Searching for Devote Parents

[Rudyj]

Greetings everyone!

I would like to invite the community to join a fun challenge that I call searching for "Devote Parents" (Щирі Батьки by ukrainian).

For a given pattern P1, a Devote Parent is a strict phoenix configuration P0 (where no live cell survives to the next generation, i.e., every cell dies by underpopulation or overcrowding) that gives birth to pattern P1 in exactly one generation, while none of the parent's cells survive into P1.

I find finding minimal or interesting Devote Parents for various still lifes, oscillators, and spaceships to be a very intriguing problem. Below are 18 examples of Devote Parents that I have found for common patterns (tub, beehive, pond, loaf, block, boat, ship, aircraft carrier, glider phases, blinker, beacon, clock, toad, and pentadecathlon phases).

I invite anyone interested to try finding Devote Parents for other known structures or to minimize the population/bounding box of my examples!

Best regards,
Ruduj (Рудий)

Patterns (RLE Code Blocks)

01. Tub (5 cells)

Code: Select all

x = 3, y = 3, rule = B3/S23
obo$bo$obo!

02. Beehive (8 cells)

Code: Select all

x = 5, y = 6, rule = B3/S23
2b2o2$2bobo$obo2$b2o!

03. Pond (8 cells)

Code: Select all

x = 4, y = 4, rule = B3/S23
o2bo$b2o$b2o$o2bo!

04. Loaf (11 cells)

Code: Select all

x = 7, y = 6, rule = B3/S23
4b2o$b2o$4bobo$obobo2$3b2o!

05. Block (22 cells)

Code: Select all

x = 6, y = 8, rule = B3/S23
ob2obo$b4o$2b2o$bo2bo2$2b2o$6o$2b2o!

06. Boat (14 cells)

Code: Select all

x = 7, y = 7, rule = B3/S23
2bo$2bo$5o$2bo$2bobobo$6bo$3b2o!

07. Ship (13 cells)

Code: Select all

x = 7, y = 7, rule = B3/S23
2bo$2bo$5o$2bo3bo$2bobo$5bo$3bo!

08. Aircraft Carrier (26 cells)

Code: Select all

x = 7, y = 10, rule = B3/S23
ob2o$b5o$2b2o$bo$3bobo$bobo$5bo$3b2o$b5o$3b2obo!

09. Glider L-form (7 cells)

Code: Select all

x = 5, y = 5, rule = B3/S23
2bobo$o$ob2o2$2bo!

10. Glider S-form (12 cells)

Code: Select all

x = 7, y = 5, rule = B3/S23
obo$o2b2o$3b4o$bo2bo$4bo!

11. Blinker (4 cells)

Code: Select all

x = 4, y = 3, rule = B3/S23
2obo2$bo!

12. Beacon (28 cells)

Code: Select all

x = 10, y = 10, rule = B3/S23
bo$2bobo$b3o3bo$ob3o2bo$4b2o$4b2o$2bo2b3obo$2bo3b3o$5bobo$8bo!

13. Clock (26 cells)

Code: Select all

x = 6, y = 12, rule = B3/S23
bo$bo$3obo$3obo$bo$o2bo$2bo2bo$4bo$bob3o$bob3o$4bo$4bo!

14. Toad phase 1 (38 cells)

Code: Select all

x = 10, y = 12, rule = B3/S23
5bo2$3b5o$b4ob4o$3b5o3$2b5o$4ob4o$2b5o2$4bo!

15. Toad phase 2 (10 cells)

Code: Select all

x = 6, y = 6, rule = B3/S23
3b2o2$o2bobo$obo2bo2$b2o!

16. Pentadecathlon phase 0 (20 cells)

Code: Select all

x = 11, y = 7, rule = B3/S23
3b2obobo$bo$bob2obobo$7bo2bo$2obo2bobo$3bo$2o!

17. Pentadecathlon phase 4 (40 cells)

Code: Select all

x = 10, y = 9, rule = B3/S23
bobo2bobo$4b2o$o2b4o2bo$b3o2b3o$b2o4b2o$b3o2b3o$o2b4o2bo$4b2o$bobo2bobo!

18. Pentadecathlon phase 6 (20 cells)

Code: Select all

x = 12, y = 5, rule = B3/S23
o2bo4bo2bo$b2o6b2o$b2o6b2o$b2o6b2o$o2bo4bo2bo!

[LuveelVoom]

There is a program called LLS which would be able to find these patterns very efficiently:
https://conwaylife.com/wiki/Tutorials/LLS
I'm not versed enough in it to know how to do that, but I'm sure other people on this forum know how.

