Gerard Y. Vichniac. Simulating physics with cellular automata. Physica, 10D:96--116, 1984.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....for performance bottlenecks. Simpler systems can also be potentially used to verify the correctness of the ensuing protocols. To achieve this, such translations should be efficient and should preserve the basic properties across the original and the translated system. In re cent years (see [68, 36, 97, 29], several authors have suggested building cellular automata based computers for simulating physics. The results presented here are pertinent to this basic theme in two ways. We believe that SDS based computers are better suited for simu luring socio technical systems. Second, regardless, of the ....

G. Vichniac. Simulating Physics with Cellular Au- tomata. Physica, 10D, pp. 96-115, 1984.

....superluminal phase waves (or beats) stemming from correlated information which has spread throughout the system. 2.3. 2 Voting Rules The dynamics of many CA can be described as a voting process where a cell tends to take on the values of its neighbors, or in some circumstances, opposing values [93]. Voting rules are characteristically irreversible because the information in a cell is often erased without contributing to another cell, and irreversibility is equivalent to destroying information. In practice, it is usually pretty clear when a rule is irreversible 29 because frozen or ....

....have one predecessor. Usually the recurrence time is astronomical because there are so many variables and few conservation laws, but for the specific system shown in figure 2 10, the period is a mere 40926 steps. Cellular automata are well suited for doing dynamical simulations of Ising models [19, 20, 93], where each cell contains one spin (1 = up, Gamma1 = down) Many variations are possible, and figure 2 11 shows one such model that is a reversible, second order CA which conserves the usual Ising Hamiltonian, H = GammaJ i;j s i s j ; 2.1) where J is a coupling constant, and Delta ....

G'erard Y. Vichniac. Simulating physics with cellular automata. Physica D, 10:96--116, 1984.

.... Norman Margolus, and, for a while, G erard Vichniac and Charles Bennett) developed both high performance cellular automata machines (cam6[32] and cam8[20] and a vast pool of expertise in programming all sorts of aspects of physics in the language of programmable matter (see, for example, [41] and Mark Smith s doctoral thesis[27] The present initiative is a natural continuation of that program. 2.2 Legacies It will be useful to acknowledge and hopefully transcend a number of minor annoyances that cellular automata have had to live with as a matter of historical legacy. To begin ....

Vichniac, Gerard, \Simulating physics with cellular automata," Physica D 10 (1984), 96-115.

....the cellular automaton paradigm. Inspired by Fredkin s billiard ball model of computation[19] Margolus arrived in 1983 at a very simple computation universal ica[41] that is suggestive of how a computer could in principle be built out of microscopic mechanics. At about the same time, Vichniac[83] and Creutz[13] pioneered the used of cellular automata for the microcanonical modeling of Ising spin systems. The introduction of dedicated cellular automata machines[71] encouraged much new experimental work on ica, and stimulated further theoretical developments. For instance, according to ....

....of the form q i X , as in (17) is much more general than a difference operator of the form fq t i X Gamma , as in (16) We shall briefly present two examples of secondorder ica that combine richness of behavior with economy of means. #9 The Q2R rule, introduced by G erard Vichniac [83] (for more detail, see [77, Chapter 17] is the simplest microcanonical model of a twodimensional Ising spin system. The two elements of the state alphabet A = f ; #g can be thought of as the two orientations of a spin 1 2 particle tied to each lattice site. The neighborhood consists of the ....

Vichniac, G'erard, "Simulating physics with cellular automata," Physica 10D (1984), 96--115.

....rules. The updating selects the new state of each cell so as to conform to the value currently hold by the majority of the neighbors. Typically, in these majority rules, the state is either 0 or 1. A very interesting behavior is observed with the twisted majority rule proposed by G. Vichniac [44]: in two dimensions, each cell considers its Moore neighborhood (i.e itself plus its eight nearest neighbors) and computes the sum of the cells having a value 1. This sum can be any value between 0 and 9. The new state s ij (t 1) of each cell is then determined from this local sum, according to ....

