Difference between revisions of "Cellular Automaton"
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| − | Cellular automatons are mathematical models used to create complicated systems using simple rules. They are usually in the format of a grid, and each "cell" in the grid, i.e. 4 adjacent lattice points that make a square, has 2 states. Over time, each cell follows special rules based on what cells are surrounding it that determine its state. These rules determine what the cellular automaton acts like. | + | '''Cellular automatons''' are mathematical models used to create complicated systems using simple rules. They are usually in the format of a grid, and each "cell" in the grid, i.e. 4 adjacent lattice points that make a square, has 2 states. Over time, each cell follows special rules based on what cells are surrounding it that determine its state. These rules determine what the cellular automaton acts like. |
| − | An example of | + | An example of this is Conway's Game of Life. |
| − | + | * Each cell is either in the state of "dead" or "alive". | |
| − | + | * In each generation, the following rules are followed to determine a cell's state: | |
| − | + | * A live cell with fewer than 2 living cells (including touching by corners) dies. | |
| − | + | * A live cell with 2 or 3 live neighbors stays alive. | |
| − | + | * A live cell with 4 live neighbors dies. | |
| − | + | * A dead cell with exactly 3 living neighbors comes to life. | |
Though cellular automatons follow simple rules, they are Turing-complete and can be used as computers. | Though cellular automatons follow simple rules, they are Turing-complete and can be used as computers. | ||
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Latest revision as of 14:30, 15 February 2025
Cellular automatons are mathematical models used to create complicated systems using simple rules. They are usually in the format of a grid, and each "cell" in the grid, i.e. 4 adjacent lattice points that make a square, has 2 states. Over time, each cell follows special rules based on what cells are surrounding it that determine its state. These rules determine what the cellular automaton acts like.
An example of this is Conway's Game of Life.
- Each cell is either in the state of "dead" or "alive".
- In each generation, the following rules are followed to determine a cell's state:
- A live cell with fewer than 2 living cells (including touching by corners) dies.
- A live cell with 2 or 3 live neighbors stays alive.
- A live cell with 4 live neighbors dies.
- A dead cell with exactly 3 living neighbors comes to life.
Though cellular automatons follow simple rules, they are Turing-complete and can be used as computers.
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