[Hdjensofjfnen]

With Logic Life Search, I checked your solutions for the still lifes.

The smallest solution for a block is 14 cells:

Code: Select all

x = 6, y = 6, rule = B3/S23
ob2obo$b4o$2b2o$bo2bo2$2b2o!

The smallest solution for a boat is 13 cells:

Code: Select all

x = 7, y = 7, rule = B3/S23
4bo$4bo$3b3o$o2b2obo$obo2$b2o!

The smallest solution for an aircraft carrier is 8 cells:

Code: Select all

x = 6, y = 5, rule = B3/S23
bo$o4bo$2b2o$o4bo$4bo!

Your solutions for the tub, beehive, pond, loaf, and ship are all minimal.

The search setup is relatively simple -- we specify two generations:
- In generation 0, all cells of the target pattern are off (0) and the other cells are indeterminate (*)
- In generation 1, all cells of the target pattern are on (1) and the other cells are off (0)
We also provide enough extra space around the pattern (e.g. 5 extra rows and 5 extra columns on each side) to investigate all plausibly minimal parents. Finally, we impose a population constraint to find solutions with fewer than a desired number of cells (e.g. -p '<9' to find only solutions with 8 or fewer cells). UNSATISFIABLE means that a solution is not possible under the population constraint.

For example, here is the input file for a tub:

Code: Select all

*,*,*,*,*,*,*,*,*,*,*,*,*
*,*,*,*,*,*,*,*,*,*,*,*,*
*,*,*,*,*,*,*,*,*,*,*,*,*
*,*,*,*,*,*,*,*,*,*,*,*,*
*,*,*,*,*,*,*,*,*,*,*,*,*
*,*,*,*,*,*,0,*,*,*,*,*,*
*,*,*,*,*,0,*,0,*,*,*,*,*
*,*,*,*,*,*,0,*,*,*,*,*,*
*,*,*,*,*,*,*,*,*,*,*,*,*
*,*,*,*,*,*,*,*,*,*,*,*,*
*,*,*,*,*,*,*,*,*,*,*,*,*
*,*,*,*,*,*,*,*,*,*,*,*,*
*,*,*,*,*,*,*,*,*,*,*,*,*

0,0,0,0,0,0,0,0,0,0,0,0,0
0,0,0,0,0,0,0,0,0,0,0,0,0
0,0,0,0,0,0,0,0,0,0,0,0,0
0,0,0,0,0,0,0,0,0,0,0,0,0
0,0,0,0,0,0,0,0,0,0,0,0,0
0,0,0,0,0,0,1,0,0,0,0,0,0
0,0,0,0,0,1,0,1,0,0,0,0,0
0,0,0,0,0,0,1,0,0,0,0,0,0
0,0,0,0,0,0,0,0,0,0,0,0,0
0,0,0,0,0,0,0,0,0,0,0,0,0
0,0,0,0,0,0,0,0,0,0,0,0,0
0,0,0,0,0,0,0,0,0,0,0,0,0
0,0,0,0,0,0,0,0,0,0,0,0,0

[Entity Valkyrie 2]

Greetings everyone!

I would like to invite the community to join a fun challenge that I call searching for "Devote Parents" (Щирі Батьки by ukrainian).

For a given pattern P1, a Devote Parent is a strict phoenix configuration P0 (where no live cell survives to the next generation, i.e., every cell dies by underpopulation or overcrowding) that gives birth to pattern P1 in exactly one generation, while none of the parent's cells survive into P1.

I find finding minimal or interesting Devote Parents for various still lifes, oscillators, and spaceships to be a very intriguing problem. Below are 18 examples of Devote Parents that I have found for common patterns (tub, beehive, pond, loaf, block, boat, ship, aircraft carrier, glider phases, blinker, beacon, clock, toad, and pentadecathlon phases).

I invite anyone interested to try finding Devote Parents for other known structures or to minimize the population/bounding box of my examples!

Best regards,
Rudyj (Рудий)

Here's is a 9-cell one for eater 1:

Code: Select all

#C            чи  це  і і     и
#C Я не знаю,        м н мальн й
#C            это ли  и и     ы
           
x = 6, y = 5, rule = B3/S23
2bobo2$3bobo$o4bo$ob2o!

