Lab 4: The Game of Life: One of Eight Rule
Take a piece of graph paper (the smaller the squares, the more fun you will have!) and shade in a single square in the middle of the page. This is stage 0.
To acheive stage 1, shade every square on the paper that has one and only one shaded neighbor. Any square that is already shaded in this construction will remain shaded forever, so the center square remains shaded.
Continue in this fashion, at each stage shading only boxes that have exactly one shaded neighbor (hence the title "one of eight"), retaining all squares that have been shaded in previous stages. The first five stages are given in the figures belows.
See how far you can take this. Your assignment is to complete a minimum of 15 stages. Be careful, it is not obvious how this develops and evolves. You have to watch to make sure that you are shading neither too many nor too few squares. How does the pattern develop? What interesting features of the pattern impress you?
Check out stage 15 and stage 46!
