bo2bobo2bobobob2obobo2bobob2obo2b11obobobo3bo4bob2obo$o4b3o4b2obo4b
2o4bobobo3bo2bobobobo2bo2b2ob2obo4bobo4bo7bobob5o2bobobob6o$5o10bob2o
3b4obobob3ob2obobobobobo4bo3bob2o2bo2bo4b2ob4o2bo5b3obobo6bo$4bob2o4b
4obob3o3bobobo5bo2bobobobob2o3bo3bobo4b7ob2o4bobo2b3o3bobob4o$3obo2bo
3bo5bo4b3o2bobob3obob2obobobobo2bob2ob2o2b4o11b3o2bobo3b3o2bo5bo$o2bob
2o4bob5ob2o3bobo2bobo2b2obo2bobobo2b3obo4b2o4bob2o2b5o3b2o2b3o4b2ob5o$
bobo5b2obo6bob3o2bobo3bo5b2o2bobo6bob2o3b2o2bobo2bo2bo2bobo2b2o3b4o3bo
$2obob2o2bo2bo2b3o8bob3ob6o2b3o2b4ob2obob3o2bobo2b3o5bob3o2b3o3bob2o2b
o$3bobobobob2obo3b9o4bo5bobo3bobo2bobo8b2ob3o9bo3bobo2b2obo2bob2o2bo$
3bobobobo4b4o9b3obobobobo2bo2bo2bobo2b8o6b5o6b3o2bobobobobo3b3o$b2obo
2bobob2o5bo2b2o2bo3bobob2obobobo3b2obobobo7bob4o5bob4o3bobo3bobo2bobo$
bo2bob2ob2ob2ob2obo2bo2bob3o2bo4bobob2o3bobobo2b8obo3b2o2b2obo3bobo2bo
3bob2obobob2o$2bobobo9bob2obob2o4b2ob4obobo2bo2bobobo12b2o3bo4bo2b2ob
2ob2ob2o4bobobo$b2obo2b5ob2obo2bobo4b2o2bobo4bobobo2b2obob4ob4ob2obob
2ob5o3bo2bo2bo5b3o2bobo$2bobo7b2o2b3o2b4obo3bobo2b3obob3o3bo4bobo2bobo
2bo2bo10b2o2bo2b5o2b3ob2o$2bobobobobo4bo3b2o3bobo2b2obobo3bobo3b2o2b4o
3bobo2bobobo2b7o7b3o5bo4bo$b2o2bob2ob4obo2bo2b2obobobo2bobob2obo3bobo
7b4ob4o2bob2obo4b8o5b2obo2b2o2bo$o2bobo8b2obobobo2bobobobo2bobo2b5o2b
6obo8bobo2bo3bo9bob2o2bo2bobo2b2obo$b2obobob5o4bobobo2bobobo2b3obobo5b
obo4bo3b2ob2o2bob2obo2b10obobobobo2bob2obo2bo$4bobobo4b4o2bob2obobob3o
5bobob2obo2b2o3b3obobobobo2bobobo10b2obobob2obo2bobobo$b2obobo2b3o5b2o
5bobo4bob2obob2obobo4bo6bo3bobobo2bobo2b3ob3o4bobo4bobo2bob2o$o2bo2b3o
3b4obo6bobob4obo2bo5bob4o2bob2obobo2bo2bobo2bobo2bobo2b3obo2b4obo3bo$b
o2b2o3b3o3bobobob2obobobo5b3ob3obobo3b4obobob3o3bobobo2b2o3bobo2bob2ob
o3bo3b2ob2o$2b2o3b2o4bobobob2obobobo2b5o3bo2bobo2b3o5bobo4b4obobobo5bo
b2obo2bobobo6bob2o$5b2o2b6obobo3bobob2obo4b2obobo2b3o3b6obob2obo4bobob
5obo2bob2obobob2o5bo$2b3o2bobo6bo2bob2obo4bob2o3b2obobo3b2o9bobo2b4o2b
2o4bob3o5bobo3bo3b2o$bo3bobobob4ob3o3bobob2obobob2o3b2obob2o2b5ob3o3b
2o3bobo3b2obo4b5obob3obo3bob2o$bobo2bo2bobo2b2o3b2o3bob2ob2o2bob2o4b2o
bobo4bobo2b3o2bobo2bob2obobob2obo3bobo3bo2bo2bob2o$2ob2obobo3bo4bo3b4o
8bobob4o3bo2b2o2bobobo3bobobobobo4bo2bo2bobo4b2obo3bobo$6bob5ob2ob4o4b
9obobo2bob2obobobobobo2bobo2bobobobob2obobo2b2ob4obobob3o2bo$2ob2o2bo
6bobo5b3o4bo4bo3bobobo2bo3bobob4obobobo2b2obobo2bob2o6bobobo4b2ob2o$bo
bo4b6o2bob4o4bo4b2obob3obo2b3obobobo5bo2bobobo3bo2bobo2bob4obobob5o2bo
2bo$o2bobo7bobobo5bob2o5bo2bo4b3o3bobo3b5o3bobo2bobob3o2bobobo2bobobo
5bo2bobo$2obob7o3bo3b5obo6bo3b4o3b2obobob2o5b3o2b4obo4b2o2bo2bobobobob
2o2bob2ob2o$bob2o7b3ob3obo5bo3bob4o3bobo2bobobobo2b3o4b2o6b4o4b2obobob
obobobobobo$o5bob2o2bo3bo5b4obobobo4b2obob3o2bobo3b2o2b3obo2bob3o4b4o
2bobob2obo3bobobo$4ob2obo7bob4obo3bobo3b2obobo5b2obobo6bo2bo2b2obo2b3o