[Hdjensofjfnen]

Here's is a 9-cell one for eater 1:

Code: Select all

#C            чи  це  і і     и
#C Я не знаю,        м н мальн й
#C            это ли  и и     ы
           
x = 6, y = 5, rule = B3/S23
2bobo2$3bobo$o4bo$ob2o!

LLS finds an 8-cell solution, which is minimal:

Code: Select all

x = 6, y = 6, rule = B3/S23
bobo$o$2bo$2bobo$5bo$3bo!

Not every still life allows a solution: for example, the ørb (15 cells) is unsolvable (given my search setup). Can anyone find smaller?

EDIT: The honeycomb (12 cells) is also unsolvable.

EDIT 2: The loaf siamese loaf (11 cells) is also unsolvable.

EDIT 3: The barge siamese loaf (10 cells) is also unsolvable.

EDIT 4: Here's a question: is there a still life that does not admit a finite-population solution, but admits an infinite-population solution à la American Dream?

[speedydelete]

Not every still life allows a solution: for example, the ørb (15 cells) is unsolvable (given my search setup). Can anyone find smaller?

Are you sure you have set it up right? I believe that theoretically there could be one hundreds of cells big but none smaller, even for small objects.

[Hdjensofjfnen]

Are you sure you have set it up right? I believe that theoretically there could be one hundreds of cells big but none smaller, even for small objects.

Admittedly, I haven't, although perhaps this could be addressed by including a border of indeterminate cells on the border of generation 1 (allowing some cells far from the desired still life to be on in generation 1, showing that a solution is feasible even if it does not fit inside the allotted box).

Here's an explicit disproof of a solution for the loaf siamese loaf, which takes advantage of symmetry. (I haven't yet found a disproof of a solution for the barge siamese loaf.) Purple denotes cells that must be off and must turn on in the next generation; salmon denotes a particular such cell. Blue denotes cells that must be off and must remain off in the next generation; red denotes a particular such cell. Green denotes cells that must be on and must turn off in the next generation; pink denotes a particular such cell. Cells newly implicated to be off in generation 0 are marked in light blue.

Code: Select all

x = 61, y = 54, rule = LifeSuper
2.2G8.2H8.2H7.J2H7.B2H7.B2H6.D$.G2.G6.H2AH6.H2AH6.HCAH5.JH2AH5.BN2AH
5.D$G.G.G5.H.H.H5.HJNJH5.HBHBH5.HDHBH5.HBHBH5.D$G2.G6.HA.H6.HAJH6.HAB
H6.HABH6.HABH$.2G8.2H8.2H8.2H8.2H8.2H7.D6$12.2H8.2H7.J2H7.B2H7.B2H6.D
$11.HA.H6.HAJH6.HCBH5.JHABH5.BNABH5.D$10.H.HAH5.HJNAH5.HBHAH5.HDHAH5.
HBHAH5.D$10.HA.H6.HAJH6.HABH6.HABH6.HABH$11.2H8.2H8.2H8.2H8.2H7.D6$
12.2H8.2H7.J2H7.B2H7.B2H6.D$11.H2AH6.H2AH6.HCAH5.JH2AH5.BN2AH5.D$10.H
.H.H5.HJNJH5.HBHBH5.HDHBH5.HBHBH5.D$10.H.AH6.HJAH6.HBAH6.HBAH6.HBAH$
11.2H8.2H8.2H8.2H8.2H7.D6$12.2H8.2H6.D$11.H2AH6.HACH5.D$10.H.HAH5.H.H
AH5.D$10.H2.H6.H2.H$11.2H8.2H7.D5$12.2H8.2H8.2H6.D$11.HA.H6.HABH6.HAB
H5.D$10.H.HAH5.HBNAH5.HBHCH5.D$10.H.AH6.HBAH6.HBAH$11.2H8.2H8.2H7.D6$
12.2H8.2H8.2H6.D$11.H.AH6.HBAH6.HBAH5.D$10.H.HAH5.HBNAH5.HBHCH5.D$10.
H.AH6.HBAH6.HBAH$11.2H8.2H8.2H7.D!

[I6_I6]

[...]
Here's an explicit disproof of a solution for the loaf siamese loaf, which takes advantage of symmetry. (I haven't yet found a disproof of a solution for the barge siamese loaf.)[...]

