Think Complexity, 2nd Edition

Chapter 6. Game of Life

In this chapter we consider two-dimensional cellular automatons, especially John Conway’s Game of Life (GoL). Like some of the 1-D CAs in the previous chapter, GoL follows simple rules and produces surprisingly complicated behavior. And like Wolfram’s Rule 110, GoL turns out to be universal; that is, it can compute any computable function, at least in theory.

Complex behavior in GoL raises issues in the philosophy of science, particularly related to scientific realism and instrumentalism. I discuss these issues and suggest additional reading.

At the end of the chapter, I demonstrate ways to implement GoL efficiently in Python.

Conway’s GoL

One of the first cellular automatons to be studied, and probably the most popular of all time, is a 2-D CA called “The Game of Life”, or GoL for short. It was developed by John H. Conway and popularized in 1970 in Martin Gardner’s column in Scientific American. See https://thinkcomplex.com/gol.

The cells in GoL are arranged in a 2-D grid, that is, an array of rows and columns. Usually the grid is considered to be infinite, but in practice it is often “wrapped”; that is, the right edge is connected to the left, and the top edge to the bottom.

Each cell in the grid has two states—live and dead—and 8 neighbors—north, south, east, west, and the four diagonals. This set of neighbors is sometimes called a “Moore neighborhood”.

Like the 1-D CAs in the previous chapters, GoL evolves over time according to rules, which are like simple ...