The game of life: some answers
Here are some answers to the questions posed in the classroom activity on the game of life.
- Diagonal lines of any length always die out.
- Examples of simple initial patterns that always remain the same are the block of four, the "beehive" and the "loaf".
From left to right: the block of four, the beehive and the loaf.
- Example of patterns that oscillate with aperiod two are the "blinker", the "toad" and the "beacon".
From left to right: blinker, the toad and the beacon.
- Generally, it appears that patterns eventually settle down on some "stable" configuration with components that oscillate between a small number of patterns. Few initial configurations die out. Sub-components tend to develop some symmetry which does not disappear.