Here's a disproof for the barge siamese loaf annotated the same way, which turned out to be basically the exact same as your loaf siamese loaf disproof, just without one of the cases:

Code: Select all

x = 61, y = 45, rule = B3/S23Super
2.2G8.2H8.2H8.2H7.J2H7.B2H6.D$.G2.G6.H.AH6.HJAH5.JHBAH5.BHDAH5.BNBAH5.
D$G.G.G5.HAH.H5.HANJH5.HCHBH5.HAHBH5.HAHBH5.D$.G.G7.HAH7.HAH7.HAH7.HA
H7.HAH$2.G9.H9.H9.H9.H9.H7.D6$12.2H8.2H7.J2H7.B2H7.B2H6.D$11.H2AH6.H2A
H6.HCAH5.JH2AH5.BN2AH5.D$10.H.H.H5.HJNJH5.HBHBH5.HDHBH5.HBHBH5.D$11.H
AH7.HAH7.HAH7.HAH7.HAH$12.H9.H9.H9.H9.H7.D6$12.2H8.2H6.D$11.H2AH6.HAC
H5.D$10.H.HAH5.H.HAH5.D$11.H.H7.H.H$12.H9.H7.D6$12.2H8.2H8.2H6.D$11.H
A.H6.HABH6.HABH5.D$10.H.HAH5.HBNAH5.HBHCH5.D$11.HAH7.HAH7.HAH$12.H9.H
9.H7.D6$12.2H8.2H8.2H6.D$11.H.AH6.HBAH6.HBAH5.D$10.H.HAH5.HBNAH5.HBHC
H5.D$11.HAH7.HAH7.HAH$12.H9.H9.H7.D!

EDIT:
Devote parents for the long boat, barge, very long ship, very long boat and long barge, each with 9, 10, 13, 14 and 15 cells, respectively:

Code: Select all

x = 51, y = 7, rule = B3/S23
2b2o6bob2o8b2o10b2o8bob2o2$obobo5bobobo5bobobo7bobobo7bobobo$o2bo6bo2b
o6bo2bo2bo5bo2bo2bo5bo2bo2bo$2bobo7bobo7bobobo7bobobo7bobobo2$23b2o10b
2obo8b2obo!

They were found by hand, but they still look pretty minimal.

EDIT 2:
I think the best way to find the smallest unsolvable SL would be to try all of the ones with less than 10 cells.
Since I don't have any programs to help me with that, I'll be doing as many as I can by hand (so most of them probably won't be minimal).

Solution for snake:

Code: Select all

x = 10, y = 8, rule = B3/S23
o$bobo$3o3bo2bo$3obo3bo$bo3bob3o$o2bo3b3o$6bobo$9bo!

Python:

Code: Select all

x = 9, y = 7, rule = B3/S23
4bo$4bo$ob5o$4bo3bo$b2obobo$8bo$4b2o!

Tub with tail:

Code: Select all

x = 7, y = 8, rule = B3/S23
obo$bo2bo$obobo2$obo2bo$3b2o$b5o$3b2obo!

Hat:

Code: Select all

x = 8, y = 6, rule = B3/S23
3bobo2$4bo$obobobo$7bo$b2o2bo!

[C_R_116]

Are devote grandparents just devote parents of devote parents like this?

Code: Select all

x = 12, y = 12, rule = LifeHistory
2.E2.E$2.E2.E$8E$2.E.2E$2.E3.E.E$8.E$3.E$3.E.E3.E$6.2E.E$4.8E$6.E2.E$
6.E2.E!

Or do they have to be strictly devote? (Cells must only be on for one generation.)

Code: Select all

x = 12, y = 12, rule = LifeHistory
2.E$2.E$4E$2.E.E.E$2.E5.E$5.E2.E$3.E2.E$3.E5.E$5.E.E.E$8.4E$9.E$9.E!

[LuveelVoom]

Hmm, if an "unfaithful" pattern (one that has no devote predecessors) occurs in a pattern, then the pattern itself is unfaithful. This means that it should be easy to prove large sets of patterns unfaithful

[I6_I6]

Hmm, if an "unfaithful" pattern (one that has no devote predecessors) occurs in a pattern, then the pattern itself is unfaithful. This means that it should be easy to prove large sets of patterns unfaithful

What's the smallest pattern without a devote parent?

Reduced the snake solution from 26 to just 8 cells:

Code: Select all

x = 6, y = 4, rule = B3/S23
bo3bo$o2bo$2bo2bo$o3bo!

[synperiplanar]

What's the smallest pattern without a devote parent?

unless im missing something this should just be the dot

[I6_I6]

What's the smallest pattern without a devote parent?

unless im missing something this should just be the dot

Counterexample:

Code: Select all

x = 3, y = 3, rule = B3/S23Super
2.A$AD$A!

