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Sawtooth (cellular Automaton)
In a cellular automaton, a finite pattern is called a sawtooth if its population grows without bound but does not tend to infinity. In other words, a sawtooth is a pattern with population that reaches new heights infinitely often, but also infinitely often drops below some fixed value. Their name comes from the fact that their plot of population versus generation number looks roughly like an ever-increasing sawtooth wave. In rules with small replicators For instance, in Rule 90, a one-dimensional elementary cellular automaton, the population size starting from a single live cell follows Gould's sequence, which has a self-similar sawtooth pattern. On each step whose number is a power of two, the population crashes from a high of the step number plus one to a low of only two live cells. As the population grows with this pattern, its live cells trace out the rows of a Sierpinski triangle. The sawtooth shape of this pattern can be used to recognize physical processes that behave ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gould Sawtooth
Gould may refer to: People * Gould (name), a surname Places United States * Gould, Arkansas, a city * Gould, Colorado, an unincorporated community * Gould, Ohio, an unincorporated community * Gould, Oklahoma, a town * Gould, West Virginia, an unincorporated community * Gould City, Michigan * Gould City, Washington * Gould Township, Minnesota Multiple countries * Gould Lake (other) * Mount Gould (other) Elsewhere * Gould (crater), a lunar crater formation * Gould Coast, Antarctica * Gould Dome, Alberta, Canada Other uses * Gould baronets, two titles, one in the Baronetage of England and one in the Baronetage of Great Britain * Gould Belt, a partial ring of stars in the Milky Way * Gould designation, a type of star identifier * Gould League, an independent Australian organisation promoting environmental education * Gould Electronics, a company involved in the electronics and semiconductor industries * Gould Racing, a British motorsport company * USC Gould S ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sawtooth CA Popgraph
Sawtooth may refer to: Science and technology * Tooth of a saw blade (original meaning) * Sawtooth wave, a type of waveform * Sawtooth (cellular automaton) * Tokamak sawtooth, a phenomenon in plasma physics * Sawtooth, code name for the Power Mac G4 * Sawtooth coriander, a herb also called Culantro * Sawtooth eel * Sawtooth Software Arts and media * Sawtooth (film), a 2004 American thriller and drama film * ''Sawtooth'' (album), an album by British electronic musician Jonny L Places * The Sawtooth, between Mount Evans and Mount Bierstadt in Colorado, United States * Sawtooth Bridges, rail viaducts on Northeast Corridor in Kearny, New Jersey * Sawtooth City, Idaho, United States * Sawtooth National Forest Sawtooth National Forest is a United States National Forest, National Forest that covers 2,110,408 acres (854,052 ha) in the U.S. states of Idaho (~96 percent) and Utah (~4 percent). Managed by the U.S. Forest Service in the United States Depart ..., Idaho, United States ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sawtooth Life
Sawtooth may refer to: Science and technology * Tooth of a saw blade (original meaning) * Sawtooth wave, a type of waveform * Sawtooth (cellular automaton) * Tokamak sawtooth, a phenomenon in plasma physics * Sawtooth, code name for the Power Mac G4 * Sawtooth coriander, a herb also called Culantro * Sawtooth eel * Sawtooth Software Arts and media * Sawtooth (film), a 2004 American thriller and drama film * ''Sawtooth'' (album), an album by British electronic musician Jonny L Places * The Sawtooth, between Mount Evans and Mount Bierstadt in Colorado, United States * Sawtooth Bridges, rail viaducts on Northeast Corridor in Kearny, New Jersey * Sawtooth City, Idaho, United States * Sawtooth National Forest Sawtooth National Forest is a United States National Forest, National Forest that covers 2,110,408 acres (854,052 ha) in the U.S. states of Idaho (~96 percent) and Utah (~4 percent). Managed by the U.S. Forest Service in the United States Depart ..., Idaho, United States ... [...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] |
Sawtooth Wave
The sawtooth wave (or saw wave) is a kind of non-sinusoidal waveform. It is so named based on its resemblance to the teeth of a plain-toothed saw with a zero rake angle. A single sawtooth, or an intermittently triggered sawtooth, is called a ramp waveform. The convention is that a sawtooth wave ramps upward and then sharply drops. In a reverse (or inverse) sawtooth wave, the wave ramps downward and then sharply rises. It can also be considered the extreme case of an asymmetric triangle wave. The equivalent piecewise linear functions x(t) = t - \lfloor t \rfloor x(t) = t \bmod 1 based on the floor function of time ''t'' is an example of a sawtooth wave with period 1. A more general form, in the range −1 to 1, and with period ''p'', is 2\left( - \left\lfloor + \right\rfloor\right) This sawtooth function has the same phase as the sine function. While a square wave is constructed from only odd harmonics, a sawtooth wave's sound is harsh and clear and its spectrum contai ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
