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Breeder (CA)
In cellular automata such as Conway's Game of Life, a breeder is a pattern that exhibits quadratic growth, by generating multiple copies of a secondary pattern, each of which then generates multiple copies of a tertiary pattern. Classification Breeders can be classed by the relative motion of the patterns. The classes are denoted by three-letter codes, which denote whether the primary, secondary and tertiary elements respectively are moving (M) or stationary (S). The four basic types are: # SMM – A gun that fires out rakes. # MSM – A puffer that leaves guns in its wake. # MMS – A rake that fires out puffers. # MMM – A rake that fires out more rakes, such that there are no stationary elements. A spacefiller In Conway's Game of Life and related cellular automata, a spacefiller is a pattern that spreads out indefinitely, eventually filling the entire space with a still life pattern. It typically consists of three components: stretchers that resem ... (which also ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chart Animation
A chart (sometimes known as a graph) is a graphical representation for data visualization, in which "the data is represented by symbols, such as bars in a bar chart, lines in a line chart, or slices in a pie chart". A chart can represent tabular numeric data, functions or some kinds of quality structure and provides different info. The term "chart" as a graphical representation of data has multiple meanings: * A data chart is a type of diagram or graph, that organizes and represents a set of numerical or qualitative data. * Maps that are adorned with extra information ( map surround) for a specific purpose are often known as charts, such as a nautical chart or aeronautical chart, typically spread over several map sheets. * Other domain-specific constructs are sometimes called charts, such as the chord chart in music notation or a record chart for album popularity. Charts are often used to ease understanding of large quantities of data and the relationships between parts ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 '' 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 determines the new state of e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conway's Game Of Life
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. Rules The universe of the Game of Life is 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 '' 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 two live neighbours dies, as if by underpopulation. # Any live cell with two or three live neig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quadratic Growth
In mathematics, a function or sequence is said to exhibit quadratic growth when its values are proportional to the square of the function argument or sequence position. "Quadratic growth" often means more generally "quadratic growth in the limit", as the argument or sequence position goes to infinity – in big Theta notation, f(x)=\Theta(x^2). This can be defined both continuously (for a real-valued function of a real variable) or discretely (for a sequence of real numbers, i.e., real-valued function of an integer or natural number variable). Examples Examples of quadratic growth include: *Any quadratic polynomial. *Certain integer sequences such as the triangular numbers. The nth triangular number has value n(n+1)/2, approximately n^2/2. For a real function of a real variable, quadratic growth is equivalent to the second derivative being constant (i.e., the third derivative being zero), and thus functions with quadratic growth are exactly the quadratic polynomials, as these a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gun (cellular Automaton)
In a cellular automaton, a gun is a pattern with a main part that repeats periodically, like an oscillator, and that also periodically emits spaceships. There are then two periods that may be considered: the period of the spaceship output, and the period of the gun itself, which is necessarily a multiple of the spaceship output's period. A gun whose period is larger than the period of the output is a pseudoperiod gun. In the Game of Life, for every ''p'' greater than or equal to 14, it is possible to construct a glider gun in which the gliders are emitted with period ''p''. Since guns continually emit spaceships, the existence of guns in Life means that initial patterns with finite numbers of cells can eventually lead to configurations with limitless numbers of cells, something that John Conway himself originally conjectured to be impossible. However, according to Conway's later testimony, this conjecture was explicitly intended to encourage someone to disprove it – i.e., ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rake (cellular Automaton)
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. In Conway's Game of Life, the discovery of rakes was one of the key components needed to form the ''breeder'', the first known pattern in Life in which the number of live cells exhibits quadratic growth. A breeder is formed by arranging several rakes so that the '' gliders''—the smallest possible spaceships—they generate interact to form a sequence of '' glider guns'', patterns which emit gliders. The emitted gliders fill a growing triangle of the plane of the game. More generally, when a rake exists for a cellular automaton rule (a mathematical function defining the next iteration to be derived f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Puffer Train
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] |
Spacefiller
In Conway's Game of Life and related cellular automata, a spacefiller is a pattern that spreads out indefinitely, eventually filling the entire space with a still life pattern. It typically consists of three components: stretchers that resemble spaceships at the four corners of the pattern, a growing boundary region along the edges of the pattern, and the still life in the interior pattern. It resembles a breeder in that both types of patterns have a quadratic growth In mathematics, a function or sequence is said to exhibit quadratic growth when its values are proportional to the square of the function argument or sequence position. "Quadratic growth" often means more generally "quadratic growth in the limit" ... rate in their numbers of live cells, and in both having a three-component architecture. However, in a breeder the moving part of the breeder (corresponding to the stretcher) leaves behind a fixed sequence of glider guns which fill space with gliders, moving obj ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
