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Rule 110
The 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. Definition In an elementary cellular automaton, a one-dimensional pattern of 0s and 1s evolves according to a simple set of rules. Whether a point in the pattern will be 0 or 1 in the new generation depends on its current value, as well as on those of its two neighbors. The Rule 110 automaton has the following set of rules: The name "Rule 110" derives from the fact that this rule can be summarized in the binary sequence 01101110; interpreted as a binary number, this corresponds to the decimal value 110. History In 2004, Matthew Cook published a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elementary Cellular Automaton
In mathematics and computability theory, an elementary cellular automaton is a one-dimensional cellular automaton where there are two possible states (labeled 0 and 1) and the rule to determine the state of a cell in the next generation depends only on the current state of the cell and its two immediate neighbors. There is an elementary cellular automaton ( rule 110, defined below) which is capable of universal computation, and as such it is one of the simplest possible models of computation. The numbering system There are 8 = 23 possible configurations for a cell and its two immediate neighbors. The rule defining the cellular automaton must specify the resulting state for each of these possibilities so there are 256 = 223 possible elementary cellular automata. Stephen Wolfram proposed a scheme, known as the Wolfram code, to assign each rule a number from 0 to 255 which has become standard. Each possible current configuration is written in order, 111, 110, ..., 001, 000, and the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Turing Machine
A Turing machine is a mathematical model of computation describing an abstract machine that manipulates symbols on a strip of tape according to a table of rules. Despite the model's simplicity, it is capable of implementing any computer algorithm. The machine operates on an infinite memory tape divided into discrete cells, each of which can hold a single symbol drawn from a finite set of symbols called the alphabet of the machine. It has a "head" that, at any point in the machine's operation, is positioned over one of these cells, and a "state" selected from a finite set of states. At each step of its operation, the head reads the symbol in its cell. Then, based on the symbol and the machine's own present state, the machine writes a symbol into the same cell, and moves the head one step to the left or the right, or halts the computation. The choice of which replacement symbol to write and which direction to move is based on a finite table that specifies what to do for each com ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nature (journal)
''Nature'' is a British weekly scientific journal founded and based in London, England. As a multidisciplinary publication, ''Nature'' features peer-reviewed research from a variety of academic disciplines, mainly in science and technology. It has core editorial offices across the United States, continental Europe, and Asia under the international scientific publishing company Springer Nature. ''Nature'' was one of the world's most cited scientific journals by the Science Edition of the 2019 '' Journal Citation Reports'' (with an ascribed impact factor of 42.778), making it one of the world's most-read and most prestigious academic journals. , it claimed an online readership of about three million unique readers per month. Founded in autumn 1869, ''Nature'' was first circulated by Norman Lockyer and Alexander Macmillan as a public forum for scientific innovations. The mid-20th century facilitated an editorial expansion for the journal; ''Nature'' redoubled its efforts in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rule 184
Rule 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. The number of particles remains unchanged throughout the simulation. Because of this application, Rule 184 is sometimes called the "traffic rule". * Rule 184 also models a form of deposition of particles onto an irregular surface, in which each local minimum of the surface is filled with a particle in each step. At each step of the simulation, the number of particles increases. Once placed, a particle never moves. * Rule 184 can be understood in term ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rule 90
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 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''. When started from a single live cell, Rule 90 has a time-space diagram in the form of a Sierpiński triangle. The behavior of any other configuration can be explained as a superposition of copies of this pattern, combined using the exclusive or function. Any configuration with only finitely many nonzero cells becomes a replicator that eventually fills the array with copies of itself. When Rule 90 is started from a random initial configuration, its configuration remains random at each time step. Its tim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rule 30
Rule 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. For instance, a pattern resembling Rule 30 appears on the shell of the widespread cone snail species ''Conus textile''. Rule 30 has also been used as a random number generator in Mathematica, and has also been proposed as a possible stream cipher for use in cryptography. Rule 30 is so named because 30 is the smallest Wolfram code which describes its rule set (as described below). The mirror image, complement, and mirror complement of Rule 30 have Wolfram codes 86, 135, and 149, respectivel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ca110-interaction2