....coupled in the sense that each pair (s i ; s j ) of neighbor spins contributes an amount GammaJ s i s j to the energy of the system. Intuitively, the dynamics of such a system is that a spin flips (s i Gammas i ) if this is favorable in view of the energy of the local configuration. Vichniac [44], in the 1980s, has proposed a CA rule, called the Q2R, simulating the behavior of an Ising spin dynamics. The model is as follows: We consider a two dimensional square lattice such that each site holds a spin s i which is either up (s i = 1) or down (s i = 0) instead of Sigma1) The coupling ....

G. Vichniac. Simulating physics with cellular automata. Physica D, 10:96-- 115, 1984.

....to be computationuniversal ( Berlekamp et al. 1982 ] In physics cellular automata provide discrete models for a branch of dynamical systems theory that studies the emergence of well characterized collective phenomena such as ordering, turbulence, chaos, symmetry breaking, fractality,etc. Vichniac, 1984 ] Bennett and Grinstein, 1985 ] Wolfram, 1984 ] Wolfram, 1983 ] There, research departs from the equilibrium statistical physics (cf. section 2.1.1) and investigates dynamics outside static stability points. Finally, cellular automata models nd their way into biological modeling as ....

G. Y. Vichniac. Simulating physics with cellular automata. Physica D, 10:96-116, 1984.

....Additive CA have been studied by several authors (see for example [5,14,19] Despite their simplicity that allows an algebraic analysis, additive CA exhibit many of the complex features of general CA. They have been used for modeling and approximating many physical phenomena (see for example [21]) We prove that they are chaotic according to the definition of chaos given by Devaney. We show that the sensitivity of the local rule on which a CA is based plays a crucial role in determining its chaotic evolution. Informally, we say that a map f is sensitive to one of its input variables if ....

G. Y. Vichniac, Simulating Physics with Cellular Automata. Physica D 10, 96-116, 1990

.... rule, and local, transitions are determined by the configuration of types on a finite set of neighboring sites [18, 13] These models can be thought as interacting particle systems and their connections with statistical mechanics models have been widely studied in past years (see, for instance, [9, 17, 19, 20]) A particular example of cellular automata, known as bootstrap percolation, has been introduced in [5] to model some magnetic systems. More informations on the physical relevance of this model are given in [10, 4] In bootstrap percolation only two different types are associated to each site: ....

G.Y. Vichniac (1984). Simulating physics with cellular automata. Phys. D 10, 96.

.... same rule, and local, transitions are determined by the con guration of types on a nite set of neighboring sites [18, 13] These models can be thought as interacting particle systems and their connections with statistical mechanics models have been widely studied in past years (see, for instance, [9, 17, 19, 20]) A particular example of cellular automata, known as bootstrap percolation, has been introduced in [5] to model some magnetic systems. More informations on the physical relevance of this model are given in [10, 4] In bootstrap percolation only two di erent types are associated to each site: ....

G.Y. Vichniac (1984). Simulating physics with cellular automata. Phys. D 10, 96.

.... fluid (and more directions for An than for Z n ) 10 We expect (work in progress) that, with our approach, we will be less bothered by 10 The LGA are a computational model of physics based on cellular automata [Fey82, Min82, FT82, Tof84, TM87, Sny47, Ung58, Mar84, SW86, Mac86, Tof77b, Tof77a, Vic84, Wol83, Zus69, Hil55, Svo86] For this CA approach in general, emphasis is placed on the simplicity of the local transition rules for each cellular automaton [FHP86] The processors in our methodology are not restricted to simple cellular automaton like rules. 32 the symmetries of A 3 . It ....

G. Vichniac. Simulating physics with cellular automata. Physica 10D, pages 96--116, 1984.

....Tommaso To#oli, and Norman Margolus[87, 39, 61] The idea of building special purpose machines to simulate these physics like models on a fine grained space [88, 61] originated there. A good review of the kind of cellular automata modeling done in the early 1980 s is given by Gerard Vichniac [93]. During this time, Stephen Wolfram visited the Information Mechanics Group and was stimulated by their work. In 1983 Wolfram popularized cellular automata as a simple mathematical model to investigate self organization in 3 statistical mechanics [94, 71] Beyond this, no useful insights towards ....