bo3bobobo4b4o3bob2o$3bobo2bo2bo3b2obo8bob4obobobob4o3bob4obobobo4bobob
o2bobo2b2obo2b4o4b2obobo$2obo2bobobobobo6b2o2b2obo3bobobobobo3bob2o5b
2obob2o3bo2bob2o2bobo2bobobo4bo2bob2obo$obobobobobobob2ob5o4bobob2o3bo
2bo2bob2obo2b3o3bobo3b2obobobo3bobo2bobobob3obobo4b2o$2bobobobobobo2bo
bo5bo2bo2bo2b3o3b3o3bo3b2o2b2obobob2obobobobo2b2o2b3obo2bo2bobob4obo2b
o$2bobobobobob2obo2b6o3bobobo9b2obo6bo2bobobobobobobobobo2b2o4b2obobo
2bo4bobob2o$b2ob2obo2bobo2b3o2bo7bo2b4o2bobo2bobob4obobo2bobobobobob2o
bobo4bobo3bobobo2b2o3bobo$bo5bobo2bobo3bo3b2o2bobobo3b4ob3o2bobo2bobob
3o2bo2bo2bo4bob6obob2obobob2o2b4o2bo$2b6ob2obo2bobo3b2o2bobobob2o5bo5b
obobo2b2o3b2obobobo2b3obo7bobo2bobo3b2o4b3o$11bob3ob2o5b2obo2bo2b4obob
obobo2bob2o3bo4bobo2b2o2bobob5obo2bobo2bobo3bobo$4ob5obo13bob2obobo4bo
b2ob2obobo2bob2ob4obob2o2b2o2bobo3bo2bobobob2ob4ob2ob2o$o2bobo3bo2b4ob
2o6bo2bobob4obo7bob2obo2bo6bo2bobo2b2o2bobo2bobobobo7bo3bobo$5bobo2b2o
3bobo2bo2bob2obo2bo4bo2b2ob4obo2bobo2b3obobobo2bo5bob4obobobob5o3b2o$
4bobob2o2bo2bo2bob4o2bo2bobob2o5bobo4bobobob2o2bobobob2obob5o5bo2bobob
o4b3o2b2o$3bo2bobo2bobob2obo5bo3b2ob2o2b5o2bob2obobobo3bobobob2o3bobo
5b3obobo2bo3b2obo2bo2bo$3b4obob2obo4b5o2b3o6bo4bobobo2bobobo2b3obo2bo
3b3obo2b3o3b2obobob4o2bobob2o$o7bo2bobob3o5b2o4b6ob2obobobobo2bo2b2o3b
ob2o2b2o4bobo4bo3b2obo6bo2bo$4ob4o2bobobo2b5o3b3obo5b2obo2b2obobobobo
2bo2bo2b2o2b4o2b5ob2o3bobob3ob2obo$3bobo3b2o2bo2bo6b3o6b3o4bo4bobo2bo
2bob2obobo2bo5b2o6bob3o2bobo2bo3b2o$2obo3bo2bobob2ob4obo2bob5o2bob2ob
5o2bobobobo2bobobobob5o3bob2obo3bob2o2bobob2o2bo$obo2bob2o3bo3bo3bobo
3bo5bo2bobo5bobobobobobo4bob2obo4b4obo2bo3bo3b3o2bobobobo$3b3o3b3ob2ob
o2bo3b3o2b3o2b2o2bob3obobobobo2bob3obo5b4o5bo2b2o3b3o3bobobobo2bo$6bob
o4bo2bobob3o3b2o3b2o2b2obo2bobobobo2bobo4bobob2obo3bob3ob2o3bobo3b2o2b
obob2obo$b4obob4obob2obobo2bobo2b2o4bo3bobo2bobob2obob4o3b2obo4b2obo2b
o2b4o3b2obob2obobo2b2o$o4bo5bobobo2bobo2bobobo2b5ob2obob3obo3bo6b3o3bo
bo3bobobo2bo4b3obobo2bobobobo$4obob4o2bobob2o2b3ob2o2bo5bobo2bo4b3o2b
4obo3bobo2b4o2bob2obob2o3bobob2obobobo2b2o$3bobobo2bob2o2bo2b2o9b4obob
o4b3o3b2o3bob5obobo6bo4bobob2obobo3bo2bo2bobo$2obobo2bo2bo2bobobo2bob
7o3bob2ob4o2bobo3bo2bo7bo2bob5ob4obo3bobobobo3bob2o2bo$o2bo2bob2obo2bo
bob2obobo6b2obo4bo3bo3b3o2bob6obo2b2obo4bo5b3obo3bobobobo2bob2o$bob4o
4b4obo4bobob4obobob3obob2ob3o3b3o6bob2obo2bob2obob4o3bob4obob2obo3bo$
2o5b4o5bob3obo2bo2bo3bo4bobo3bo2b3o3b5obo4bob2obo2bobo4bobo5b2o4b2o2bo
$2b4obo2bob2obo2bo3bobo3bobo2b3obo2b2obobo3b2o6b2ob2obo4bobo3b4obobob
2o4b3o2bob2o$2bo2bo2bobobo3b2o4bo2b4ob3o3bob2o2bo2b2o2bob5o4bo2b6ob4o
3bobobobob4o3bobo$6bobobobob2o4b2obobo7bo2bo3bobobo2bobobo2bo5bobo6bo
4bo4bobobobo3bobo2bob2o$5b2obobo2bo2bobo2bobobob2ob3o2b2o3bobob2o2bobo
5bobobobobob2obob3o5bobobo2bo2bobobo2b2o$9b2o4b2ob2o4b2ob2obo10bo7bo5b
2ob2o3b2obob2obo6b2ob2o2b2o3b2ob2o!

