Wolfram codeWolfram code is a widely used numbering system for one-dimensional cellular automaton rules, introduced by Stephen Wolfram in a 1983 paper and popularized in his book A New Kind of Science. The code is based on the observation that a table specifying the new state of each cell in the automaton, as a function of the states in its neighborhood, may be interpreted as a k-digit number in the S-ary positional number system, where S is the number of states that each cell in the automaton may have, k = S2n + 1 is the number of neighborhood configurations, and n is the radius of the neighborhood.
Rule 110The Rule 110 cellular automaton (often called simply Rule 110)is an elementary cellular automaton with interesting behavior on the boundary between stability and chaos. In this respect, it is similar to Conway's Game of Life. Like Life, Rule 110 with a particular repeating background pattern is known to be Turing complete. This implies that, in principle, any calculation or computer program can be simulated using this automaton. In an elementary cellular automaton, a one-dimensional pattern of 0s and 1s evolves according to a simple set of rules.
Rule 90In the mathematical study of cellular automata, Rule 90 is an elementary cellular automaton based on the exclusive or function. It consists of a one-dimensional array of cells, each of which can hold either a 0 or a 1 value. In each time step all values are simultaneously replaced by the exclusive or of their two neighboring values. call it "the simplest non-trivial cellular automaton", and it is described extensively in Stephen Wolfram's 2002 book A New Kind of Science.
Cellular automatonA cellular automaton (pl. cellular automata, abbrev. CA) is a discrete model of computation studied in automata theory. Cellular automata are also called cellular spaces, tessellation automata, homogeneous structures, cellular structures, tessellation structures, and iterative arrays. Cellular automata have found application in various areas, including physics, theoretical biology and microstructure modeling. 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).
Stephen WolframStephen Wolfram (ˈwʊlfrəm ; born 29 August 1959) is a British-American computer scientist, physicist, and businessman. He is known for his work in computer science, mathematics, and theoretical physics. In 2012, he was named a fellow of the American Mathematical Society. He is currently an adjunct professor at the University of Illinois Department of Computer Science. As a businessman, he is the founder and CEO of the software company Wolfram Research where he works as chief designer of Mathematica and the Wolfram Alpha answer engine.
Rule 184Rule 184 is a one-dimensional binary cellular automaton rule, notable for solving the majority problem as well as for its ability to simultaneously describe several, seemingly quite different, particle systems: Rule 184 can be used as a simple model for traffic flow in a single lane of a highway, and forms the basis for many cellular automaton models of traffic flow with greater sophistication. In this model, particles (representing vehicles) move in a single direction, stopping and starting depending on the cars in front of them.
Rule 30Rule 30 is an elementary cellular automaton introduced by Stephen Wolfram in 1983. Using Wolfram's classification scheme, Rule 30 is a Class III rule, displaying aperiodic, chaotic behaviour. This rule is of particular interest because it produces complex, seemingly random patterns from simple, well-defined rules. Because of this, Wolfram believes that Rule 30, and cellular automata in general, are the key to understanding how simple rules produce complex structures and behaviour in nature.
Conway's Game of LifeThe Game of Life, also known simply as Life, is a cellular automaton devised by the British mathematician John Horton Conway in 1970. It is a zero-player game, meaning that its evolution is determined by its initial state, requiring no further input. One interacts with the Game of Life by creating an initial configuration and observing how it evolves. It is Turing complete and can simulate a universal constructor or any other Turing machine.
Turing completenessIn computability theory, a system of data-manipulation rules (such as a model of computation, a computer's instruction set, a programming language, or a cellular automaton) is said to be Turing-complete or computationally universal if it can be used to simulate any Turing machine (devised by English mathematician and computer scientist Alan Turing). This means that this system is able to recognize or decide other data-manipulation rule sets. Turing completeness is used as a way to express the power of such a data-manipulation rule set.
