Four rules, walking shapes

Each square is alive or dead. At every tick, each one looks at its eight neighbours:

1. A live cell with fewer than two live neighbours dies, of loneliness.
2. A live cell with two or three live neighbours survives.
3. A live cell with more than three live neighbours dies, of crowding.
4. A dead cell with exactly three live neighbours comes alive.

Click or drag on the grid to bring cells to life. Start with the glider: five cells that shift their shape every tick and, every four ticks, reappear exactly as before, one square further along the diagonal. Nothing in the rules mentions movement, yet the glider moves.