15 gliders, because RCT.

[Bullet51]

15 gliders, because RCT.

You need to prove that random.rle is synthesizable in the first place. As we know, there are unsynthesiable still lifes.

[qqd]

Here is an explicit proof that a 1-cell-thick diehard can last arbitrarily long:

Code: Select all

x = 146, y = 1, rule = B3/S23
11o2b6o2b3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob
3ob3ob3ob3ob3ob3ob3ob3ob3ob3o3b3o!

To increase the lifespan, add 3 blinkers to the beginning of the blinker fuse shown above (moving the igniting reaction accordingly).
That was pretty easy though, and might even be known.
Our next task is to prove that a diehard has the above property as well as the property that its envelope can have an arbitrarily large bounding box. This pattern proves it explicitly:

Code: Select all

x = 309, y = 1, rule = B3/S23
11o2b6o2b3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3o3b3o5b3o10b7o
85b7o10b3o5b3o3b3ob3o5b3o3b3ob3ob3ob3ob3ob3ob3ob3ob3ob3o2b6o2b11o!

To increase lifespan, add 3 blinkers each to each fuse on the left and right sides of the pattern (add it at the leftmost part of the fuse for the left side, and the rightmost part of the fuse for the right side, moving igniting reactions accordingly). To increase the bounding box of the envelope, just move the entire right side of the pattern two cells right.

[HerscheltheHerschel]

Here is an explicit proof that a 1-cell-thick diehard can last arbitrarily long:

Code: Select all

x = 146, y = 1, rule = B3/S23
11o2b6o2b3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob
3ob3ob3ob3ob3ob3ob3ob3ob3ob3o3b3o!

To increase the lifespan, add 3 blinkers to the beginning of the blinker fuse shown above (moving the igniting reaction accordingly).
That was pretty easy though, and might even be known.
Our next task is to prove that a diehard has the above property as well as the property that its envelope can have an arbitrarily large bounding box. This pattern proves it explicitly:

Code: Select all

x = 309, y = 1, rule = B3/S23
11o2b6o2b3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3o3b3o5b3o10b7o
85b7o10b3o5b3o3b3ob3o5b3o3b3ob3ob3ob3ob3ob3ob3ob3ob3ob3o2b6o2b11o!

To increase lifespan, add 3 blinkers each to each fuse on the left and right sides of the pattern (add it at the leftmost part of the fuse for the left side, and the rightmost part of the fuse for the right side, moving igniting reactions accordingly). To increase the bounding box of the envelope, just move the entire right side of the pattern two cells right.

Here's proof that a 3-cell-thick diehard can last arbitrarily long:

Code: Select all

x = 130, y = 3, rule = B3/S23
2o$b2o2b3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3o
b3ob3ob3ob3ob3ob3ob3ob3ob3o3b3o$2o!

[confocaloid]

Is it feasible to run searches to eliminate possibility of a compact mod-7 period-14 gun? Did someone already do that?
The gun engine either would be turned 180 degrees after 7 ticks, or would be mirror-reflected after 7 ticks. There are multiple different possibilities for the relative positions of the output streams. The reduction in complexity due to symmetry might be sufficient to get interesting negative results (or find a compact true period 14 gun, if one exists).

Code: Select all

x = 57, y = 28, rule = LifeHistory
39.2A$38.2A$3C2D12B23.C4D12B$C4D12B23.3DCD12B$DC3D12B23.2D2CD6BF5B$5D
12B23.2DCDC12B$17B23.11BF5B$17B23.11BF5B$4B3F10B23.10BF6B$3BF3BF9B23.
9BF3BF3B$3BF3BF9B23.9BF3BF3B$6BF10B23.10B3F4B$5BF11B23.17B$5BF11B23.
17B$12BCDC2D23.12B5D$5BF6BD2C2D23.12B3DCD$12BDC3D23.12B4DC$12B5D23.
12B2D3C6$3D7.3D27.3D7.3D$.D3.3D2.D.D28.D3.3D4.D$.D8.D.D28.D10.D$.D3.
3D2.D.D28.D3.3D4.D$.D8.3D28.D10.D!