Gerard Y. Vichniac. Simulating physics with cellular automata. Physica, 10D:96--116, 1984.

....for considering non dissipating wave fronts 2 Notation, Definitions and Assumptions The major purpose of this section is to specify (Definition 5) the class M of reasonable lattice computers. 2 While the methodology we employ herein bears a resemblance to that of cellular automata approaches [Fey82, Min82, FT82, Tof84, TM87, Sny47, Ung58, Mar84, SW86, Mac86, Tof77b, Tof77a, Vic84, Wol83, Zus69, Hil55, Svo86], our philosophy of algorithmic locality is not subject to the same apparent computational limitations. Koc91] see the last section of the Appendix) considers dissipating wavefronts in one variety of lattice computer only and his algorithm is based on discretizing the wave equation. 3 See ....

G. Vichniac. Simulating physics with cellular automata. Physica 10D, pages 96--116, 1984.

....Machine 2. 21 phase transition [11] scaling [10] that relates critical point exponents [36] critical slowing down, and so forth. The numerical techniques applied to it appear to be endless: the Monte Carlo Metropolis algorithm, microcanonical cluster Monte Carlo[21] Ising cellular automata [70, 69, 21], deterministic heat bath [32, 44] parallel Monte Carlo [56] multispin encoding [78] multigrid techniques [38] Monte Carlo renormalization group [39, 65] and so on. In order to capture the kinetic behavior of a liquid gas fluid it is apropos to explore other simple models following after ....

Gerard Y. Vichniac. Simulating physics with cellular automata. Physica, 10D:96--116, 1984. 43

....26, 27] The idea of building special purpose machines to simulate physics like models on a fine grained space [28, 27] originated there and today still remains a strength of that group. A good review of the kind of cellular automata modeling done in the early 1980 s is given by Gerard Vichniac [29]. During this time, Stephen Wolfram visited the Information Mechanics Group and was stimulated by their work. In 1983 Wolfram popularized cellular automata as a simple mathematical model to investigate self organization in statistical mechanics[2, 30] After visiting the MIT Information Mechanics ....

Gerard Y. Vichniac. Simulating physics with cellular automata. Physica, 10D:96--116, 1984.

....are square meshes, i.e. meshes whose underlying sets are finite subsets of Z 2 . CAM [TM87] features such a partially simulated mesh with the addition of simulated toroidal connections. 3 While the methodology we employ herein bears a resemblance to that of cellular automata approaches [Fey82, Min82, FT82, Tof84, TM87, Sny47, Ung58, Mar84, SW86, Mac86, Tof77b, Tof77a, Vic84, Wol83, Zus69, Hil55, Svo86], our philosophy of algorithmic locality is not subject to the same apparent computational limitations. 3. in any reasonable (See Section 2) bounded lattice computer M(D) where D is contained in any one of a wide class of lattices, nearly perfect wave front broadcasts are possible (See ....

G'erard Y. Vichniac. Simulating physics with cellular automata. Physica 10D, pages 96--116, 1984.

.... Some of the workers in the cellular automata approach to physics (see, for example, Feynman (1982) Minsky (1982) Fredkin and Toffoli (1982) Toffoli (1984) Toffoli and Margolus (1987) Margolus (1984) Salem and Wolfram (1986) Thinking Machines (1986) Toffoli (1977b) Toffoli (1977a) Vichniac (1984), Wolfram (1983) Svozil (1986) Frisch, Hasslacher and Pomeau (1986) and Hasslacher (1987) seem to take this idea seriously. The theory of Cellular Automata (Neumann (1966) Burks (1970) and Codd (1968) is a clean, theoretical model for representing discrete space, especially from the point ....

Vichniac, G. (1984). Simulating physics with cellular automata. Physica 10D, 96--116.

