|
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] |
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] |
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] |
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 from ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
Bill Gosper
Ralph William Gosper Jr. (born April 26, 1943), known as Bill Gosper, is an American mathematician and programmer. Along with Richard Greenblatt, he may be considered to have founded the hacker community, and he holds a place of pride in the Lisp community. The Gosper curve and Gosper's algorithm are named after him. Becoming a hacker In high school, Gosper was interested in model rockets until one of his friends was injured in a rocketry accident and contracted a fatal brain infection.. Gosper enrolled in MIT in 1961, and he received his bachelor's degree in mathematics from MIT in 1965 despite becoming disaffected with the mathematics department because of their anti-computer attitude. In his second year at MIT, Gosper took a programming course from John McCarthy and became affiliated with the MIT AI Lab. His contributions to computational mathematics include HAKMEM and the MIT Maclisp system. He made major contributions to Macsyma, Project MAC's computer algebra system. G ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Martin Gardner
Martin Gardner (October 21, 1914May 22, 2010) was an American popular mathematics and popular science writer with interests also encompassing magic, scientific skepticism, micromagic, philosophy, religion, and literatureespecially the writings of Lewis Carroll, L. Frank Baum, and G. K. Chesterton.Martin (2010) He was a leading authority on Lewis Carroll; '' The Annotated Alice'', which incorporated the text of Carroll's two Alice books, was his most successful work and sold over a million copies.Martin Gardner obituary (2010) He had a lifelong interest in magic and illusion and in 1999, ''MAGIC'' magazine named him as one of the "10 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wheels, Life And Other Mathematical Amusements
''Wheels, Life and Other Mathematical Amusements'' is a book by Martin Gardner published in 1983. The Basic Library List Committee of the Mathematical Association of America has recommended its inclusion in undergraduate mathematics libraries. Contents ''Wheels, Life and Other Mathematical Amusements'' is a book of 22 mathematical games columns that were revised and extended after being previously published in ''Scientific American''. It is Gardner's 10th collection of columns, and includes material on Conway's Game of Life, supertasks, intransitive dice, braided polyhedra, combinatorial game theory, the Collatz conjecture, mathematical card tricks, and Diophantine equations such as Fermat's Last Theorem. Reception Dave Langford reviewed ''Wheels, Life and Other Mathematical Amusements'' for ''White Dwarf A white dwarf is a Compact star, stellar core remnant composed mostly of electron-degenerate matter. A white dwarf is very density, dense: in an Earth sized volume, it p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Life-like Cellular Automaton
A cellular automaton (CA) is (in the sense of being similar to Conway's Game of Life) if it meets the following criteria: * The array of cells of the automaton has two dimensions. * Each cell of the automaton has two states (conventionally referred to as "alive" and "dead", or alternatively "on" and "off") * The neighborhood of each cell is the Moore neighborhood; it consists of the eight adjacent cells to the one under consideration and (possibly) the cell itself. * In each time step of the automaton, the new state of a cell can be expressed as a function of the number of adjacent cells that are in the alive state and of the cell's own state; that is, the rule is ''outer totalistic'' (sometimes called ''semitotalistic''). This class of cellular automata is named for the Conway's Game of Life, Game of Life (B3/S23), the most famous cellular automaton, which meets all of these criteria. Many different terms are used to describe this class. It is common to refer to it as the "Life f ... [...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 A gun is a device that Propulsion, propels a projectile using pressure or explosive force. The projectiles are typically solid, but can also be pressurized liquid (e.g. in water guns or water cannon, cannons), or gas (e.g. light-gas gun). So ... 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 (which a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