Find the remaining gun periods.

Glider gun omniperiodicity
p14/p15 LWSS guns
LWSS/MWSS/HWSS true-period guns
[...]

[...]
true period-14 glider gun
[...]
Can we get minimum period LWSS guns?
[...]

[confocaloid]

Is it feasible to run searches to eliminate possibility of a compact mod-7 period-14 gun? Did someone already do that?
The gun engine either would be turned 180 degrees after 7 ticks, or would be mirror-reflected after 7 ticks. There are multiple different possibilities for the relative positions of the output streams. The reduction in complexity due to symmetry might be sufficient to get interesting negative results (or find a compact true period 14 gun, if one exists).
[...]

I think one could also search for a compact mod4 p16 gun in a similar way.
Now that a true period 16 glider gun is known, it is possible to make proof-of-concept examples of the idea (see below). There are only four essentially distinct phases, instead of 16.

With bounding box 73-by-73, these patterns are unlikely to reappear from a direct search.
On the other hand, if there are known engineered solutions of this puzzle, then probably there are also unknown elementary guns of the same type that are two or three times smaller. Maybe even small enough to be discovered.

Code: Select all

#C (Rot90CCW) A capped mod4 p16 glider gun, made of four instances
#C of the first known p16 glider gun ( https://conwaylife.com/forums/viewtopic.php?p=179363#p179363 )
x = 73, y = 73, rule = B3/S23
27b2o29b2o$26bob3o27bo$26bo4bo24bobo$25b2obobobo23b2o$28bo2bo6b2o$25b2ob2o2b
3o2bo2bo$26bobob6o2b3o$26bo3b8o12b2o$27b2o9bo12b2o$37b2o11bo2$46b2o$47b2o$o
45bo$3o28b2o4b2o$3bo26bo2b2ob3o3b2o$2b2o26bo6bo5b2o$3b3o25bo2b2o6bo$4b2o21b2o
3b4o$4bobo19bobo$26bo$9bo15b2o$8b2o31b3o3b2o$8bobo27bo2b3o3b2o$22b2o13bobo2b
2o$13bo8b2o14bo12bo15bobo$12b2o37b3o11b3ob3o$12bobo13b3o23bo9bo7bo$27bo15b2o
8bo10bob4ob2o$19b2o2bo3bo3bo9bob2o8bo3bo9bo3bo$15b9o3bo2bobo7bo17bo6b2o2bobo$
14bo2b6o6bobo2bo8bo9bo5bo5b2obobo$5b2o7bo3bo11bo3bo4b2obo9bo6bo5b3obo$4bobo6b
2o2bo6bo9bo4b2o11bo2bo2b2o5b3o$4bobob2o5bo7bobo5b3o31b3o$5bobobo6b2o6bo40b2o$
7bo8b3o35bo10bo$6b2o8b3o29bo6bo2bo4bobobo$5b3o31b3o5bobo5b3o5b2obobo$5b3o24b
2o4bo9bo17bobo$3bob3o7b2o13bob2o4bo3bo23b2o$2bobob2o2bo4b2o12bo8bo2bobo$bobo
2b2o7b2o15bo7bobo2bo5b2o$bo3bo22b2obo9bo3bo3bobo4bobo$2ob4obo9b2o8b2o15bo3b2o
6b2o$o7bo9bo23b3o12bo$b3ob3o11b3o$3bobo15bo12bo14b2o9bobo$33bobo13b2o10b2o$
24b6o4bo26bo$24b4o2bo$27b2o2bo14b2o16bobo$29b2o15bo18b2o$44bobo18bo$34b2o8b2o
$32b2ob2o$32bo2bo33b2o$28bo3bo2bo5bo27bo$26b2o5b2o4b4o27b3o$27b2o9bo3bo29bo$
38bo2bo$24bo16bo$22b2o16bo$23b2o9b2o$34bo9b2o$20bo14b8o3bo$18b2o12b3o2b6obobo
$19b2o11bo2bo2b3o2b2ob2o$33b2o6bo2bo$15b2o23bobobob2o$14bobo24bo4bo$14bo27b3o
bo$13b2o29b2o!

