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Computational Universality and 1/f Noise in Elementary Cellular Automata [article]

Shigeru Ninagawa
2013 arXiv   pre-print
It is speculated that there is a relationship between 1/f noise and computational universality in cellular automata.  ...  The fitness is estimated from the power spectrum in consideration of the similarity to 1/f-type spectrum.  ...  In the final section we discuss the relationship between computational universality and 1/f noise in CAs.  ... 
arXiv:1307.4938v1 fatcat:oorrc6gzl5al7nypq76tlhpedu

1∕fαspectra in elementary cellular automata and fractal signals

Jan Nagler, Jens Christian Claussen
2005 Physical Review E  
On the one hand our analysis reveals that one automaton displays 1/f spectra though considered as trivial, and on the other hand that various automata classified as chaotic/complex display no 1/f spectra  ...  From the widespread occurrence of (elementary) cellular automata patterns in chemistry, physics and computer sciences, there are various candidates to show spectra similar to our results.  ...  The thermal 1/f 2 decay of rule 110 (grey) as a typical member of Class 4 is shown for comparison.  ... 
doi:10.1103/physreve.71.067103 pmid:16089916 fatcat:fd3dia4ynzhatptznwrfykqzp4

Cellular Automata Model for a Specific Traffic Regime and 1/f Noise

Reuben Thieberger
2015 Computer Technology and Application  
All the cases can be written as 1/ f a .  ...  In addition to checking different densities we check also the influence of changes in the number of cars which were added.  ...  This will become clearer D DAVID PUBLISHING Cellular Automata Model for a Specific Traffic Regime and 1/f Noise 31 when we will explain the rules which we use.  ... 
doi:10.17265/1934-7332/2015.01.005 fatcat:kyoeddbc7jastkgvijwh7rpqba

Evolution of Cellular Automata toward a LIFE-Like Rule Guided by 1/ƒ Noise

Shigeru NINAGAWA
2010 IEICE transactions on information and systems  
There is evidence in favor of a relationship between the presence of 1/ f noise and computational universality in cellular automata.  ...  These results support the relationship between the presence of 1/ f noise and computational universality. key words: cellular automaton, genetic algorithm, computational universality, 1/ f noise  ...  A version of this paper first appeared in the Proceedings of ECAL 2005 [33] .  ... 
doi:10.1587/transinf.e93.d.1489 fatcat:zegtanv52zap3gz3ut7ow4p2xe

Damage spreading and Lyapunov exponents in cellular automata

F. Bagnoli, R. Rechtman, S. Ruffo
1992 Physics Letters A  
After the introduction of a small noise elementary cellular automata reveal the same type of transition.  ...  Using the concept of the Boolean derivative we study damage spreading for one dimensional elementary cellular automata and define their maximal Lyapunov exponent.  ...  In Fig. 2 , we show the location of all the 88 minimal elementary rules with noise in the (µ, λ) diagram, starting with α 0 = 0.5.  ... 
doi:10.1016/0375-9601(92)90185-o fatcat:kopzbl7ibjh3fpjh56nzkpefce

Toy Models of Top Down Causation

Adrian Kent
2020 Entropy  
I describe probabilistic toy models based on cellular automata that illustrate possibilities and difficulties with these ideas.  ...  They also give a way of defining a form of panprotopsychist property dualism, in which consciousness and material physics causally affect one another.  ...  He noted the particularly interesting and complex behaviour of the automaton defined by rule 110 in his classification.  ... 
doi:10.3390/e22111224 pmid:33286992 pmcid:PMC7711512 fatcat:pgoru477h5gqvji5frlkcy2rxq

Toy Models of Top Down Causation [article]

Adrian Kent
2020 arXiv   pre-print
I describe toy models based on probabilistic cellular automata that illustrate possibilities and difficulties with these ideas.  ...  They also give a way of defining a form of panprotopsychist property dualism, in which consciousness and material physics causally affect one another.  ...  He noted the particularly interesting and complex behaviour of the automaton defined by rule 110 in his classification.  ... 
arXiv:1909.12739v2 fatcat:am4s4sekuvbcff2i442vh347ya

Logical Gates via Gliders Collisions [chapter]

Genaro J. Martínez, Andrew Adamatzky, Kenichi Morita
2018 Reversibility and Universality  
An elementary cellular automaton with memory is a chain of finite state machines (cells) updating their state simultaneously and by the same rule.  ...  Some cellstate transition rules support gliders, compact patterns of non-quiescent states translating along the chain.  ...  Elementary Cellular Automaton Rule 22 Rule 22 is an ECA with the following local function: The local function ϕ R22 has a probability of 37.5% to get states 1 in the next generation and much higher probability  ... 
doi:10.1007/978-3-319-73216-9_9 dblp:conf/birthday/MartinezAM18 fatcat:cmvpnjtk7rduzdjpwhksv4lfzu

