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Spacefiller (CA)
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 obje ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spacefiller Animation
In Conway's Game of Life and related cellular automaton, cellular automata, a spacefiller is a pattern that spreads out indefinitely, eventually filling the entire space with a Still life (cellular automaton), still life pattern. It typically consists of three components: stretchers that resemble spaceship (cellular automaton), 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 (cellular automaton), breeder in that both types of patterns have a quadratic growth 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 glider (cellular automaton), gliders, moving objects (gliders or spaceships) rather than still life patterns. With a spacefiller, unlike a breeder, every point in ... [...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] |
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] |
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] |
Still Life (cellular Automaton)
In Conway's Game of Life and other cellular automata, a still life is a pattern that does not change from one generation to the next. The term comes from the art world where a still life painting or photograph depicts an inanimate scene. In cellular automata, a still life can be thought of as an oscillator with unit period. Classification A pseudo still life consists of two or more adjacent islands ( connected components) which can be partitioned (either individually or as sets) into non-interacting subparts, which are also still lifes. This compares with a strict still life, which may not be partitioned in this way. A strict still life may have only a single island, or it may have multiple islands that depend on one another for stability, and thus cannot be decomposed. The distinction between the two is not always obvious, as a strict still life may have multiple connected components all of which are needed for its stability. However, it is possible to determine whether a still l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 di ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Breeder (cellular Automaton)
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] |
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] |
Glider Gun
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] |
Glider (cellular Automaton)
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] |
