While John Conway’s Game of Life (a cellular automaton)
appears to be quite different from Milton Bradley’s Game of Life (a rather trite board game), there are a few
prevailing similarities. For instance, both represent scenarios where there is
a finite number of situations a player can occupy; both involve witnessing the
overall evolution of its players; and both can be considered “zero-player”
games, in the sense that Conway’s Game of Life requires no players and Milton
Bradley’s Game of Life should really
never have any players, especially if Klaus Teuber’s Settler’s of Catan is within easy reach. Dr. Ursula Whitcher,
Department of Math, focuses less on the comparison of complex mathematical
phenomenon to popular board games and more on just the mathematical phenomenon part
in her active learning activity featuring John Conway’s Game of Life:
Setting:
20-minute activity implemented in a 100-level course; 6 pods with 5 students
per pod
Purpose of the
activity: Students explore and discuss Conway's Game of Life using the
Google Easter egg, as displayed on pod computers.
Setup for the
activity: Googling Conway's Game of Life produces an implementation of the
cellular automaton "game." The
game can be paused and restarted.
How the activity
unfolded in the classroom: Groups explore different starting
configurations, trying to answer three questions:
- Can you make a pattern that stays the same for several seconds?
- Can you make a pattern that oscillates between a couple of states?
- Can you make a pattern that moves across the screen?
This activity leads into a discussion of the formal rules of
the "game."
After the activity:
Students use the formal rules of Conway's Game of Life on homework and exam
problems. Cellular automata are also a
possible example for a final exam essay.
Additional comments
from instructor: Other possible prompts to explore with this activity
include:
- Can you make a pattern that disappears/dies out?
- Can you guess some of the rules of the game?
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