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Turmite
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 a triangular tiling. It has been shown that turmites in general are exactly equivalent in power to one-dimensional Turing machines with an infinite tape, as either can simulate the other. History Langton's ants were invented in 1986 and declared "equivalent to Turing machines". Independently, in 1988, Allen H. Brady considered the idea of two-dimensional Turing machines with an orientation and called them "TurNing machines". Apparently independently of both of these, Greg Turk investigated the same kind of system and wrote to A. K. Dewdney about them. A. K. Dewdney named them "tur-mites" in his "Computer Recre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Langton's Ant
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. Rules Squares on a plane are colored variously either black or white. We arbitrarily identify one square as the "ant". The ant can travel in any of the four cardinal directions at each step it takes. The "ant" moves according to the rules below: * At a white square, turn 90° clockwise, flip the color of the square, move forward one unit * At a black square, turn 90° counter-clockwise, flip the color of the square, move forward one unit Langton's ant can also be described as a cellular automaton, where the grid is colored black or white and the "ant" square has one of eight different colors assigned to encode the combination of black/white state and the cu ... [...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 mathematics, discrete cells, each of which can hold a single symbol drawn from a finite set of symbols called the Alphabet (formal languages), 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, which direction to move the head, and whet ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paterson's Worms
Paterson's worms are a family of cellular automata devised in 1971 by Mike Paterson and John Horton Conway to model the behaviour and feeding patterns of certain prehistoric worms. In the model, a worm moves between points on a triangular grid along line segments, representing food. Its turnings are determined by the configuration of eaten and uneaten line segments adjacent to the point at which the worm currently is. Despite being governed by simple rules the behaviour of the worms can be extremely complex, and the ultimate fate of one variant is still unknown. The worms were studied in the early 1970s by Paterson, Conway and Michael Beeler, described by Beeler in June 1973, and presented in November 1973 in Martin Gardner's "Mathematical Games" column in ''Scientific American''. Electronic Arts' 1983 game ''Worms?'' is an interactive implementation of Paterson's worms, where each time a worm has to turn in a way that it lacks a rule for, it stops and lets the user choose a dir ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Greg Turk
Greg Turk is an American-born researcher in the field of computer graphics and a professor at the School of Interactive Computing in the College of Computing at the Georgia Institute of Technology (Georgia Tech). His paper "Zippered polygon meshes from range images", concerning the reconstruction of surfaces from point data, brought the " Stanford bunny", a frequently used example object in computer graphics research, into the CGI lexicon. Turk actually purchased the original Stanford Bunny and performed the initial scans on it. He is also known for his work on simplification of surfaces, and on reaction–diffusion-based texture synthesis. In 2008, Turk was the technical papers chair of SIGGRAPH 2008. In 2012, Greg Turk was awarded the ACM Computer Graphics Achievement Award 2012. Education and computer graphics research After receiving his Ph.D. from the University of North Carolina at Chapel Hill under the supervision of Henry Fuchs in 1992, Turk was a postdoctoral researcher ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Busy Beaver
In theoretical computer science, the busy beaver game aims to find a terminating Computer program, program of a given size that (depending on definition) either produces the most output possible, or runs for the longest number of steps. Since an endless loop, endlessly looping program producing infinite output or running for infinite time is easily conceived, such programs are excluded from the game. Rather than traditional programming languages, the programs used in the game are n-state Turing machine, Turing machines, one of the first mathematical models of computation. Turing machines consist of an infinite tape, and a finite set of states which serve as the program's "source code". Producing the most output is defined as writing the largest number of 1s on the tape, also referred to as achieving the highest score, and running for the longest time is defined as taking the longest number of steps to halt. The ''n-''state busy beaver game consists of finding the longest-running ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hexagonal Tiling