Carbonic anhydrase-related protein 11 is a protein that in humans is encoded by the ''CA11'' gene. Function Carbonic anhydrases (CAs) are a large family of zinc metalloenzymes that catalyze the reversible hydration of carbon dioxide. They participate in a variety of biological processes, including respiration, calcification, acid-base balance, bone resorption, and the formation of aqueous humor, cerebrospinal fluid, saliva, and gastric acid. They show extensive diversity in tissue distribution and in their subcellular localization. CA XI is likely a secreted protein, however, radical changes at active site residues completely conserved in CA isozymes with catalytic activity, make it unlikely that it has carbonic anhydrase activity. It shares properties in common with two other acatalytic CA isoforms, CA VIII and CA X. CA XI is most abundantly expressed in brain, and may play a general role in the central nervous system. Interactions CA11 has been shown to interact with ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ca110-structures2
Carbonic anhydrase-related protein 11 is a protein that in humans is encoded by the ''CA11'' gene. Function Carbonic anhydrases (CAs) are a large family of zinc metalloenzymes that catalyze the reversible hydration of carbon dioxide. They participate in a variety of biological processes, including respiration, calcification, acid-base balance, bone resorption, and the formation of aqueous humor, cerebrospinal fluid, saliva, and gastric acid. They show extensive diversity in tissue distribution and in their subcellular localization. CA XI is likely a secreted protein, however, radical changes at active site residues completely conserved in CA isozymes with catalytic activity, make it unlikely that it has carbonic anhydrase activity. It shares properties in common with two other acatalytic CA isoforms, CA VIII and CA X. CA XI is most abundantly expressed in brain, and may play a general role in the central nervous system. Interactions CA11 has been shown to interact with ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spaceship (CA)
In a cellular automaton, a finite pattern is called a spaceship if it reappears after a certain number of generations in the same orientation but in a different position. The smallest such number of generations is called the period of the spaceship. Description The speed of a spaceship is often expressed in terms of ''c'', the metaphorical speed of light (one cell per generation) which in many cellular automata is the fastest that an effect can spread. For example, a glider in Conway's Game of Life is said to have a speed of c/4, as it takes four generations for a given state to be translated by one cell. Similarly, the ''lightweight spaceship'' is said to have a speed of c/2, as it takes four generations for a given state to be translated by two cells. More generally, if a spaceship in a 2D automaton with the Moore neighborhood is translated by (x, y) after n generations, then the speed v is defined as: This notation can be readily generalised to cellular automata with d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cyclic Tag System
A tag system is a deterministic computational model published by Emil Leon Post in 1943 as a simple form of a Post canonical system. A tag system may also be viewed as an abstract machine, called a Post tag machine (not to be confused with Post–Turing machines)—briefly, a finite-state machine whose only tape is a FIFO queue of unbounded length, such that in each transition the machine reads the symbol at the head of the queue, deletes a constant number of symbols from the head, and appends to the tail a symbol-string that depends solely on the first symbol read in this transition. Because all of the indicated operations are performed in a single transition, a tag machine strictly has only one state. Definitions A ''tag system'' is a triplet (''m'', ''A'', ''P''), where * ''m'' is a positive integer, called the ''deletion number''. * ''A'' is a finite alphabet of symbols, one of which is a special ''halting symbol''. All finite (possibly empty) strings on ''A'' are called ' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polynomial Complexity
In computer science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm. Time complexity is commonly estimated by counting the number of elementary operations performed by the algorithm, supposing that each elementary operation takes a fixed amount of time to perform. Thus, the amount of time taken and the number of elementary operations performed by the algorithm are taken to be related by a constant factor. Since an algorithm's running time may vary among different inputs of the same size, one commonly considers the worst-case time complexity, which is the maximum amount of time required for inputs of a given size. Less common, and usually specified explicitly, is the average-case complexity, which is the average of the time taken on inputs of a given size (this makes sense because there are only a finite number of possible inputs of a given size). In both cases, the time complexity is generally expressed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
