Conways' Game of Life is a well known cellular automaton "played" on an infinite grid, filled with cells that are either alive or dead. Once given an initial state, the board evolves according to rules indefinitely. Those rules are:
- Any live cell with 2 or 3 living neighbours (the 8 cells immediately around it) lives to the next state
- Any dead cell with exactly 3 living neighbours becomes a living cell
- Any other cell becomes a dead cell
Let \$B_i\$ be the board state at the \$i\$th step, beginning with \$B_0\$ as the starting configuration, before any of the evolution rules are applied. We then define a "fixed board" to be a board state \$B_i\$ such that there is a board state \$B_j\$, with \$j > i\$, such that \$B_i = B_j\$ (that is, all cells in both boards are identical). In other words, if a board state is ever repeated during the evolution of the board, it is a fixed board.
Due to the nature of Game of Life, this definition means that a "fixed board" is either constant, or the only evolution is a fixed periodic set of states.
For example, the following board states are fixed, as \$B_{217} = B_{219}\$, where \$B_{217}\$ is the left board:
The left board state happened to be the 217th generation of this starting state, taken from this challenge.
Note that the empty board is a fixed board, and that any patterns of infinite growth, or spaceship like patterns can never result in a fixed board.
This is an answer-chaining challenge where each answer is a starting state, and the number of generations it takes to reach a fixed board must be strictly larger than the previous answer.
The \$n\$th answer should be a starting configuration of cells within an \$n \times n\$ bounding box such that, if the \$n-1\$th answer took \$p_{n-1}\$ generations to reach a fixed board, the \$n\$th answer takes \$p_n > p_{n-1}\$ generations to reach a fixed board. Note that the "number of generations" is defined as the lowest \$i\$ such that \$B_i\$ is a fixed board. For example, the empty board takes \$0\$ generations, as \$B_0\$ is already a fixed board.
Each answer's score is \$i\$, the number of generations to a fixed board.
I have posted the starting answer, for \$n = 2\$, with \$p = 1\$, below.
Rules
- You must wait an hour between posting two answers
- You may not post two answers in a row
- You can edit your answer at any point to change its score. However, keep in mind the following:
- If your answer is the latest, people may be working on a follow-up answer, so changing yours may invalidate their attempt
- If your answer is in the middle of the chain, you may edit it to any score, so long as it is within the bounds of the previous and later answers.
- The answer with the highest score (i.e. the latest) at any given point in time is the winner
bo2b3o4b2o$o9bobo3bo$o4bo6bo3b2o$5o4bo5bobo$8b2o$8b2o$9b2o$6bo3b2o6b2o$5bobobo2b2o3bobo$6bo4b3o5bo$b2o13bo$3o5bo6b2o$2o4bo2bo$4o2bo2bo$2o5bo$o$o$2obo9bob3o$2bo9b3o$13b5o!
\$\endgroup\$