Code: Select all

#C (Rot90CW) A capped mod4 p16 glider gun, made of four instances
#C of the first known p16 glider gun ( https://conwaylife.com/forums/viewtopic.php?p=179363#p179363 )
x = 73, y = 73, rule = B3/S23
27b2o29b2o$26bob3o27bo$26bobo2bo24bobo$25b2o2b2obo23b2o$28bob2o6b2o$25b2obo6b
obo2bo$26bobo9b3o10b3o$26bobobo5b2o15bo$27bo3b5o2bo13bo$37b2o$47b3o$49bo$32bo
15bo$o30b3o$3o27b2obo9b3o$3bo33b2o6bo$2b2o34b2o4bo$37b2o$5b2o20b2o8bo$5bobo
18bobo3bo$5bo20bo5bo9b2o$25b2o15b2o$9b2o31bobo2b2o$9bobo26bo4b2o2b2o$9bo12b2o
13bobo$21bo2bo13bo12bo15bobo$13b2o9bo18bo7b3o11b3ob3o$13bobo5bo2bo18b2o9bo9bo
7bo$13bo6b2ob2o3b3o11b2obo7b2o10b4ob3o$20bo2bo4b3o10bo2b3o22bobo$20bobo5b3o9b
obobo11b2o7bo2b2obo$16bo4bo9b3o5bobobo11b2obo5bo3bobo$5b2o8b3o13b3o3b3o2bo11b
2ob2o5bo4bo$4bobo7bo2b2o5bo6b3o4bob2o11b2ob3o5bo$4bobob2o4bo3bo4bobo13b2o12bo
10bo$5bobobo5b2obo5bo15bo13b2o8bo2bo$7bo9b2o36bob2o6bo$5bo2bo23bo15bo7bo6bobo
bo$8bo4bo18b2o13bobo6bobo4b2obobo$8bo5bo16b2obo4b3o6bo17bobo$3bo4bo2bo2bo15bo
2b3o3b3o7bo16b2o$2bobo3bo2b2o2bo13bobobo5b3o6bobo$bob2o2bo4b4o12bobobo9b3o6bo
5bo$bobo22b3o2bo10b3o3bobo4bobo$3ob4o10b2o7bob2o11b3o4bo6b2o$o7bo9bo9b2o$b3ob
3o11b3o7bo31bo$3bobo15bo12bo14b2o8bobo$33bobo13b2o9b2o$24b2o3b3o2bo$24b2o39bo
$32bo13b2o15bobo$32bo13bo17b2o$44bobo$35bobo6b2o$29bo4bo3bo2bo$29b2o6bo2bobo
26b2o$30bob5o3bobo26bo$26bo4b4o6bo28b3o$25bo7bo38bo$25b3o2$22bo$21bo12b2o$21b
3o10bo2b5o3bo$35b2o5bobobo$18bo13b3o9bobo$17bo14bo2bobo6bob2o$19bo13b2o6b2obo
$15bo24bob2o2b2o$14bob2o23bo2bobo$14bo27b3obo$13b2o29b2o!

[confocaloid]

Partial crosspost from "Thread for basic questions". Which of these are/can be settled now?

From: Allan Wechsler
Date: Fri, 10 Apr 1992 11:01-0400
Subject: Missions


I think this is the first time that so many influential Life hackers
have had such fast access to a common forum. Wouldn't it be a good
occasion to restate some of the most outstanding problems? Here are a
few that spring to mind:

0. Provide a coherent, intuitive, rigorizable account of what
constitutes a Life "object".

1. Life is known to be universal. Write a compiler whose target is
Life.

2. Find a stable pattern that is its own only predecessor.

3. Prove the existence of oscillators of all positive integral periods.

4. Prove the existence of gliders of all velocities permitted by
2(dx+dy)<=dt.

5. Characterize the functions F(t) such that Life patterns exist whose
populations grow as O(F(t)). Provide explicit examples where possible.

6. Find the smallest area containing a pattern with no predecessor.

7. Find the minimal population for a pattern with no predecessor.

8. Provide bounds for the maximum period of an oscillator that fits at all
phases into an XxY rectangle.

9. Provide bounds for the maximum period of an oscillator that fits at
some phase into an XxY rectangle. In particular, consider X=1.

10. Demonstrate the existence of a pattern which possesses parents but
no grandparents.

11. Provide a statistical but rigorous account of the end state of
randomly initialized universes. Characterize "fires" and "quiet areas"
and provide probabilistic analyses of the prevalence of these two phases
with time.

12. Prove Schroeppel's "Cool Out" conjecture: if a configuration C is
locally stable over a rectangle R, then there exists a configuration C*
such that (a) C* is locally equal to C over R; and (b) C* is globally
stable.

13. For what oscillation regimes other than stability is an analog of
Schroeppel's Conjecture true?

14. Settle the question of how many distinct three-glider collisions
there are.

15. Does there exist a finite stable pattern which can defend itself
against any single glider?

[LuveelVoom]

EDIT by dvgrn: reworked slightly to avoid incorrect attribution in the quote.