EDIT:
Any pattern where any cell has 6 or more neighbors cannot have a devote parent, because there aren't enough dead cells around it to birth the cell in question in the devote parent.

An example is the bullet heptomino:

Code: Select all

x = 17, y = 5, rule = B3/S23Super
16.D$.G6.AHA5.D$3G5.HNH5.D$3G5.3H$16.D!

The central cell cannot be birthed by a devote parent because it only has 2 eligible dead neighbors.

(Edit 2: Basically what C_R_116 is saying in the post after this)

[C_R_116]

What's the smallest pattern without a devote parent?

Any pattern that has a cell with more than 6 adjacent cells has no devote parent (there aren't enough cells for birth.)

Code: Select all

x = 28, y = 3, rule = B3/S23
bo3b2o3b2o3b3o2bobo2bobo$3o2b3o2b3o2b3o2b3o3b2o$3o3b2o2bobo2bo4bobo2b
3o!

So I'd say the minimum # of cells required is 7.

[Rudyj]

Just a quick note: the Phoenix 1 oscillator is actually a Devote Parent to itself.

[I6_I6]

Hook with tail:

Code: Select all

x = 10, y = 10, rule = B3/S23
3bobo$o2bobo$2b6o$ob3ob4o$o2b5o$2bo$o4bo$bobobo2$4bobo!

[AbhpzTa]

All strict still lifes up to 9 cells:

Code: Select all

x = 154, y = 91, rule = B3/S23
ob2obo$b4o$2b2o$bo2bo13bobo$19bo$2b2o14bobo13$2bobo$bo$3bo$bo2b2o$4b4o
$5bo$5bo8$21bo$21bo$3bo15b5o26bo15bo3bo$bo15bo3bo12bobo12bo4bo10bo2bo$
bob2obo12bobo13bo2bo12b2o14bo2bo$6bo11bo15bobobo10bo4bo10bo3bo$4bo15bo
32bo$35b2obo11$2b2o15b2o13bobo14b2o$5b2o26bo15bo5bo$bobo13bobobo13bo
15bobo$3bobobo9bo2bo14bobo13bo3bo$19bobo27b5o$3b2o31bobo12bo$51bo8$53b
o77bo$53bo79bo$20b2o11bob2o14b4o11b2o31bo2bo12b2o14bobo$2bo2bo11b2o34b
4o12bo12bobobo12bo13bo17bo$3b2o15bobobo8bobobo11bobo2bo12bobo13bo13b5o
bo11bobo2bo8bo4bo$3b2o11bobobo12bo2bo2bo9bo2bobo8bob2o15bobobo12bo3bo
11bo2bo11bobobo$2bo2bo16b2o11bobobo7b4o13b3obo17bo12bobo11b4o3bo$19b2o
28b4o12bo31bo17b4o14bobo$36b2obo10bo13bo2bobo15b2o12b2o15bo$50bo65bo7$
22bo80bo27bo$22bo2bo72bob2o29bo$6bo12bob3o11bobo13b2o16bobo10bobo14b4o
13bo2bo9b5obo11b2o$4bo2bo12b5o71bo3b3o13bo14bo13bo$5bo11bobo2b2obo10bo
12bobobo12bobobo10bobo13bo3bo13b4obo10bobobo11bobo$3bo3bo9bo15b2obobob
o8bo2bo2bo9bo4bo12bobo10b3o3bo10b4o3bo8bo5bo11bo3bo$3bo12b3obob2obo25b
obobo11bo13bo14b3obo14bo2bo12b2o12b5obo$bo3bo10b3obo14bo2b2o25bo2b5o8b
ob2o12b2o2bo13bobo16b2o11bo5bo$3b2o12bo5b2o27b2obo12b7o22b3o13bo34bob
2o$2b4o11bo51bo2bo9bo15bobobo12b2o$bob2obo62bo2bo24bo!

[synperiplanar]

Counterexample:

Code: Select all

x = 3, y = 3, rule = B3/S23Super
2.A$AD$A!

wait mb i lwk thought that said WITH a devote parent

[LuveelVoom]

Hook with tail:

Code: Select all

x = 10, y = 10, rule = B3/S23
3bobo$o2bobo$2b6o$ob3ob4o$o2b5o$2bo$o4bo$bobobo2$4bobo!

This actually has given me an idea to open a new frontier in the field of object devotion.

