J.E. Hanson and J.P. Crutchfield, Computational mechanics of cellular automata: an ex'ample, Physica D, Series D 103, 169-189, 1997.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....delay between origins of signals The notion of signal defined in definition 8 does not include the gliders of the Ganhe of Life [3] Open Problem 39 : Another notion of signal. Define another notion of signal which could capture signals which are not recognizable by any filtering method [27, 56], as shown on the Figure 1. Figure 1: Circled sites (at the crossing of two usual signals) may be un derstood as sonhe signal which seem to be atomized and then reconstructed. Indeed: 23 Open Problem 40 : What is really a signal Is it possible to give a general definition of a signal ....

J.E. Hanson and J.P. Crutchfield, Computational mechanics of cellular automata: an ex'ample, Physica D, Series D 103, 169-189, 1997.

....is 1=2. It seems that the rule 54 also belongs to [ s] h 0] Actually, g e particles disappearance is an irreversible phenomenon as proved in [17] that will occur more and more rarely when the particles g e become fewer and fewer but the number of g e particles tends to 0 as con rmed by [4, 11] experiments. Then if any interaction between w and g 0 particles occurs, one particle disappears, we can think that the sub shift f(0001) 1110) g is D attracting for 0 1. The Proposition 3.2 raises a natural question: are the CA with unbounded damage spreading sensitive ....

....for 0 1. The Proposition 3.2 raises a natural question: are the CA with unbounded damage spreading sensitive It seems that no. Let us consider a CA 54 that simulates the rule 54 but in a uniform background. Such a CA can be formally de ned thanks to Hanson and Crutch eld s lter [11] which is a CA but only on valid con gurations. Here, we consider any extension of this CA for a measure such that a generic con guration is correct with probability 1. Experimentally, the particle number decreases like t 1=2 and thus tends to 0 so that this CA for well chosen measures tends ....

J. E. Hanson and J. P. Crutcheld. Computational mechanics of cellular automata: an example. Physica D, 103:169-189, 1997.

....is 1=2. It seems that the rule 54 also belongs to [ aas] S 0] Actually, g e particles disappearance is an irreversible phenomenon as proved in [11] that will occur more and more rarely when the particles g e become fewer and fewer but the number of g e particles tends to 0 as con rmed by [3, 8] experiments. Then if any interaction between w and g 0 particles occurs, one particle disappears, we can think that the sub shift f0001 ; 1110 g is D attracting for 0 1. The previous theorem raises a natural question: are the CA with unbounded damages spreading almost ....

....raises a natural question: are the CA with unbounded damages spreading almost everywhere sensitive to initial conditions It seems that no. Let us consider a CA 54 that simulates the rule 54 but in a uniform background. Such a CA can be formally de ned thanks to Hanson and Crutch eld s lter [8] which is a CA but only on valid con gurations. Here, we consider any extension of this CA for a measure such that a generic con guration is correct with probability 1. Experimentally, the particle number decreases like t 1=2 and thus tends to 0 so that this CA for well chosen measures tends ....

J. E. Hanson and J. P. Crutcheld. Computational mechanics of cellular automata: an example. Physica D, 103:169-189, 1997.

....is 1=2. It seems that the rule 54 also belongs to [ aes] S 0] Actually, g e particles disappearance is an irreversible phenomenon as proved in [12] that will occur more and more rarely when the particles g e become fewer and fewer but the number of g e particles tends to 0 as con rmed by [3, 8] experiments. Then if any interaction between w and g 0 particles occurs, one particle disappears, we can think that the sub shift f0001 ; 1110 g is D attracting for 0 1. The previous theorem raises a natural question: are the CAs with unbounded damage spreading almost ....

....a natural question: are the CAs with unbounded damage spreading almost everywhere sensitive to initial conditions It seems that no. Let us consider a CA 54 that simulates the rule 54 but in a uniform background. Such a CA can be formally de ned thanks to Hanson and Crutch eld s lter [8] which is a CA but only on valid con gurations. Here, we consider any extension of this CA for a measure such that a generic con guration is correct with probability 1. Experimentally, the particle number decreases like t 1=2 and thus tends to 0 so that this CA for well chosen measures tends ....

J. E. Hanson and J. P. Crutcheld. Computational mechanics of cellular automata: an example. Physica D, 103:169-189, 1997.

....graph (e.g. temporal periods) to be calculated exactly. Crutchfield and Hanson have developed a technique for extraction of domains and interactions of domains from patterns generated by cellular automata. This has been applied to rule 18, as well as a variety of other rules [20] notably rule 54 [21]. Rule 54. The behavior of rule 54 (001,100, 010, and 101 1, else 0) is transitional between very simple Wolfram class I and II behavior, and chaotic class III behavior. Like class I and II rules, random initial configurations tend under rule 54 toward simple temporally periodic states. Unlike ....

J. E. Hanson and J. P. Crutchfield, Computational Mechanics of Cellular Automata: An Example, these proceedings.

....as rule 22, 30, or 110, could be analyzed this way; rule 30, for instance, has been proposed as a good cryptographic source of random numbers [36] and a fast prediction algorithm for it would make this use inadvisable. Rule 54 has a more complex chemistry of travelling particles than rule 18 does [16], and it is unclear how to predict their motion efficiently. So far we have been unsuccessful at applying our methods to these CAs. Can these results be extended to CAs with looser algebraic structure We note that of the 24 non isomorphic quasigroups of order 4, for example, 14 are polyabelian ....

J.E. Hanson and J.P. Crutchfield, "Computational mechanics of cellular automata: an example." Santa Fe Institute Working Paper 95-10-095, to appear in Physica D, Proceedings of the International Workshop on Lattice Dynamics.

....interaction of gliders can be traced at the lowest level of the system s basic components and their local interactions which are completely defined. This ability to see two levels of behaviour simultaneously, the underlying and emergent, allow insights into the mechanics of self organization (e.g.[6]) a) Ordered dynamics (class 2) about 100time steps. Rule af d1 db 47 b) Complex dynamics (class 4) about 500 time steps. Rule 6c 1e 53 a8 c) Chaotic dynamics (class 3) about 140 time steps. Rule 99 4a 6a 65 Figure 3: Typical 1d CA Space time patterns showing ordered, complex and chaotic ....

....are supposed to be rare[11] Most rules are either ordered or chaotic, though ordered rules become increasingly rare for larger k. In k3 rule space the only two sets of glider rules that occur (rule 54 and 110, and their equivalents[13] see figure4) have been the focus of particular study (e.g. [6]) a)k3 rule 110 b)k3 rule 54 Figure 4: Space time patterns of the only rules in k3 rulespace that support interacting gliders, rule 54 and 110 (and their equivalents[13] The rules are in decimal. n=150, about 200 time steps are shown from random initial states. The color of cells relate to the ....

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Hanson,J.E., and J.P.Cruchfield (1997) "Computational Mechanics of Cellular Automata, An example", Pysica D, vil. 103, 169-189.

....that lead from states in one domain to those in another. Including these transition paths in the set of allowed transitions, the transducer can recognize both regular domains and the particles. A more detailed example of how to extend the transducer to incorporate the particles can be found in [8]. Using this extended transducer, the condensation time t c is then defined as the first time step at which filtering the lattice does not generate any disallowed transitions. The occurrence of the condensation time is illustrated in figure 1(a) for OE dens5 . The condensation time (t c = 4 in ....

Hanson, J. E., Crutchfield, J. P.: Computational Mechanics of Cellular Automata: An Example. Physica D 103 (1997) 169--189.

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