Minesweeper meets Life (puzzle)

[Macbi]

I have a starting pattern. If I apply the rule S0/B2 I get this pattern:



If I apply the rule S01/B3 I get this pattern:



What pattern did I start with?

I think this puzzle is not too easy, not too hard. It has a unique answer.

[apg]

The solution: (RLE encoded to avoid spoilers)

Code: Select all

x = 11, y = 8, rule = B3/S01
9bo$3bo4bo$3bo6bo$$ooboboo$$3bo$3bo!

I've encountered Minesweeper-like puzzles in Life when trying to stabilise still-lifes or drifter searcher results.

[Extrementhusiast]

A new puzzle:
B35/S24 with 2 gens:

Code: Select all

..O.O..
....O..
...OO..
O.OOOOO
....O.O
..OOOOO
...O.O.
...OO..

B36/S125 (2x2) with 3 gens:

Code: Select all

O.O...
O.....
....O.
.....O
......
OO...O
O...O.
O.....
O.O...

What did I start with?

Hint: The answer is three times the number that is midway between the two numbers, each of whom has a rectangle with that area and perimeter. Confused? The number 8, for instance, in a 2x4 rectangle, has area 8 but perimeter 12. A 2x2 rectangle has perimeter 8 but area 4. Find two rectangles where their perimeters equal their respective areas, note their numbers, add them up, then divide by two.

Further hint: (1=on, 0=off, code solutions into binary)

Code: Select all

4*7
5*4
7*3
11+6
37-8
x+x=x*x=solution
56/2

[Macbi]

Further hint: (1=on, 0=off, code solutions into binary)

Code: Select all

4*7
5*4
7*3
11+6
37-8
x+x=x*x=solution
56/2

That is a weird way to write a number.

Code: Select all

x = 5, y = 7, rule = B3/S23
3o$obo$obobo$o3bo$3obo$2bo$3o!