The large cluster of cells in the top left serves to insert one cell around a set of other cells. This is a sort of “component”, in a similar way to still life synthesis components. One can imagine a set of “devonents”, which edgily insert sets of cells; these can be combined to create the edges of some objects, as long as you can fit them all into the same space.

However… this is entirely irrelevant, as we have SAT solvers to find any devote parent anyway.

[I6_I6]

Curl:

Code: Select all

x = 12, y = 9, rule = B3/S23
4bo2b2o$5bo$ob2o3bobo$5bo$b2o4bobo$4b2obobo$ob10o$4bobo2bo$4bobo2bo!

It's fun to do these by hand.

EDIT:
Cis-barge with tail:

Code: Select all

x = 7, y = 6, rule = B3/S23
2bobobo$o2bo$obobobo$6bo$ob2o$5b2o!

Trans-barge with tail:

Code: Select all

x = 7, y = 8, rule = B3/S23
ob2o2$obobobo$o2bo$2bobobo$6bo2$5b2o!

[Rudyj]

Hook with tail:

Code: Select all

x = 10, y = 10, rule = B3/S23
3bobo$o2bobo$2b6o$ob3ob4o$o2b5o$2bo$o4bo$bobobo2$4bobo!

Here I found a simpler pattern:

Code: Select all

x = 10, y = 9, rule = B3/S23
8bo$2bob2obo$3b6o$o3b4obo$2bo$o2bobo$bo3bo2$4b2o!

[LuveelVoom]

Rudyj, could you elaborate on devote ancestry?

Which of these definitions is correct for a devote grandparent (in order of increasing strictness):
-No cell of the devote grandparent is on in the final pattern (the grandchild)
-No cell of the devote grandparent is on in its child, and its child is a devote parent of the final pattern, but the grandchild can have on cells that were on in the devote grandparent (Thus, phoenix 1 is a devote grandparent of itself)
-No cell of the devote grandparent ever turns on again in the evolution
-No cell of the devote grandparent ever turns on again in the evolution, and its child is a devote parent.

I might be missing one or two possible formulations here.

[Rudyj]

Dear LuveelVoom,

​I became fascinated with Conway's Life back when I was a schoolboy and did a lot of systematic work, but due to various circumstances, there was a nearly 30-year break. Only two months ago did I learn about this website and simulators like Golly. I dug up my old notebooks and realized that half of my research duplicated what was done before me, while the other half was independently discovered by others later and can be found on this site. Only the idea of Devote Parents, which came to me in 1997, remained undeveloped, so I recently shared it with everyone. I'm glad it piqued the interest of other researchers, though it is just an idea rather than a formal theory. I haven't looked deeper than one generation back, so feel free to define new rules for devote ancestors yourself!

​I would like to thank everyone who responded for their interest and for breathing new life into the notes in my yellowed old notebooks.

​Best regards,

Rudyj 

[Rudyj]

Here are the Devote Parents for some watercraft.
Canoe (17 cells):

Code: Select all

x = 9, y = 7, rule = B3/S23
3bobo2$4bobo$2bo3bo$2bob5o$o5bo$2b2obo!

Cis-boat with tail (25 cells):

Code: Select all

x = 10, y = 9, rule = B3/S23
8bo$4b2obo$2b7o$o3b4obo$obo$3bobo$bo3bo2$4b2o!

Long ship (52 cells):

Code: Select all

x = 12, y = 12, rule = B3/S23
5bobo$5bobo$4b5o$4b2obobo$2b3o3b4o$4o2bo2bo$2bo2bo2b4o$4o3b3o$2bobob2o
$3b5o$4bobo$4bobo!

The last one is really big, can someone reduce it?

[I6_I6]

Dear LuveelVoom,

​I became fascinated with Conway's Life back when I was a schoolboy and did a lot of systematic work, but due to various circumstances, there was a nearly 30-year break. Only two months ago did I learn about this website and simulators like Golly. I dug up my old notebooks and realized that half of my research duplicated what was done before me, while the other half was independently discovered by others later and can be found on this site. Only the idea of Devote Parents, which came to me in 1997, remained undeveloped, so I recently shared it with everyone. I'm glad it piqued the interest of other researchers, though it is just an idea rather than a formal theory. I haven't looked deeper than one generation back, so feel free to define new rules for devote ancestors yourself!

​I would like to thank everyone who responded for their interest and for breathing new life into the notes in my yellowed old notebooks.

​Best regards,

Rudyj 

I (and probably many others) would be very interested to know what else you have in your notebooks. Who knows, maybe you've independently discovered something before any other lifenthusiast knew about it!