I believe this is it:

0. Provide a coherent, intuitive, rigorizable account of what
constitutes a Life "object". UNSOLVED

1. Life is known to be universal. Write a compiler whose target is
Life. SOLVED I BELIEVE? UNSURE

2. Find a stable pattern that is its own only predecessor. SOLVED

3. Prove the existence of oscillators of all positive integral periods. SOLVED

4. Prove the existence of gliders of all velocities permitted by
2(dx+dy)<=dt. UNSOLVED? SOLVED FOR SLOPE 0 AND 1

5. Characterize the functions F(t) such that Life patterns exist whose
populations grow as O(F(t)). Provide explicit examples where possible. UNSOLVED

6. Find the smallest area containing a pattern with no predecessor. UNSOLVED

7. Find the minimal population for a pattern with no predecessor. UNSOLVED

8. Provide bounds for the maximum period of an oscillator that fits at all
phases into an XxY rectangle. UNSOLVED

9. Provide bounds for the maximum period of an oscillator that fits at
some phase into an XxY rectangle. In particular, consider X=1. UNSOLVED

10. Demonstrate the existence of a pattern which possesses parents but
no grandparents. SOLVED

11. Provide a statistical but rigorous account of the end state of
randomly initialized universes. Characterize "fires" and "quiet areas"
and provide probabilistic analyses of the prevalence of these two phases
with time. UNSOLVED?

12. Prove Schroeppel's "Cool Out" conjecture: if a configuration C is
locally stable over a rectangle R, then there exists a configuration C*
such that (a) C* is locally equal to C over R; and (b) C* is globally
stable. CONJECTURE DISPROVEN

13. For what oscillation regimes other than stability is an analog of
Schroeppel's Conjecture true? WHAT IS THIS?????

14. Settle the question of how many distinct three-glider collisions
there are. APPROXIMATELY SOLVED?

15. Does there exist a finite stable pattern which can defend itself
against any single glider? IF THIS IS ONE GLIDER TOTAL, SOLVED. IF THIS IS ONE GLIDER AS IN A SLOW SALVO, UNSOLVED.

[confocaloid]

^^

(1) Do not repost a long quote of something that was posted just above your post.

(2) Do not edit the quoted text, other than replacing irrelevant parts with something like "..." or "[...]". Do not put words into someone else's mouth.

[...] As a rule, it is rarely helpful and it shouldn't be necessary to edit the quoted text at all (only trim it to remove parts that aren't relevant). Any requests for clarification, corrections, suggestions and so on should go in your reply, which should be outside the quoted text. It should be easy to tell who wrote what.

[Jormungant]

Well, the post was edited with "answers" (as dvgrn noted), so technically it is not a repost, that being said, I would love to know how come no 15 is solved (even in a restricted case)... I might need a link to believe it.

[LuveelVoom]

Well, the post was edited with "answers" (as dvgrn noted), so technically it is not a repost, that being said, I would love to know how come no 15 is solved (even in a restricted case)... I might need a link to believe it.

Dvgrn provides an answer here, it has probably been answered earlier: viewtopic.php?f=17&t=2036&p=199750&hilit=Glider#p199757

[confocaloid]

That doesn't seem to settle the problem.

The question in #15 says: "15. Does there exist a finite stable pattern which can defend itself against any single glider?"

The way I read that, it essentially asks for an "universal stable glider eater". Imagine something like eater 2, but instead of being able to eat a glider arriving on one of a few specific glider lanes, it can eat a glider arriving on any lane (as long as the glider interacts at all, it will be eaten, and the "universal eater" will recover after finitely many ticks).

It may or may not be necessary to avoid any leftover junk separate from the "universal eater", it might be "universal catalyst" rather than an eater. But at least it would need to recover itself.

A sparse array of blocks doesn't seem to answer the question in any way. It is a different question.

Well, the post was edited with "answers" (as dvgrn noted), so technically it is not a repost, that being said, I would love to know how come no 15 is solved (even in a restricted case)... I might need a link to believe it.

Dvgrn provides an answer here, it has probably been answered earlier: viewtopic.php?f=17&t=2036&p=199750&hilit=Glider#p199757

[dvgrn]

Well, the post was edited with "answers" (as dvgrn noted), so technically it is not a repost, that being said, I would love to know how come no 15 is solved (even in a restricted case)... I might need a link to believe it.

There is a sense in which #15 is solved. If you interpret "defend itself" as "does not catastrophically explode", then a defended area surrounded by a sparse field of blocks is reliably defended against any single glider.

If you know that a single glider will collide with a target area in a particular time period, then we can combine that with mscibing's ash-clearing mechanism:

1) wait long enough that the single glider has safely collided and the dust has settled;
2) clear the entire area covered by the sparse-field-of-blocks defense;
3) use standard universal construction to rebuild the sparse field of blocks.

After some very large number of ticks, the self-defending pattern will return precisely to its initial state. In the absence of more gliders coming in, it will become a very large, very high-period oscillator. "Stable" in one sense of stable -- but probably not the intended sense!

The thing is, the pattern can't tell if a glider has come in or not. So, for example, there's no known way to reliably have an arbitrary incoming glider reliably send a signal to the rebuild mechanism. It all adds up to a very unsatisfactory and fragile kind of "self-defense".

We can also build huge stacks of highway robbers that can handle _almost_ any incoming glider -- any percentage of incoming glider lanes strictly less than 100% can be covered by a large enough highway-robber arrangement, I believe. But that's also not a very satisfactory kind of self-defense -- we don't know any way to reliably defend-and-recover for those few key incoming glider lanes at the corners.