Investigation of Rule 73 as Case Study of Class 4 Long-Distance Cellular Automata [article]

Lucas Kang
2013 arXiv   pre-print
The most widely known form of CA, the elementary cellular automaton (ECA), has been studied in particular due to its simple form and versatility.  ...  Namely, "long-distance cellular automata" (LDCA), a construct that had been described in the past, but never studied.  ...  This corresponds in the glider system to being able to encode  ... 
arXiv:1310.3311v1 fatcat:4t24y6mw4bekfdnqb5bby4e754

Statistical mechanics of cellular automata

Stephen Wolfram
1983 Reviews of Modern Physics  
Statistical properties of the structures generated are found to lie in two universality classes, independent of the details of the initial state or the cellular automaton rules.  ...  A detailed analysis is given of "elementary" cellular automata consisting of a sequence of sites with values 0 or 1 on a line, with each site evolving deterministically in discrete time steps according  ...  -1)+ f(k -2); f(O)=O, f( 1)= 1].  ... 
doi:10.1103/revmodphys.55.601 fatcat:vgilksyghrbz3cmiqpcjdph3by

Conservative Reversible Elementary Cellular Automata and their Quantum Computations [chapter]

Anas N.
2011 Cellular Automata - Innovative Modelling for Science and Engineering  
The main contribution of this research is the creation of a new algorithm that can be used in noisy discrete systems modeling using conservative reversible elementary cellular automata (CRECA) and the  ...  These are auxiliary outputs and inputs from which a reversible map is www.intechopen.com Conservative Reversible Elementary Cellular Automata and their Quantum Computations 59 constructed (cf.  ...  An Elementary Cellular Automaton (ECA) is a collection of "colored" cells on a grid of specified shape that evolves through a number of discrete time steps according to a set of rules which are based on  ... 
doi:10.5772/16155 fatcat:bmya7ayfabae5byigkgnmhfwmm

Connectionist-Symbolic Machine Intelligence using Cellular Automata based Reservoir-Hyperdimensional Computing [article]

Ozgur Yilmaz
2015 arXiv   pre-print
Input is randomly projected onto the initial conditions of automaton cells and nonlinear computation is performed on the input via application of a rule in the automaton for a period of time.  ...  Cellular automaton is used as the reservoir of dynamical systems.  ...  Vector addition defined in [39] is used to form the conceptors of each class: T i = sign( 50 j=1 F ij − 0.5 0.5 ).  ... 
arXiv:1503.00851v3 fatcat:b4mbomhexjezfitvhsny4yjkga

NONINVERTIBLE TRANSFORMATIONS AND SPATIOTEMPORAL RANDOMNESS

J. A. GONZÁLEZ, A. J. MORENO, L. E. GUERRERO
2006 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering  
In a similar fashion, we explain why some well-known spatiotemporal systems have been found to produce very complex dynamics in numerical simulations.  ...  We show that, in some cases, these systems can produce completely unpredictable dynamics.  ...  Representation of Rule 110 cellular automaton. 111 110 101 100 011 010 001 000 0 1 1 0 1 1 1 0 Table 3.  ... 
doi:10.1142/s0218127406016859 fatcat:xvu3qgmn7nf6nnjkibyqfprjjq

Definition and Identification of Information Storage and Processing Capabilities as Possible Markers for Turing-universality in Cellular Automata [article]

Yanbo Zhang
2018 arXiv   pre-print
To identify potential universal cellular automata, a method is developed to measure information processing capacity of elementary cellular automata.  ...  By observing these two features, potential universal cellular automata are classified into a certain class, and all elementary cellular automata can be classified into four groups, which correspond to  ...  Lingfei Wu in University of Chicago, Dr. Qianyuan Tang in Nanjing University, Dr. Kaiwen Tian in University of Pennsylvania and Dr. Hector Zenil in Karolinska Institutet.  ... 
arXiv:1803.06919v1 fatcat:axiwsm6hmbddtewkc56cksz7f4

Stochastic Cellular Automata Solve the Density Classification Problem with an Arbitrary Precision

Nazim Fates, Marc Herbstritt
2011 Symposium on Theoretical Aspects of Computer Science  
The density classification problem consists in using a binary cellular automaton (CA) to decide whether an initial configuration contains more 0s or 1s.  ...  This problem is known for having no exact solution in the case of binary, deterministic, one-dimensional CA. Stochastic cellular automata have been studied as an alternative for solving the problem.  ...  x t c+1 ) A Stochastic Elementary Cellular Automaton (sECA) is also defined by a local transition rule, but the next state of a cell is known only with a given probability.  ... 
doi:10.4230/lipics.stacs.2011.284 dblp:conf/stacs/Fates11 fatcat:nwtvqgueerdzhmdftrsz5w2bxa
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