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Seeds (cellular Automaton)
Seeds is a cellular automaton in the same family as the Game of Life, initially investigated by Brian Silverman and named by Mirek Wójtowicz. It consists of an infinite two-dimensional grid of cells, each of which may be in one of two states: ''on'' or ''off''. Each cell is considered to have eight neighbors (Moore neighborhood), as in Life. In each time step, a cell turns on or is "born" if it was off or "dead" but had exactly two neighbors that were on; all other cells turn off. Thus, in the notation describing the family of cellular automata containing Life, it is described by the rule B2/S. In Game of Life terminology, a pattern in which all cells that were on turn off at each step is called a ''phoenix''. All patterns in Seeds have this form. Even though all live cells are constantly dying, the small birth requirement of two cells means that nearly every pattern in Seeds explodes into a chaotic mess that grows to cover the entire universe. Thus, in Wolfram's classificatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Seeds 140 Generations
A seed is an embryonic plant enclosed in a protective outer covering, along with a food reserve. The formation of the seed is a part of the process of reproduction in seed plants, the spermatophytes, including the gymnosperm and angiosperm plants. Seeds are the product of the ripened ovule, after the embryo sac is fertilized by sperm from pollen, forming a zygote. The embryo within a seed develops from the zygote, and grows within the mother plant to a certain size before growth is halted. The seed coat arises from the integuments of the ovule. Seeds have been an important development in the reproduction and success of vegetable gymnosperm and angiosperm plants, relative to more primitive plants such as ferns, mosses and liverworts, which do not have seeds and use water-dependent means to propagate themselves. Seed plants now dominate biological niches on land, from forests to grasslands both in hot and cold climates. The term "seed" also has a general meaning that antedat ... [...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] |
Life-like Cellular Automaton
Life-Like was a manufacturer of model trains and accessories. In 1960, the company purchased the assets of the defunct Varney Scale Models and began manufacturing model trains and accessories under the name Life-Like in 1970. In 2005 the parent company, Lifoam Industries, LLC, chose to concentrate on their core products and sold their model railroad operations to hobby distributor Wm. K. Walthers. Today, the Life-Like trademark is used by Walthers for HO Scale Buildings. History Life-Like Products was founded by brothers Lou and Sol Kramer, whose parents were Lithuanian immigrants residing in Baltimore, Maryland. Their experience in the hobby industry began in the 1930s when they became interested in constructing model airplanes. With money borrowed from their mother, the brothers formed the Burd Model Airplane Manufacturing Co. and sold their own model airplane kits using balsa wood they would salvage from discarded banana crates. As the business grew, their line had expanded to ... [...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] |
Brian Silverman
Brian Silverman is a Canadian computer scientist, the creator of many programming environments for children,Computing Pioneer Returns to CMK 2010 Faculty! , Constructing Modern Knowledge, September 29, 2010. and a researcher in . Silverman was a student at the in the 1970s, where he was one of the creators of a computer that pl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Association Of America
The Mathematical Association of America (MAA) is a professional society that focuses on mathematics accessible at the undergraduate level. Members include university, college, and high school teachers; graduate and undergraduate students; pure and applied mathematicians; computer scientists; statisticians; and many others in academia, government, business, and industry. The MAA was founded in 1915 and is headquartered at 1529 18th Street, Northwest in the Dupont Circle neighborhood of Washington, D.C. The organization publishes mathematics journals and books, including the '' American Mathematical Monthly'' (established in 1894 by Benjamin Finkel), the most widely read mathematics journal in the world according to records on JSTOR. Mission and Vision The mission of the MAA is to advance the understanding of mathematics and its impact on our world. We envision a society that values the power and beauty of mathematics and fully realizes its potential to promote human flourishing ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 ''ex ... [...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] |
Oscillator (cellular Automaton)
In a cellular automaton, an oscillator is a pattern that returns to its original state, in the same orientation and position, after a finite number of generations. Thus the evolution of such a pattern repeats itself indefinitely. Depending on context, the term may also include spaceships as well. The smallest number of generations it takes before the pattern returns to its initial condition is called the ''period'' of the oscillator. An oscillator with a period of 1 is usually called a still life, as such a pattern never changes. Sometimes, still lifes are not taken to be oscillators. Another common stipulation is that an oscillator must be finite. Examples In Conway's Game of Life, finite oscillators are known to exist for all periods except 19 and 41. Additionally, until July 2022, the only known examples for period 34 were considered trivial because they consisted of essentially separate components that oscillate at smaller periods. For instance, one can create a period 34 osc ... [...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] |
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 (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] |
