Game Of Life

This week we're going to get introduced to simulation as a means of experimentation and exploration. We are also going to consider the concept of emergent behavior —- what it is and how it comes to be. Finally, we are going to get our hands dirty a little bit by playing with Conway's "Game of Life." This should provide us with insight into both of the above topics and set the stage for more complex techniques and approaches that we will explore later in the semester.


  1. Read Gardner's Scientific American article on "Life". The version in your coursepack is from the book Wheels, Life, and other Mathematical Amusements by Martin Gardner, 1983 (10th printing), W.H. Freeman & Co. This is a slightly updated version from that which appeared in Scientific American in 1970. This is the article that introduced the game to a wider audience. This is like a snap shot of another world that existed before the home computer. And it also provides insight into the people who find this sort of thing fascinating (that set would certainly include me).
  2. Read the "What is the Game of Life?" web site and try out some patterns for yourself. This article provides a very nice introduction to the Game of Life. In addition to describing its intricacies, it also provides both a blank Life grid that allows you to set up your own Game and a set of pre-defined patterns that you can watch evolve.
  3. Look through the "Game of Life exhibit" web site. This provides some nice examples of just what can be done within the simple rules of Life. Be sure to look in the Pattern Collection under "Rakes and Breeders" and "Ships and Trains" —- but don't stop there because there are lots more interesting things to look at.
  4. Download and become familiar with Golly, "an open-source, cross-platform application for exploring Conway's Game of Life and other cellular automata."
  5. On your personal page create a list of three of your favorite life patterns. You'll have an opportunity to show them in class.
  6. Play with a probabilistic version of the GoL:
    • Probabilistic Life: This is the version that I find to be the most compelling and interesting. It's very much in the spirit of what Conway did, and is probably what he would have done if he could have designed the game assuming everyone had powerful computers at their disposal. (Remember, this was designed as a recreactional mathematics game.)
    • 3D Game of Life: A three-dimensional Game of Life. This has the same types of rules but instead of eight neighbors, these players can have twenty-six neighbors. Be sure to "grab" one of the balls (by clicking down on it) and spin the game around to get different views of it. I find that this version is hard to get any intuition about.
    • Another 3D Game of Life: This one is a bit more difficult to play than the above but I found it more interesting overall.
  7. Look through a smattering of the other web sites in Background for the Game of Life

Background for the Game of Life

You are not required (or even expected) to refer to the following resources; however, you might find them interesting and useful if you are going to continue exploring this topic.

  1. GoL objects
    • Most seen "Game of Life" objects: Provides a vocabulary that you can use when talking about recurring patterns that you see in the GoL
    • Tons of information about objects, etc.: Be sure to look under the "Object lists" portion of the page. Each set of items provides a different way of grouping GoL objects. Consider the page "Oscillators and pseudo-oscillators". Click on any of the pictures in the page. This will bring up a Web page containing some strange code. This is RLE data. This can be saved to a file and then loaded into a Life program (such as Golly). You can run this game and see what evolves.
    • GoL status page: Describes what is know about objects in the GoL. Similar information to that shown in the previous resource but organized in a different manner.
    • Browsable pattern catalog and other information
  2. Rendell's Web page describing this specific Turing Machine: This basically tells us that the rules that define the GoL aren't just interesting — they're sufficiently complex that they can (in theory, and probably in theory only) be used to compute anything that can be computed.
  3. Hacker Emblem: Eric S. Raymond has proposed that the glider be the emblem representing the entire hacker community.
  4. Spacefillers
  5. Wheels, Life, and other Mathematical Amusements, by Martin Gardner, W.H. Freeman and Company, Chapters 20-22, pp.\ 214-57.
  6. Poundstone's The Recursive Universe: Cosmic complexity and the limits of scientific knowledge, NTC/Contemporary Publishing, 1985. A wonderful book about Life and all that can be learned about physics and knowledge by applying its lessons.
  7. Slides for the class
  8. The Cellular Automaton Programming Paradigm

Questions to consider

You should prepare notes (for yourself) for class discussion. I want us to have an informed discussion during this first class. In later classes we will also have formal presentations; however, in this one I simply want to have a discussion

  1. What is the Game of Life?
  2. How do the individual cells in a GoL evolve?
  3. What causes the complexity of GoLs to appear?
  4. Is the GoL deterministic or stochastic? Whatever you answered, what changes to the game rules would change your answer?
  5. What is meant by an "emergent phenomena"? Give an example from the GoL.
  6. What type of (simplified) social processes might be modelled by the GoL?
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