....of solid objects (which consist of an aggregate of single particles) As will be clear, our algorithms necessarily carefully control the timing of the message sending that simulates particle motion. While the underpinning we employ herein bears a resemblance to that of cellular automata approaches [Fey82, Min82, FT82, Tof84, TM87, Mar84, SW86, Mac86, Tof77b, Tof77a, Vic84, Wol83, Svo86, FHP86, Has87] our philosophy of algorithmic locality is not subject to the same apparent computational limitations. For example, although 2 dimensional analogical fluid flow simulations (based on the lattice A 2 ) can be carried out quite successfully with the cellular automata approach [SW86, Mac86] there ....

G'erard Y. Vichniac. Simulating physics with cellular automata. Physica 10D, pages 96--116, 1984.

....herein successfully simulate certain constant speed motions virtually linear in real time. Our general approach is related to, but not the same as, the computational models of physics based on cellular automata [Sny47, Hil55, Ung58, Zus69, Tof77a, Tof77b, Fey82, FT82, Min82, Wol83, Mar84, Tof84, Vic84, Mac86, Svo86, SW86, TM87] Lattice Gas models [Has87] are often studied using cellular automata to simulate complex physical phenomena. In a cellular automaton implementation of a Lattice Gas model, emphasis is placed on the simplicity of the local transition rule for the cellular automaton ....

G'erard Y. Vichniac. Simulating physics with cellular automata. Physica 10D, pages 96--116, 1984.

....to the cellular automaton paradigm. Inspired by Fredkin s billiard ball model of computation[19] Margolus arrived in 1983 at a very simple computation universal ica[41] that is suggestive of how a computer could in principle be built out of microscopic mechanics. At about the same time, Vichniac[83] and Creutz[13] pioneered the used of cellular automata for the microcanonical modeling of Ising spin systems. The introduction of dedicated cellular automata machines[71] encouraged much new experimental work on ica, and stimulated further theoretical developments. For instance, according to ....

.... Gamma , as in (16) We shall briefly present two examples of second order ica that combine richness of behavior with economy of means. 9 Figure 1: Equilibrium configurations of Q2R above the critical energy (left) and at the critical energy (right) The Q2R rule, introduced by G erard Vichniac[83] (for more detail, see [77, Chapter 17] is the simplest microcanonical model of a two dimensional Ising spin system. The two elements of the state alphabet A = f ; #g can be thought of as the two orientations of a spin 1 2 particle tied to each lattice site. The neighborhood consists of the ....

Vichniac, G'erard, "Simulating physics with cellular automata, " Physica D 10 (1984), 96--115.

.... growth, reproduction, competition and evolution [Toffoli and Margolus, 1987, Langton, 1984, Burks, 1970, Smith, 1969] CAs also provide a means for modeling physical phenomena by reducing them to their basic, elemental laws (rules) Toffoli, 1980, Fredkin and Toffoli, 1982, Margolus, 1984, Vichniac, 1984, Bennett and Grinstein, 1985] CAs exhibit three notable features: massive parallelism, locality of cellular interactions, and simplicity of basic components (cells) They perform computations in a distributed fashion on a spatially extended grid. As such they differ from the standard approach to ....

G. Vichniac. Simulating physics with cellular automata. Physica D, 10:96-- 115, 1984.

.... automaton can be found in [245] In the early 1980s, a number of researchers began to study cellular automata as models of complex dynamical systems and, more generally, as an alternative to differential equations McCOLL : SPECIAL PURPOSE PARALLEL COMPUTING in modelling physical phenomena [112, 259, 363, 382, 402]. Researchers such as Toffoli and Margolus have also produced various special purpose parallel machines for the simulation of cellular automata models [260, 261, 362, 364] These machines provide performance at least several orders of magnitude greater than with a sequential computer, for a ....

G Y Vichniac. Simulating physics with cellular automata. In Farmer et al. [112], pages 96--116.

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Gerard Y. Vichniac. Simulating physics with cellular automata. Physica, 10D:96--116, 1984.

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Gerard Y. Vichniac. Simulating physics with cellular automata. Physica, 10D:96--116, 1984.

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G.Y. Vichniac. Simulating Physics with Cellular Automata. Physica D, 10:96--116, 1984.

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G. Y. Vichniac. Simulating physics with cellular automata. Physica D, 10:96--116, 1984.

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