In geometry, the hexagonal tiling or hexagonal tessellation is a regular tiling of the Euclidean plane, in which exactly three hexagons meet at each vertex. It has Schläfli symbol of or (as a Truncation (geometry), truncated triangular tiling). English mathematician John Horton Conway, John Conway called it a hextille. The internal angle of the hexagon is 120 degrees, so three hexagons at a point make a full 360 degrees. It is one of List of regular polytopes#Euclidean tilings, three regular tilings of the plane. The other two are the triangular tiling and the square tiling. Structure and properties The hexagonal tiling has a structure consisting of a regular hexagon only as its prototile, sharing two vertices with other identical ones, an example of monohedral tiling. Each vertex at the tiling is surrounded by three regular hexagons, denoted as 6.6.6 by vertex configuration. The dual of a hexagonal tiling is triangular tiling, because the center of each hexagonal tiling ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Models Of Computation
In computer science, and more specifically in computability theory and computational complexity theory, a model of computation is a model which describes how an output of a mathematical function is computed given an input. A model describes how units of computations, memories, and communications are organized. The computational complexity of an algorithm can be measured given a model of computation. Using a model allows studying the performance of algorithms independently of the variations that are specific to particular implementations and specific technology. Categories Models of computation can be classified into three categories: sequential models, functional models, and concurrent models. Sequential models Sequential models include: * Finite-state machines * Post machines ( Post–Turing machines and tag machines). * Pushdown automata * Register machines ** Random-access machines * Turing machines * Decision tree model * External memory model Functional models Functio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Artificial Life
Artificial life (ALife or A-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 computer scientist, 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 computer hardware, hardware; and ''wet artificial life, wet'', from biochemistry. Artificial life researchers study traditional biology by trying to recreate aspects of biological phenomena. Overview Artificial life studies the fundamental processes of living systems in artificial environments in order to gain a deeper understanding of the complex information processing that define such systems. These topics are broad, but often include Evolutionary algorithm, evolutionar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MathWorld
''MathWorld'' is an online mathematics reference work, created and largely written by Eric W. Weisstein. It is sponsored by and licensed to Wolfram Research, Inc. and was partially funded by the National Science Foundation's National Science Digital Library grant to the University of Illinois at Urbana–Champaign. History Eric W. Weisstein, the creator of the site, was a physics and astronomy student who got into the habit of writing notes on his mathematical readings. In 1995 he put his notes online and called it "Eric's Treasure Trove of Mathematics." It contained hundreds of pages/articles, covering a wide range of mathematical topics. The site became popular as an extensive single resource on mathematics on the web. In 1998, he made a contract with CRC Press and the contents of the site were published in print and CD-ROM form, titled ''CRC Concise Encyclopedia of Mathematics''. The free online version became only partially accessible to the public. In 1999 Weisstein we ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integer Lattice
In mathematics, the -dimensional integer lattice (or cubic lattice), denoted , is the lattice (group), lattice in the Euclidean space whose lattice points are tuple, -tuples of integers. The two-dimensional integer lattice is also called the square lattice, or grid lattice. is the simplest example of a root lattice. The integer lattice is an odd unimodular lattice. Automorphism group The automorphism group (or group (mathematics), group of congruence relation, congruences) of the integer lattice consists of all permutations and sign changes of the coordinates, and is of order of a group, order 2''n'' ''n''!. As a matrix group it is given by the set of all ''n'' × ''n'' signed permutation matrices. This group is group isomorphism, isomorphic to the semidirect product :(\mathbb Z_2)^n \rtimes S_n where the symmetric group ''S''''n'' acts on (Z2)''n'' by permutation (this is a classic example of a wreath product). For the square lattice, this is the group o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ed Pegg, Jr
Ed, ed or ED may refer to: Arts and entertainment * ''Ed'' (film), a 1996 film starring Matt LeBlanc * Ed (''Fullmetal Alchemist'') or Edward Elric, a character in ''Fullmetal Alchemist'' media * ''Ed'' (TV series), a TV series that ran from 2000 to 2004 * ED, an abbreviated term for ending theme songs in anime Businesses and organizations * Ed (supermarket), a French brand of discount stores founded in 1978 * Consolidated Edison, from their NYSE stock symbol * United States Department of Education, a department of the United States government * Enforcement Directorate, a law enforcement and economic intelligence agency in India * European Democrats, a loose association of conservative political parties in Europe * Airblue (IATA code ED), a private Pakistani airline * Eagle Dynamics, a Swiss software company Places * Ed, Kentucky, an unincorporated community in the United States * Ed, Sweden, a town in Dals-Ed, Sweden * Erode Junction railway station, in Erode, Tamil Nad ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
