We’ve tried evolving some random soups and we have seen a few still life patterns and some oscillator patterns.
Now let’s make our investigation more systematic. This is where we need to start thinking much more mathematically. Rather than starting with a random soup, we will start with the smallest patterns and work up.
Each time we add more live cells, we’ll think about how many different arrangements we can make. Then we’ll see how many generations it takes for the pattern to stabilise or die out.
A pattern with only one live cell is clearly doomed, it will die in the next generation. How about patterns with just 2 live cells. What will happen to them?
Can you have a doomed pattern with any number of live cells? How would you arrange the grid to make such a pattern doomed?
Let’s call a pattern that’s not certainly doomed, a useful pattern. These are the ones worth investigating.
Think of all the useful 3 cell patterns there can be. How many do you get? Are some of them actually the same pattern?
Try out the patterns to see which ones evolve into a still life or an oscillator.
Take the next logical step and move on to useful four cell patterns.