Simple Rules \( \rightarrow \) Surprising Results

Computer Science Level 2

Conway's Game of Life is a simple algorithm that produces complex and often beautiful results. It is played on a grid and follows the rules below.

  • Any live cell with fewer than two live neighbors dies, simulating under-population.
  • Any live cell with two or three live neighbors lives on to the next generation.
  • Any live cell with more than three live neighbors dies, simulating overcrowding.
  • Any dead cell with exactly three live neighbors becomes a live cell, simulating reproduction.

If the image above is the first generation (where black cells are living), which of the following would be the second?

Details and assumptions

Every cell not on the edges of the grid has \( 8 \) neighbors: namely, any cell that is horizontally, vertically, or diagonally adjacent.

A generation constitutes one simultaneous application of the rules to every cell in the grid.


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