Elementary Cellular Automaton
In mathematics and computability theory, an elementary cellular automaton is a one-dimensional cellular automaton where there are two possible states (labeled 0 and 1) and the rule to determine the state of a cell in the next generation depends only on the current state of the cell and its two immediate neighbors. There is an elementary cellular automaton (rule 110, defined below) which is capable of universal computation, and as such it is one of the simplest possible models of computation. The numbering system There are 8 = 23 possible configurations for a cell and its two immediate neighbors. The rule defining the cellular automaton must specify the resulting state for each of these possibilities so there are 256 = 223 possible elementary cellular automata. Stephen Wolfram proposed a scheme, known as the Wolfram code, to assign each rule a number from 0 to 255 which has become standard. Each possible current configuration is written in order, 111, 110, ..., 001, 000, and the re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gould's Sequence
Gould's sequence is an integer sequence named after Henry W. Gould that counts how many odd numbers are in each row of Pascal's triangle. It consists only of power of two, powers of two, and begins:. :1, 2, 2, 4, 2, 4, 4, 8, 2, 4, 4, 8, 4, 8, 8, 16, 2, 4, ... For instance, the sixth number in the sequence is 4, because there are four odd numbers in the sixth row of Pascal's triangle (the four bold numbers in the sequence 1, 5, 10, 10, 5, 1). Additional interpretations The th value in the sequence (starting from ) gives the highest power of 2 that divides the central binomial coefficient \tbinom, and it gives the numerator of 2^n/n! (expressed as a fraction in lowest terms). Gould's sequence also gives the number of live cells in the th generation of the Rule 90 cellular automaton starting from a single live cell.. It has a characteristic growing sawtooth wave, sawtooth shape that can be used to recognize physical processes that behave similarly to Rule 90.. Related sequences ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Self-similarity
__NOTOC__ In mathematics, a self-similar object is exactly or approximately similar to a part of itself (i.e., the whole has the same shape as one or more of the parts). Many objects in the real world, such as coastlines, are statistically self-similar: parts of them show the same statistical properties at many scales. Self-similarity is a typical property of fractals. Scale invariance is an exact form of self-similarity where at any magnification there is a smaller piece of the object that is similar to the whole. For instance, a side of the Koch snowflake is both symmetrical and scale-invariant; it can be continually magnified 3x without changing shape. The non-trivial similarity evident in fractals is distinguished by their fine structure, or detail on arbitrarily small scales. As a counterexample, whereas any portion of a straight line may resemble the whole, further detail is not revealed. A time developing phenomenon is said to exhibit self-similarity if the numerical v ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
American Mathematical Monthly
''The American Mathematical Monthly'' is a mathematical journal founded by Benjamin Finkel in 1894. It is published ten times each year by Taylor & Francis for the Mathematical Association of America. The ''American Mathematical Monthly'' is an expository journal intended for a wide audience of mathematicians, from undergraduate students to research professionals. Articles are chosen on the basis of their broad interest and reviewed and edited for quality of exposition as well as content. In this the ''American Mathematical Monthly'' fulfills a different role from that of typical mathematical research journals. The ''American Mathematical Monthly'' is the most widely read mathematics journal in the world according to records on JSTOR. Tables of contents with article abstracts from 1997–2010 are availablonline The MAA gives the Lester R. Ford Awards annually to "authors of articles of expository excellence" published in the ''American Mathematical Monthly''. Editors *2022– ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Highlife (cellular Automaton)
Highlife is a cellular automaton similar to Conway's Game of Life. It was devised in 1994 by Nathan Thompson. It is a two-dimensional, two-state cellular automaton in the " Life family" and is described by the rule B36/S23; that is, a cell is born if it has 3 or 6 neighbors and survives if it has 2 or 3 neighbors. Because the rules of HighLife and Conway's Life (rule B3/S23) are similar, many simple patterns in Conway's Life function identically in HighLife. More complicated engineered patterns for one rule, though, typically do not work in the other rule. Replicator The main reason for interest in HighLife comes from the existence of a pattern called the replicator. After running the replicator for twelve generations, the result is two replicators. The replicators will repeatedly reproduce themselves, all on a diagonal line. Whenever two replicators try to expand into each other, the pattern in the middle simply vanishes. The behavior of a row of Replicators interacting with ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