[Jormungant]

I see, I also had this stronger sense of that "stable pattern", just managing gliders bound from 1 direction and a limited (but contiguous) range would be a challenge. Some kind of fuse that burns and triggers the repair on either end, then that should be in the realm of possible.

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x = 1185, y = 1021, rule = LifeHistory
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A3.A3.A$745.A3.A3.A343.A3.A3.A$746.A3.A3.A341.A3.A3.A$747.A3.A3.A339.
A3.A3.A$748.A3.A3.A337.A3.A3.A$749.A3.A3.A335.A3.A3.A$750.A3.A3.A333.
A3.A3.A$751.A3.A3.A331.A3.A3.A$752.A3.A3.A329.A3.A3.A$753.A3.A3.A327.
A3.A3.A$754.A3.A3.A325.A3.A3.A$755.A3.A3.A323.A3.A3.A$756.A3.A3.A321.
A3.A3.A$757.A3.A3.A319.A3.A3.A$758.A3.A3.A317.A3.A3.A$759.A3.A3.A315.
A3.A3.A$760.A3.A3.A313.A3.A3.A$761.A3.A3.A311.A3.A3.A$762.A3.A3.A309.
A3.A3.A$763.A3.A3.A307.A3.A3.A$764.A3.A3.A305.A3.A3.A$765.A3.A3.A303.
A3.A3.A$766.A3.A3.A301.A3.A3.A$767.A3.A3.A299.A3.A3.A$768.A3.A3.A297.
A3.A3.A$769.A3.A3.A295.A3.A3.A$770.A3.A3.A293.A3.A3.A$771.A3.A3.A291.
A3.A3.A$772.A3.A3.A289.A3.A3.A$773.A3.A3.A287.A3.A3.A$774.A3.A3.A285.
A3.A3.A$775.A3.A3.A283.A3.A3.A$776.A3.A3.A281.A3.A3.A$777.A3.A3.A279.
A3.A3.A$778.A3.A3.A277.A3.A3.A$779.A3.A3.A275.A3.A3.A$780.A3.A3.A273.
A3.A3.A$781.A3.A3.A271.A3.A3.A$782.A3.A3.A269.A3.A3.A$783.A3.A3.A267.
A3.A3.A$784.A3.A3.A265.A3.A3.A$785.A3.A3.A263.A3.A3.A$786.A3.A3.A261.
A3.A3.A$787.A3.A3.A259.A3.A3.A$788.A3.A3.A257.A3.A3.A$789.A3.A3.A255.
A3.A3.A$790.A3.A3.A253.A3.A3.A$791.A3.A3.A251.A3.A3.A$792.A3.A3.A249.
A3.A3.A$793.A3.A3.A247.A3.A3.A$794.A3.A3.A245.A3.A3.A$795.A3.A3.A243.
A3.A3.A$796.A3.A3.A241.A3.A3.A$797.A3.A3.A239.A3.A3.A$798.A3.A3.A237.
A3.A3.A$799.A3.A3.A235.A3.A3.A$800.A3.A3.A233.A3.A3.A$801.A3.A3.A231.
A3.A3.A$802.A3.A3.A229.A3.A3.A$803.A3.A3.A227.A3.A3.A$804.A3.A3.A225.
A3.A3.A$805.A3.A3.A223.A3.A3.A$806.A3.A3.A221.A3.A3.A$807.A3.A3.A219.
A3.A3.A$808.A3.A3.A217.A3.A3.A$809.A3.A3.A215.A3.A3.A$810.A3.A3.A213.
A3.A3.A$811.A3.A3.A211.A3.A3.A$812.A3.A3.A209.A3.A3.A$813.A3.A3.A207.
A3.A3.A$814.A3.A3.A205.A3.A3.A$815.A3.A3.A203.A3.A3.A$816.A3.A3.A201.
A3.A3.A$817.A3.A3.A199.A3.A3.A$818.A3.A3.A197.A3.A3.A$819.A3.A3.A195.
A3.A3.A$820.A3.A3.A193.A3.A3.A$821.A3.A3.A191.A3.A3.A$822.A3.A3.A189.
A3.A3.A$823.A3.A3.A187.A3.A3.A$824.A3.A3.A185.A3.A3.A$825.A3.A3.A183.
A3.A3.A$826.A3.A3.A181.A3.A3.A$827.A3.A3.A179.A3.A3.A$828.A3.A3.A177.
A3.A3.A$829.A3.A3.A175.A3.A3.A$830.A3.A3.A173.A3.A3.A$831.A3.A3.A171.
A3.A3.A$832.A3.A3.A169.A3.A3.A$833.A3.A3.A167.A3.A3.A$834.A3.A3.A165.
A3.A3.A$835.A3.A3.A163.A3.A3.A$836.A3.A3.A161.A3.A3.A$837.A3.A3.A159.
A3.A3.A$838.A3.A3.A157.A3.A3.A$839.A3.A3.A155.A3.A3.A$840.A3.A3.A153.
A3.A3.A$841.A3.A3.A151.A3.A3.A$842.A3.A3.A149.A3.A3.A$843.A3.A3.A147.
