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Rule 90
In the mathematics, mathematical study of cellular automaton, cellular automata, Rule 90 is an elementary cellular automaton based on the exclusive or function. It consists of a one-dimensional array of cells, each of which can hold either a 0 or a 1 value. In each time step all values are simultaneously replaced by the exclusive or of their two neighboring values.. call it "the simplest non-trivial cellular automaton",. and it is described extensively in Stephen Wolfram's 2002 book ''A New Kind of Science''. When started from a single live cell, Rule 90 has a time-space diagram in the form of a Sierpiński triangle. The behavior of any other configuration can be explained as a superposition of copies of this pattern, combined using the exclusive or function. Any configuration with only finitely many nonzero cells becomes a replicator (cellular automaton), replicator that eventually fills the array with copies of itself. When Rule 90 is started from a random initial configuratio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
R090 Rand 0
R, or r, is the eighteenth Letter (alphabet), letter of the Latin alphabet, used in the English alphabet, modern English alphabet, the alphabets of other western European languages and others worldwide. Its name in English is English alphabet#Letter names, ''ar'' (pronounced ), plural ''ars'', or in Ireland ''or'' . The letter is the eighth most common letter in English language, English and the fourth-most common consonant (after , , and ). The letter is used to form the ending "-re", which is used in certain words such as ''centre'' in some varieties of English spelling, such as British English. Canadian English also uses the "-re" ending, unlike American English, where the ending is usually replaced by "-er" (''center''). This does not affect pronunciation. Name The name of the letter in Latin was (), following the pattern of other letters representing continuants, such as F, L, M, N and S. This name is preserved in French language, French and many other languages. ... [...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] |
Directed Acyclic Graph
In mathematics, particularly graph theory, and computer science, a directed acyclic graph (DAG) is a directed graph with no directed cycles. That is, it consists of vertices and edges (also called ''arcs''), with each edge directed from one vertex to another, such that following those directions will never form a closed loop. A directed graph is a DAG if and only if it can be topologically ordered, by arranging the vertices as a linear ordering that is consistent with all edge directions. DAGs have numerous scientific and computational applications, ranging from biology (evolution, family trees, epidemiology) to information science (citation networks) to computation (scheduling). Directed acyclic graphs are sometimes instead called acyclic directed graphs or acyclic digraphs. Definitions A graph is formed by vertices and by edges connecting pairs of vertices, where the vertices can be any kind of object that is connected in pairs by edges. In the case of a directed graph, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tree (graph Theory)
In graph theory In mathematics, graph theory is the study of ''graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of '' vertices'' (also called ''nodes'' or ''points'') which are conne ..., a tree is an undirected graph in which any two Vertex (graph theory), vertices are connected by ''exactly one'' Path (graph theory), path, or equivalently a Connected graph, connected Cycle (graph theory), acyclic undirected graph. A forest is an undirected graph in which any two vertices are connected by ''at most one'' path, or equivalently an acyclic undirected graph, or equivalently a Disjoint union of graphs, disjoint union of trees. A polytreeSee . (or directed tree or oriented treeSee .See . or singly connected networkSee .) is a directed acyclic graph (DAG) whose underlying undirected graph is a tree. A polyforest (or directed forest or oriented forest) is a directed acyclic graph whose underlying undirecte ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Forward Difference Operator
A finite difference is a mathematical expression of the form . If a finite difference is divided by , one gets a difference quotient. The approximation of derivatives by finite differences plays a central role in finite difference methods for the numerical solution of differential equations, especially boundary value problems. The difference operator, commonly denoted \Delta is the operator that maps a function to the function \Delta /math> defined by :\Delta x)= f(x+1)-f(x). A difference equation is a functional equation that involves the finite difference operator in the same way as a differential equation involves derivatives. There are many similarities between difference equations and differential equations, specially in the solving methods. Certain recurrence relations can be written as difference equations by replacing iteration notation with finite differences. In numerical analysis, finite differences are widely used for approximating derivatives, and the term "fi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prime Number
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, or , involve 5 itself. However, 4 is composite because it is a product (2 × 2) in which both numbers are smaller than 4. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself or can be factorized as a product of primes that is unique up to their order. The property of being prime is called primality. A simple but slow method of checking the primality of a given number n, called trial division, tests whether n is a multiple of any integer between 2 and \sqrt. Faster algorithms include the Miller–Rabin primality test, which is fast but has a small chance of error, and the AKS primality test, which always pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rule 90 Trees
