Spaceship Collides
The universe of the Game of Life is an infinite two-dimensional grid of square cells, each of which is in one of two possible states, alive or dead. Every cell interacts with its eight neighbors, which are the cells that are horizontally, vertically, or diagonally adjacent. At each step in time, the following transitions occur:
- Any live cell with fewer than two live neighbours dies, as if caused by under-population.
- Any live cell with two or three live neighbours lives on to the next generation.
- Any live cell with more than three live neighbours dies, as if by over-population.
- Any dead cell with exactly three live neighbours becomes a live cell, as if by reproduction.
Here are the two famous "spaceships" pattern which can "move"
Below is the initial configuration of the two spaceships. Will they collide after a finite number of iterations?
Details and Assumptions
- Despite the image, imagine it as an infinite grid.
- Collide means that at least one live cell in a spaceship is a neighbor of the other spaceship's live cell.
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1 solution
From looking at the two spaceship patters, the smaller spaceship moves one square right one square down every 4 step cycles. The larger one moves two squares right every 4 step cycles. After or about 5 such 4 step cycles, they collide.