In computability theory, a system of data-manipulation rules is said to be Turing-complete or computationally universal if it can be used to simulate any Turing machine. This means that this system is able to recognize or decode other data-manipulation rule sets. Turing completeness is used as a way to express the power of such a data-manipulation rule set. Virtually all programming languages today are Turing-complete.
The 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.
A cellular automaton 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.
Langton's ant is a two-dimensional Turing machine with a very simple set of rules but complex emergent behavior. It was invented by Chris Langton in 1986 and runs on a square lattice of black and white cells. The idea has been generalized in several different ways, such as turmites which add more colors and more states.
The Rule 110 cellular automaton 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.
A cellular automaton (CA) is Life-like if it meets the following criteria:
The glider is a pattern that travels across the board in Conway's Game of Life. It was first discovered by Richard K. Guy in 1969, while John Conway's group was attempting to track the evolution of the R-pentomino. Gliders are the smallest spaceships, and they travel diagonally at a speed of one cell every four generations, or . The glider is often produced from randomly generated starting configurations.
In a cellular automaton, a Garden of Eden is a configuration that has no predecessor. It can be the initial configuration of the automaton but cannot arise in any other way. John Tukey named these configurations after the Garden of Eden in Abrahamic religions, which was created out of nowhere.
In computer science, a turmite is a Turing machine which has an orientation in addition to a current state and a "tape" that consists of an infinite two-dimensional grid of cells. The terms ant and vant are also used. Langton's ant is a well-known type of turmite defined on the cells of a square grid. Paterson's worms are a type of turmite defined on the edges of an isometric grid.
Codd's cellular automaton is a cellular automaton (CA) devised by the British computer scientist Edgar F. Codd in 1968. It was designed to recreate the computation- and construction-universality of von Neumann's CA but with fewer states: 8 instead of 29. Codd showed that it was possible to make a self-reproducing machine in his CA, in a similar way to von Neumann's universal constructor, but never gave a complete implementation.
A block cellular automaton or partitioning cellular automaton is a special kind of cellular automaton in which the lattice of cells is divided into non-overlapping blocks and the transition rule is applied to a whole block at a time rather than a single cell. Block cellular automata are useful for simulations of physical quantities, because it is straightforward to choose transition rules that obey physical constraints such as reversibility and conservation laws.
Langton's loops are a particular "species" of artificial life in a cellular automaton created in 1984 by Christopher Langton. They consist of a loop of cells containing genetic information, which flows continuously around the loop and out along an "arm", which will become the daughter loop. The "genes" instruct it to make three left turns, completing the loop, which then disconnects from its parent.
A rake, in the lexicon of cellular automata, is a type of puffer train, which is an automaton that leaves behind a trail of debris. In the case of a rake, however, the debris left behind is a stream of spaceships, which are automata that "travel" by looping through a short series of iterations and end up in a new location after each cycle returns to the original configuration.
John von Neumann's universal constructor is a self-replicating machine in a cellular automaton (CA) environment. It was designed in the 1940s, without the use of a computer. The fundamental details of the machine were published in von Neumann's book Theory of Self-Reproducing Automata, completed in 1966 by Arthur W. Burks after von Neumann's death. It is regarded as foundational for automata theory, complex systems, and artificial life. Indeed, Nobel Laureate Sydney Brenner considered Von Neumann's work on self-reproducing automata central to biological theory as well, allowing us to "discipline our thoughts about machines, both natural and artificial."
In 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 XOR of their two neighboring values. Martin, Odlyzko & Wolfram (1984) call it "the simplest non-trivial cellular automaton", and it is described extensively in Stephen Wolfram's 2002 book A New Kind of Science.
Life without Death is a cellular automaton, similar to Conway's Game of Life and other Life-like cellular automaton rules. In this cellular automaton, an initial seed pattern grows according to the same rule as in Conway's Game of Life; however, unlike Life, patterns never shrink. The rule was originally considered by Toffoli & Margolus (1987), who called it "Inkspot"; it has also been called "Flakes". In contrast to the more complex patterns that exist within Conway's Game of Life, Life without Death commonly features still life patterns, in which no change occurs, and ladder patterns, that grow in a straight line.
Norman H. Margolus is a Canadian-American physicist and computer scientist, known for his work on cellular automata and reversible computing. He is a research affiliate with the Computer Science and Artificial Intelligence Laboratory at the Massachusetts Institute of Technology.
A reversible cellular automaton is a cellular automaton in which every configuration has a unique predecessor. That is, it is a regular grid of cells, each containing a state drawn from a finite set of states, with a rule for updating all cells simultaneously based on the states of their neighbors, such that the previous state of any cell before an update can be determined uniquely from the updated states of all the cells. The time-reversed dynamics of a reversible cellular automaton can always be described by another cellular automaton rule, possibly on a much larger neighborhood.
Artificial life is a field of study wherein researchers examine systems related to natural life, its processes, and its evolution, through the use of simulations with computer models, robotics, and biochemistry. The discipline was named by Christopher Langton, an American theoretical biologist, in 1986. In 1987, Langton organized the first conference on the field, in Los Alamos, New Mexico. There are three main kinds of alife, named for their approaches: soft, from software; hard, from hardware; and wet, from biochemistry. Artificial life researchers study traditional biology by trying to recreate aspects of biological phenomena.
LifeWiki is a wiki dedicated to Conway's Game of Life. It hosts over 2000 articles on the subject and a large collection of Life patterns stored in a format based on run-length encoding that it uses to interoperate with other Life software such as Golly.
