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Spaceship (cellular Automaton)
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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Animated Spaceships
Animation is a filmmaking technique whereby image, still images are manipulated to create Motion picture, moving images. In traditional animation, images are drawn or painted by hand on cel, transparent celluloid sheets to be photographed and exhibited on film. Animation has been recognised as an artistic medium, specifically within the Entertainment#Industry, entertainment industry. Many animations are either traditional animations or computer animations made with computer-generated imagery (CGI). Stop motion animation, in particular claymation, has continued to exist alongside these other forms. Animation is contrasted with live action, although the two do not exist in isolation. Many moviemakers have produced Live-action animation, films that are a hybrid of the two. As CGI increasingly Photorealism, approximates photographic imagery, filmmakers can easily Compositing, composite 3D animations into their film rather than using practical effects for showy visual effects (VFX). ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Cellular Automaton
A 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 ''State (computer science), 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'' 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 dete ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Speed Of Light (cellular Automaton)
In Conway's Game of Life (and related cellular automata), the speed of light is a propagation rate across the grid of exactly one step (either horizontally, vertically or diagonally) per generation. In a single generation, a cell can only influence its nearest neighbours, and so the speed of light (by analogy with the speed of light in physics) is the maximum rate at which information can propagate. It is therefore an upper bound to the speed at which any pattern can move. Notation As in physics, the speed of light is represented by the letter ''c''. This in turn is used as a reference for describing the average propagation speed of any given type of spaceship. For example, a glider 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. Lightspeed propagation While ' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Glider (Conway's Life)
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 c/4. The glider is often produced from randomly generated starting configurations. The name comes from the fact that, after two steps, the glider pattern repeats its configuration with a glide reflection symmetry. After four steps and two glide reflections, it returns to its original orientation. John Conway remarked that he wished he hadn't called it the glider. The game was developed before the widespread use of interactive computers, and after seeing it animated, he feels the glider looks more like an ant walking across the plane. Importance Gliders are important to the Game of Life because they are easily produced, can be collided with each other ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Conway's Game Of Life
The Game of Life, also known as Conway's Game of Life or simply 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 von Neumann universal constructor, universal constructor or any other Turing machine. Rules The universe of the Game of Life is Square tiling, an infinite, two-dimensional orthogonal grid of square ''cells'', each of which is in one of two possible states, ''live'' or ''dead'' (or ''populated'' and ''unpopulated'', respectively). Every cell interacts with its eight ''Moore neighborhood, neighbours'', which are the cells that are horizontally, vertically, or diagonally adjacent. At each step in time, the following transitions occur: # Any live cell with fewer than ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Moore Neighborhood
In cellular automata, the Moore neighborhood is defined on a two-dimensional square lattice and is composed of a central cell and the eight cells that surround it. Name The neighborhood is named after Edward F. Moore, a pioneer of cellular automata theory. Importance It is one of the two most commonly used neighborhood types, the other one being the von Neumann neighborhood, which excludes the corner cells. The well known Conway's Game of Life, for example, uses the Moore neighborhood. It is similar to the notion of 8-connected pixels in computer graphics. The Moore neighbourhood of a cell is the cell itself and the cells at a Chebyshev distance of 1. The concept can be extended to higher dimensions, for example forming a 26-cell cubic neighborhood for a cellular automaton in three dimensions, as used by 3D Life. In dimension ''d,'' where 0 \le d, d \in \mathbb, the size of the neighborhood is 3''d'' − 1. In two dimensions, the number of cells in an ''ext ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Reflector (cellular Automaton)
In cellular automaton, cellular automata such as Conway's Game of Life, a reflector is a pattern that can interact with a spaceship (cellular automaton), spaceship to change its direction of motion, without damage to the reflector pattern. In Life, many oscillator (cellular automaton), oscillators can reflect the Glider (Conway's Life), glider; there also exist stable reflectors composed of still life (cellular automaton), still life patterns that, when they interact with a glider, reflect the glider and return to their stable state. Types As well as whether a reflector is a still life or an oscillator, a reflector might be characterised by the angle between the input and output spaceships (for example a 180° reflector would flip a spaceship). For most spaceships, this can only be 0°, 90°, or 180°. Another property is whether the reflector is colour preserving. That is, if it doesn't change the state of a spaceship as it gets reflected. If a reflector isn't colour preservin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Puffer Train (cellular Automaton)
In a cellular automaton, a puffer train, or simply puffer, is a finite pattern that moves itself across the "universe", leaving debris behind. Thus a pattern consisting of only a puffer will grow arbitrarily large over time. While both puffers and spaceships have periods and speeds, unlike puffers, spaceships do not leave debris behind. The period of a puffer can be considered as the combination of ''two'' periods; the first is the period of the puffer itself, while the second is the apparent period of the pattern of debris produced. This is often the same as the period of the puffer, but sometimes is a factor of the period. A puffer for which the apparent period deduced from the debris is smaller than the period of the engine is a pseudoperiod puffer. Such puffers are typically produced by artificial means. A true period puffer is one in which the period of the debris matches that of the puffer. Puffers are divided into two classes, dirty puffers and clean puffers. While there i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Information
Information is an Abstraction, abstract concept that refers to something which has the power Communication, to inform. At the most fundamental level, it pertains to the Interpretation (philosophy), interpretation (perhaps Interpretation (logic), formally) of that which may be sensed, or their abstractions. Any natural process that is not completely random and any observable pattern in any Media (communication), medium can be said to convey some amount of information. Whereas digital signals and other data use discrete Sign (semiotics), signs to convey information, other phenomena and artifacts such as analog signals, analogue signals, poems, pictures, music or other sounds, and current (fluid), currents convey information in a more continuous form. Information is not knowledge itself, but the meaning (philosophy), meaning that may be derived from a representation (mathematics), representation through interpretation. The concept of ''information'' is relevant or connected t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Glider (Conway's Life)
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 c/4. The glider is often produced from randomly generated starting configurations. The name comes from the fact that, after two steps, the glider pattern repeats its configuration with a glide reflection symmetry. After four steps and two glide reflections, it returns to its original orientation. John Conway remarked that he wished he hadn't called it the glider. The game was developed before the widespread use of interactive computers, and after seeing it animated, he feels the glider looks more like an ant walking across the plane. Importance Gliders are important to the Game of Life because they are easily produced, can be collided with each other ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Turing-complete
In 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 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. A related concept is that of Turing equivalence two computers P and Q are called equivalent if P can simulate Q and Q can simulate P. The Church–Turing thesis conjectures that any function whose values can be computed by an algorithm can be computed by a Turing machine, and therefore that if any real-world computer can simulate a Turing machine, it is Turing equivalent to a Turing ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Knight (chess)
The knight (♘, ♞) is a piece in the game of chess, represented by a horse's head and neck. It moves two squares vertically and one square horizontally, or two squares horizontally and one square vertically, jumping over other pieces. Each player starts the game with two knights on the b- and g-, each located between a rook and a bishop. Movement Compared to other chess pieces, the knight's movement is unique: it moves two squares vertically and one square horizontally, or two squares horizontally and one square vertically (with both forming the shape of a capital L). Consequently, a knight alternates between light and dark squares with each move. When moving, the knight can jump over pieces to reach its destination. Knights capture in the same way, replacing the enemy piece on the square and removing it from the board. A knight can have up to eight available moves at once. Knights and pawns are the only pieces that can be moved in the chess starting position. Val ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
