cellularautomata

Cellular automata are a class of computational models that consist of a grid of cells, each in one of a finite number of states. The grid is typically one-dimensional or two-dimensional, but can be of any finite dimension. The state of each cell evolves over discrete time steps according to a fixed rule. This rule is applied to every cell in the grid simultaneously, based on the states of its neighboring cells. The set of cells that influence a cell's next state is called its neighborhood. Common neighborhood definitions include the Von Neumann neighborhood, which includes the cells directly above, below, left, and right, and the Moore neighborhood, which includes all eight adjacent cells.

The rules of a cellular automaton are often expressed as a lookup table. For a binary cellular automaton with a given neighborhood size, there are a finite number of possible configurations of neighboring cells, and for each configuration, the rule specifies whether the central cell will be in state 0 or state 1 in the next time step. A famous example is Conway's Game of Life, a two-dimensional cellular automaton where cells can be "alive" (state 1) or "dead" (state 0). The rules govern how live cells reproduce, survive, or die based on the number of their living neighbors, leading to complex emergent patterns.

Cellular automata have found applications in a variety of fields, including physics, biology, computer science, and art. They are used to model phenomena such as fluid dynamics, crystal growth, population dynamics, and pattern formation. Their simplicity, combined with their capacity for generating complex behavior from simple rules, makes them a powerful tool for exploring emergent properties and computational universality. Despite their simple underlying mechanism, cellular automata can exhibit highly intricate and unpredictable behavior, making them a subject of ongoing research and fascination.