Rule or ruling may refer to: Education * Royal University of Law and Economics (RULE), a university in Cambodia Human activity * The exercise of political or personal control by someone with authority or power * Business rule, a rule pertaining to the structure or behavior internal to a business * School rule, a rule that is part of school discipline * Sport rule, a rule that defines how a sport is played * Game rule, a rule that defines how a game is played * Moral, a rule or element of a moral code for guiding choices in human behavior * Norm (philosophy), a kind of sentence or a reason to act, feel or believe * Rule of thumb, a principle with broad application that is not intended to be strictly accurate or reliable for every situation * Unspoken rule, an assumed rule of human behavior that is not voiced or written down * Slide rule, a mechanical analog computer Science * Rule of inference or transformation rule, a term in logic for a function which takes premises and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Decimal
The decimal numeral system (also called the base-ten positional numeral system and denary or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers of the Hindu–Arabic numeral system. The way of denoting numbers in the decimal system is often referred to as ''decimal notation''. A ''decimal numeral'' (also often just ''decimal'' or, less correctly, ''decimal number''), refers generally to the notation of a number in the decimal numeral system. Decimals may sometimes be identified by a decimal separator (usually "." or "," as in or ). ''Decimal'' may also refer specifically to the digits after the decimal separator, such as in " is the approximation of to ''two decimals''". Zero-digits after a decimal separator serve the purpose of signifying the precision of a value. The numbers that may be represented in the decimal system are the decimal fractions. That is, fractions of the form , where is an integer, and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Number
A binary number is a number expressed in the base-2 numeral system or binary numeral system, a method of mathematical expression which uses only two symbols: typically "0" (zero) and "1" ( one). The base-2 numeral system is a positional notation with a radix of 2. Each digit is referred to as a bit, or binary digit. Because of its straightforward implementation in digital electronic circuitry using logic gates, the binary system is used by almost all modern computers and computer-based devices, as a preferred system of use, over various other human techniques of communication, because of the simplicity of the language and the noise immunity in physical implementation. History The modern binary number system was studied in Europe in the 16th and 17th centuries by Thomas Harriot, Juan Caramuel y Lobkowitz, and Gottfried Leibniz. However, systems related to binary numbers have appeared earlier in multiple cultures including ancient Egypt, China, and India. Leibniz was specifica ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wolfram Code
Wolfram code is a widely used numbering system for one-dimensional cellular automaton rules, introduced by Stephen Wolfram in a 1983 paper and popularized in his book ''A New Kind of Science''. The code is based on the observation that a table specifying the new state of each cell in the automaton, as a function of the states in its neighborhood, may be interpreted as a ''k''-digit number in the ''S''-ary positional number system, where ''S'' is the number of states that each cell in the automaton may have, ''k'' = S2''n'' + 1 is the number of neighborhood configurations, and ''n'' is the radius of the neighborhood. Thus, the Wolfram code for a particular rule is a number in the range from 0 to ''S''''S'' − 1, converted from ''S''-ary to decimal notation. It may be calculated as follows: # List all the ''S''2''n'' + 1 possible state configurations of the neighbourhood of a given cell. # Interpreting each configuration as a number as desc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rule 90 Gate Array
Rule or ruling may refer to: Education * Royal University of Law and Economics (RULE), a university in Cambodia Human activity * The exercise of political or personal control by someone with authority or power * Business rule, a rule pertaining to the structure or behavior internal to a business * School rule, a rule that is part of school discipline * Sport rule, a rule that defines how a sport is played * Game rule, a rule that defines how a game is played * Moral, a rule or element of a moral code for guiding choices in human behavior * Norm (philosophy), a kind of sentence or a reason to act, feel or believe * Rule of thumb, a principle with broad application that is not intended to be strictly accurate or reliable for every situation * Unspoken rule, an assumed rule of human behavior that is not voiced or written down * Slide rule, a mechanical analog computer Science * Rule of inference or transformation rule, a term in logic for a function which takes premises and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Garden Of Eden Theorem
In a cellular automaton, a Garden of Eden is a configuration that has no predecessor. It can be the initial configuration of the automaton but cannot arise in any other way. John Tukey named these configurations after the Garden of Eden in Abrahamic religions, which was created out of nowhere. A Garden of Eden is determined by the state of every cell in the automaton (usually a one- or two-dimensional infinite square lattice of cells). However, for any Garden of Eden there is a finite pattern (a subset of cells and their states, called an ''orphan'') with the same property of having no predecessor, no matter how the remaining cells are filled in. A configuration of the whole automaton is a Garden of Eden if and only if it contains an orphan. For one-dimensional cellular automata, orphans and Gardens of Eden can be found by an efficient algorithm, but for higher dimensions this is an undecidable problem. Nevertheless, computer searches have succeeded in finding these patterns in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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