RJ Honicky
Evolutionary Game Theory
CMPS 272
Winter 2002
Stick Wars Cellular Automata
The Algorithm
Stick Wars is a complex Cellular Automata which is descendant from Connway's Game of Life. Like Life, Stick Wars is played on a rectangular playing area, and like Life, the birth and survival of a player at a particular location is determined by the number of immediate neighbors that a player has.
In Life, a new player is born if it has exactly 3 immediate neighbors, and it survives if it has no less that 2, and no more than 3 neighbors. If we denote the (precise) number of neighbors that a player must have to be born as B and the (precise) number of neighbors that a player must have to survive as S, then we can denote a "Life-like" game as (B/S). For example, Life itself would be denoted by (3/2,3).
Stick Wars is actually the combination of two different "Life-like" games: Sticks, and Star Wars. Sticks is denoted by (2/3,4,5,6), meaning that a new player is born when it has exactly two neighbors, and it survives unless it has only 1, or more than 6 neighbors. Star Wars is denoted by (2/3,4,5).
 |  |
| Sticks | Star Wars |
| Some rudimentary transitions for some shapes in Sticks and Star Wars |
Sticks and Star Wars are combined together by playing a certain number of rounds on the board using the Sticks rules, and then playing a certain number of rounds of Star Wars on the same board. The number of iterations of each game is variable. We can use the "*" operator to indicate that we should iterate a game a certain number of times. For example, if we are to iterate Sticks 8 times, then we can denote that as 8*(2/3,4,5,6). We can use the "+" operator to indicate playing a certain game followed by another. Thus a game of Stick Wars which iterates Sticks 7 times for every 3 games of Star Wars would be denoted as 7*(2/3,4,5,6) + 3*(2/3,4,5).
As a further complication, Stick Wars is also a Cyclic Celluar Automata, meaning that the cells cycle through various states. Each state is represented by a different color. A cell can be promoted to the next state only if "it sees sufficent representation of that next color within its prescribed local neighborhood" (See the link above). A cell dies when it is premoted a final time.
Is Stick Wars a Game?
Both Sticks and Star Wars are games with competition between players, just as Life is. Like Life, both games simulate the competition for resources, since a "neighborhood" of cells can not support more than 6 or 5 players respectively. If there are too many cells in a neighborhood, then some of the players "starve". If there are too few, then some of them get lonely and die. Also, there must be an ideal environment for a birth to take place, since if there are too many neighbors (ie. more than 2) or too few (ie less than 2), then the players can not reproduce. Thus a player can only produce offspring in the event that there are sufficient resources to be had, and there is an appropriate mate.
Seasons provide one interpretation of alternating between Sticks and Star Wars rules. In other words, by alternating between the two rules, we simulate different environments, some of which are more favorable for survival than others. Following this analogy, Star Wars would correspond to Winter, since there are fewer resources available. Stick wars on (non-tropical) Earth might be represented by 3*(2/3,4,5,6) + (2/3,4,5).
References