Life

What is Life?

This simulation is based on a game invented by mathematician John Horton Conway. Conway's Game of Life is an example of cellular automation where all cells' behavior on the grid are determined by a set of rules. The game board represents a community and each cell represents a community member. All members follow certain rules. In the game's original form, the rules are simple. If a community member has too many (meaning 4 or more) neighbors the member dies because of overcrowding. On the other hand if the member is too lonely (meaning one or less neighbors), it also dies. The last rule of the game is that if a community has the right environment (meaning exactly three neighbors) a baby community member will be born. This applet also has an added feature to make it easy to see the age of the community member - the color fades form red to blue (red being young member and blue an older member).

The original rules are set as default in this simulation. However, the user can change these settings in order to explore other patterns.

Controls and Output

  • Start: This button is at the top of the applet and begins running the applet. The button becomes Stop once the applet begins.
  • Stop: This button appears when the applet is running. When pressed, the cycle stops. The button becomes Start once the applet stops.
  • Step: This button allows the user to run one cycle at a time. This is useful to help students understand where the births and deaths occur each time.
  • Clear: This button clears the display grid and allows you to start a new trial.
  • Randomize: This button selects a random percentage of people to randomly distribute throughout the display screen.
  • Min Delay Between Iterations: This slider is located at the bottom of the applet display. By sliding the marker to the left, the time between cycles is reduced while sliding the marker to the right increases the time between cycles.
  • Pattern List: This option is located in the top most menu of the applet (in some browsers on the Macintosh, this option appears in the browser's menu bar at the top of your screen). Selecting it gives you a pull down menu of small, medium, large, very large, and huge patterns. Under each size pattern is a list of patterns in that category. Once a pattern has been selected, the user can click anywhere on the display to add persons in the chosen pattern. Students should play with various patterns and should observe their behaviors.
  • Game Setup: This option is also located in the top most menu of the applet (in some browsers on the Macintosh, this option appears in the browser's menu bar at the top of your screen). The pull down menu presents the user with four options:
    1. Change Rules: This option allows you to change whether a person lives or dies and whether a new person is born when the original has zero through eight neighbors.
    2. Change World Size: This option allows you to change the grid size. Remember, larger grids run slower.
    3. World Wraps: By selecting world wrap, you chose for the grid to wrap around the sides. By deselecting this option, puts walls up on all sides (like an island.)
    4. Colorize Cells: This option allows you to chose whether you would like the red and blue colored cells or whether you would like just plain white. Red cells are alive and fade to blue to indicate death.
  • Help: The help menu also appears in the top most menu of the applet (in some browsers on the Macintosh, this option appears in the browser's menu bar at the top of your screen). This menu allows the user to open the "What", "How", and "Why" pages.

Description

This activity allows the user to simulate a game that imitates real life. This activity would work well in mixed ability groups of three to five for about forty-five to fifty minutes if you use the exploration questions and fifteen to twenty minutes otherwise.

Place in Mathematics Curriculum

This activity can be used to:

  • demonstrate randomness
  • motivate the ideas of chaos
  • introduce the idea of order/patterns in chaos

Standards Addressed

Statistics and Probability

  • Making Inferences and Justifying Conclusions

    • Understand and evaluate random processes underlying statistical experiments
    • Make inferences and justify conclusions from sample surveys, experiments, and observational studies

  • Using Probability to Make Decisions

    • Use probability to evaluate outcomes of decisions

7th Grade

  • Data Analysis and Probability

    • The student will demonstrate through the mathematical processes an understanding of the relationships between two populations or samples.

8th Grade

  • Probability and Statistics

    • 8.11 The student will analyze problem situations, including games of chance, board games, or grading scales, and make predictions, using knowledge of probability.
    • 8.11 The student will analyze problem situations, including games of chance, board games, or

Be Prepared to

  • answer the question "How can there be order in chaos; isn't that the opposite of the definition ofchaos?"
  • discuss the idea of chaos