A3.A3.A$844.A3.A3.A145.A3.A3.A$845.A3.A3.A143.A3.A3.A$846.A3.A3.A141.
A3.A3.A$847.A3.A3.A139.A3.A3.A$848.A3.A3.A137.A3.A3.A$849.A3.A3.A135.
A3.A3.A$850.A3.A3.A133.A3.A3.A$851.A3.A3.A131.A3.A3.A$852.A3.A3.A129.
A3.A3.A$853.A3.A3.A127.A3.A3.A$854.A3.A3.A125.A3.A3.A$855.A3.A3.A123.
A3.A3.A$856.A3.A3.A121.A3.A3.A$857.A3.A3.A119.A3.A3.A$858.A3.A3.A117.
A3.A3.A$859.A3.A3.A115.A3.A3.A$860.A3.A3.A55.2A56.A3.A3.A$861.A3.A3.A
54.A56.A3.A3.A$862.A3.A3.A54.A54.A3.A3.A$863.A3.A3.A52.2A53.A3.A3.A$
864.A3.A3.A51.A53.A3.A3.A$865.A3.A3.A51.A51.A3.A3.A$866.A3.A3.A49.2A
50.A3.A3.A$867.A3.A3.A48.A50.A3.A3.A$868.A3.A3.A48.A48.A3.A3.A$869.A
3.A3.A46.2A47.A3.A3.A$870.A3.A3.A45.A47.A3.A3.A$871.A3.A3.A45.A45.A3.
A3.A$872.A3.A3.A43.2A44.A3.A3.A$873.A3.A3.A42.A44.A3.A3.A$874.A3.A3.A
42.A42.A3.A3.A$875.A3.A3.A40.2A41.A3.A3.A$876.A3.A3.A39.A41.A3.A3.A$
877.A3.A3.A39.A39.A3.A3.A$878.A3.A3.A37.2A38.A3.A3.A$879.A3.A3.A36.A
38.A3.A3.A$880.A3.A3.A36.A36.A3.A3.A$881.A3.A3.A34.2A35.A3.A3.A$882.A
3.A3.A33.A35.A3.A3.A$883.A3.A3.A33.A33.A3.A3.A$884.A3.A3.A31.2A32.A3.
A3.A$885.A3.A3.A30.A32.A3.A3.A$886.A3.A3.A30.A30.A3.A3.A$887.A3.A3.A
28.2A29.A3.A3.A$888.A3.A3.A27.A29.A3.A3.A$889.A3.A3.A27.A27.A3.A3.A$
890.A3.A3.A25.2A26.A3.A3.A$891.A3.A3.A24.A26.A3.A3.A$892.A3.A3.A24.A
24.A3.A3.A$893.A3.A3.A22.2A23.A3.A3.A$894.A3.A3.A21.A23.A3.A3.A$895.A
3.A3.A21.A21.A3.A3.A$896.A3.A3.A19.2A20.A3.A3.A$897.A3.A3.A18.A20.A3.
A3.A$898.A3.A3.A18.A18.A3.A3.A$899.A3.A3.A16.2A17.A3.A3.A$900.A3.A3.A
15.A17.A3.A3.A$901.A3.A3.A15.A15.A3.A3.A$902.A3.A3.A13.2A14.A3.A3.A$
903.A3.A3.A12.A14.A3.A3.A$904.A3.A3.A12.A12.A3.A3.A$905.A3.A3.A10.2A
11.A3.A3.A$906.A3.A3.A9.A11.A3.A3.A$907.A3.A3.A9.A9.A3.A3.A$908.A3.A
3.A7.2A8.A3.A3.A$909.A3.A3.A6.A8.A3.A3.A$910.A3.A3.A7.A5.A3.A3.A$911.
A3.A3.A5.2A4.A3.A3.A$912.A3.A3.A3.A5.A3.A3.A$913.A3.A3.A2.A4.A3.A3.A$
914.A3.A3.A.A.A.A3.A3.A$915.A3.A3.2A.2A3.A3.A$916.A3.A9.A3.A$917.A3.A
7.A3.A$918.A3.A.A.A.A3.A$919.A3.2A.2A3.A$920.A9.A$921.A7.A$922.A.A.A.
A$923.2A.2A!

This fuse has period 4 on both sides (at least the front end that is), remains to show there is no such magical corners with a fuse that burns inwards in a predictable manner, I mean, cannot be said it is known it cannot be done.

[Jormungant]

Probably found something better, a fuse wall that burns the exact same way in both direction, no matter the glider offset, and as added bonus, no run away gliders anywhere:

Code: Select all

x = 288, y = 474, rule = LifeHistory
12$19.2A.2A223.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
2A.2A110.A.A110.2A.2A$20.A.A110.2A.2A110.A.A$20.A.A111.A.A111.A.A$19.
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.2A!

[dl-rs]

I've known about the caterpillar (thouroughly) from Book. Is it possible to prove that for all (m, n), we can have a spaceship with (simplified) speed of (m, n)/(2m+2n)?