Cellular Automata in Popular Culture

Cellular Automata In Popular Culture

A cellular automaton (pl. cellular automata, abbrev. CA) is a discrete model studied in computability theory, mathematics, physics, complexity science, theoretical biology and microstructure modeling. Cellular automata (plural of automaton) are also called cellular spaces, tessellation automata, homogeneous structures, cellular structures, tessellation structures, and iterative arrays.

A cellular automaton consists of a regular grid of cells, each in one of a finite number of states, such as on and off (in contrast to a coupled map lattice). The grid can be in any finite number of dimensions. For each cell, a set of cells called its neighborhood (usually including the cell itself) is defined relative to the specified cell. An initial state (time t=0) is selected by assigning a state for each cell. A new generation is created (advancing t by 1), according to some fixed rule (generally, a mathematical function) that determines the new state of each cell in terms of the current state of the cell and the states of the cells in its neighborhood. Typically, the rule for updating the state of cells is the same for each cell and does not change over time, and is applied to the whole grid simultaneously, though exceptions are known, such as the probabilistic cellular automata and asynchronous cellular automaton.

The concept was originally discovered in the 1940s by Stanislaw Ulam and John von Neumann while they were contemporaries at Los Alamos National Laboratory. While studied some throughout the 1950s and 1960s, it was not until the 1970s and Conway's Game of Life, a two-dimensional cellular automaton, that interest in the subject expanded beyond academia. In the 1980s, Stephen Wolfram engaged in a systematic study of one-dimensional cellular automata, or what he calls elementary cellular automata; his research assistant Matthew Cook showed that one of these rules is Turing-complete. Wolfram published A New Kind of Science in 2002, claiming that cellular automata have applications in many fields of science. These include computer processors and cryptography.

The primary classifications of cellular automata as outlined by Wolfram are numbered one to four. They are, in order, automata in which patterns generally stabilize into homogenity, automata in which patterns evolve into mostly stable or oscillating structures, automata in which patterns evolving in a seemingly chaotic fashion, and automata in which patterns become extremely complex and may last for a long time, with stable local structures. This last class are thought to be computationally universal, or capable or simulating a Turing machine. Special types of cellular automata are those which are reversible, in which only a single configuration leads directly to a subsequent one, and totalistic, in which the future value of individual cells depend on the total value of a group of neighboring cells. Cellular automata can simulate a variety of real-world systems, including biological and chemical ones. There has been speculation that cellular automata may be able to model reality itself.