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Methuselah (cellular Automaton)
In cellular automata, a methuselah is a small "seed" pattern of initial live cells that take a large number of generations in order to stabilize. More specifically, Martin Gardner defines them as patterns of fewer than ten live cells which take longer than 50 generations to stabilize, although some patterns that are larger than ten cells have also been called methuselahs. Patterns must eventually stabilize to be considered methuselahs. The term comes from the Biblical Methuselah, who lived for 969 years. In Conway's Game of Life In Conway's Game of Life, one of the smallest methuselahs is the R-pentomino Derived from the Greek word for ' 5', and "domino", a pentomino (or 5-omino) is a polyomino of order 5, that is, a polygon in the plane made of 5 equal-sized squares connected edge-to-edge. When rotations and reflections are not considered to ..., a pattern of five cells first considered by Conway himself, that takes 1103 generations before stabilizing with 116 cells. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Die Hard
''Die Hard'' is a 1988 American action film directed by John McTiernan, with a screenplay by Jeb Stuart and Steven E. de Souza. Based on the 1979 novel '' Nothing Lasts Forever'', by Roderick Thorp, it stars Bruce Willis, Alan Rickman, Alexander Godunov, and Bonnie Bedelia. ''Die Hard'' follows New York City police detective John McClane (Willis) who is caught up in a terrorist takeover of a Los Angeles skyscraper while visiting his estranged wife. Reginald VelJohnson, William Atherton, Paul Gleason, and Hart Bochner feature in supporting roles. Stuart was hired by 20th Century Fox to adapt Thorp's novel into a screenplay in 1987. His finished draft was greenlit immediately by Fox, which was eager for a summer blockbuster the following year. The role of McClane was turned down by a host of the decade's most popular actors, including Arnold Schwarzenegger and Sylvester Stallone. Known mainly for work on television, Willis was paid $5million for his involvement, placing h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cellular Automata
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] |
Martin Gardner
Martin Gardner (October 21, 1914May 22, 2010) was an American popular mathematics and popular science writer with interests also encompassing scientific skepticism, micromagic, philosophy, religion, and literatureespecially the writings of Lewis Carroll, L. Frank Baum, and G. K. Chesterton.Martin (2010) He was also 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. He had a lifelong interest in magic and illusion and in 1999, MAGIC magazine named him as one of the "100 Most Influential Magicians of the Twentieth Century". He was considered the doyen of American puzzlers. He was a prolific and versatile author, publishing more than 100 books. Gardner was best known for creating and sustaining interest in recreational mathematicsand by extension, mathematics in generalthroughout the latter half of the 20th century, principally through his "Mathema ... [...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 stellar core remnant composed mostly of electron-degenerate matter. A white dwarf is very dense: its mass is comparable to the Sun's, while its volume is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Methuselah
Methuselah () ( he, מְתוּשֶׁלַח ''Məṯūšélaḥ'', in pausa ''Məṯūšālaḥ'', "His death shall send" or "Man of the javelin" or "Death of Sword"; gr, Μαθουσάλας ''Mathousalas'') was a biblical patriarch and a figure in Judaism, Christianity, and Islam. He had the longest lifespan of all those given in the Bible, dying at the age of 969. According to the Book of Genesis, Methuselah was the son of Enoch, the father of Lamech, and the grandfather of Noah. Elsewhere in the Bible, Methuselah is mentioned in genealogies in 1 Chronicles and the Gospel of Luke. His life is described in further detail in extra-biblical religious texts such as the Book of Enoch, Slavonic Enoch, and the Book of Moses. Bible commentators have offered various explanations as to why the Book of Genesis describes him as having died at such an advanced age; some believe that Methuselah's age is the result of a mistranslation, while others believe that his age is used to giv ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pentomino Animation 1 Minute Small
Derived from the Greek word for ' 5', and "domino", a pentomino (or 5-omino) is a polyomino of order 5, that is, a polygon in the plane made of 5 equal-sized squares connected edge-to-edge. When rotations and reflections are not considered to be distinct shapes, there are 12 different ''free'' pentominoes. When reflections are considered distinct, there are 18 '' one-sided'' pentominoes. When rotations are also considered distinct, there are 63 ''fixed'' pentominoes. Pentomino tiling puzzles and games are popular in recreational mathematics. Usually, video games such as ''Tetris'' imitations and ''Rampart'' consider mirror reflections to be distinct, and thus use the full set of 18 one-sided pentominoes. Each of the twelve pentominoes satisfies the Conway criterion; hence every pentomino is capable of tiling the plane. Each chiral pentomino can tile the plane without being reflected. History The earliest puzzle containing a complete set of pentominoes appeared in Henry Dud ... [...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] |
Pentomino
Derived from the Greek word for ' 5', and "domino", a pentomino (or 5-omino) is a polyomino of order 5, that is, a polygon in the plane made of 5 equal-sized squares connected edge-to-edge. When rotations and reflections are not considered to be distinct shapes, there are 12 different '' free'' pentominoes. When reflections are considered distinct, there are 18 '' one-sided'' pentominoes. When rotations are also considered distinct, there are 63 ''fixed'' pentominoes. Pentomino tiling puzzles and games are popular in recreational mathematics. Usually, video games such as ''Tetris'' imitations and ''Rampart'' consider mirror reflections to be distinct, and thus use the full set of 18 one-sided pentominoes. Each of the twelve pentominoes satisfies the Conway criterion; hence every pentomino is capable of tiling the plane. Each chiral pentomino can tile the plane without being reflected. History The earliest puzzle containing a complete set of pentominoes appeared in Henry D ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Horton Conway
John Horton Conway (26 December 1937 – 11 April 2020) was an English mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory. He also made contributions to many branches of recreational mathematics, most notably the invention of the cellular automaton called the Game of Life. Born and raised in Liverpool, Conway spent the first half of his career at the University of Cambridge before moving to the United States, where he held the John von Neumann Professorship at Princeton University for the rest of his career. On 11 April 2020, at age 82, he died of complications from COVID-19. Early life and education Conway was born on 26 December 1937 in Liverpool, the son of Cyril Horton Conway and Agnes Boyce. He became interested in mathematics at a very early age. By the time he was 11, his ambition was to become a mathematician. After leaving sixth form, he studied mathematics at Gonville and Caius College, Camb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
