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On Soliton Collisions between Localizations in Complex Elementary Cellular Automata: Rules 54 and 110 and Beyond

Genaro J. Martínez, Andrew Adamatzky, Fangyue Chen, Leon Chua
2012 Complex Systems  
The original soliton models in CAs proposed with filter automata are briefly discussed, followed by solutions in elementary CAs (ECAs) domain with the famous universal ECA rule!  ...  In this paper, a single-soliton two-component cellular automaton (CA) model of waves is presented as mobile self-localizations, also known as particles, waves, or gliders, in addition to its version with  ...  Solitons in One-Dimensional Cellular Automata A soliton is a solitary wave with nonlinear behavior that preserves its form and speed, interacting with some kind of perturbation.  ... 
doi:10.25088/complexsystems.21.2.117 fatcat:okwi7vx7rjevhfaydnuahaszni

On Soliton Collisions between Localizations in Complex Elementary Cellular Automata: Rules 54 and 110 and Beyond [article]

Genaro J. Martinez, Andrew Adamatzky, Fangyue Chen, Leon Chua
2013 arXiv   pre-print
In this paper we present a single-soliton two-component cellular automata (CA) model of waves as mobile self-localizations, also known as: particles, waves, or gliders; and its version with memory.  ...  We will discuss briefly the original soliton models in CA proposed with filter automata, followed by solutions in elementary CA (ECA) domain with the famous universal ECA Rule 110, and reporting a number  ...  Solitons in one-dimensional cellular automata A soliton is a solitary wave with non-linear behaviour that preserves its form and speed, interacting with some kind of perturbation.  ... 
arXiv:1301.6258v1 fatcat:q5z6jotj6bafni3do4zpzrrybq

Verification and reformulation of the competitive exclusion principle

Lev V. Kalmykov, Vyacheslav L. Kalmykov
2013 Chaos, Solitons & Fractals  
Here we show a mechanism of competitive coexistence based on a soliton-like behaviour of population waves.  ...  We have modelled it by the logical axiomatic deterministic individual-based cellular automata method.  ...  Previously, the paradoxical phenomenon of soliton-like (quasi-soliton) behaviour of population waves was revealed for ultra-fast chemotactic bacteria -their colliding population waves did not annihilate  ... 
doi:10.1016/j.chaos.2013.07.006 fatcat:eyrckkbcvjbgvhzksfqvf6dkam

Soliton automata with constant external edges

Miklós Krész
2008 Information and Computation  
Both from theoretical and practical point of view, it is a central question to describe soliton automata with constant external edges.  ...  Soliton automata are the mathematical models of certain possible molecular switching devices.  ...  The word soliton ("solitary wave") is applied to certain types of waves traveling relatively large distance with little energy loss.  ... 
doi:10.1016/j.ic.2008.03.014 fatcat:bpqgjnb2zjcablrjfdzlgblj5m

Soliton automata

J. Dassow, H. Jürgensen
1990 Journal of computer and system sciences (Print)  
by soliton automata.  ...  We prove a characterization of strongly deterministic soliton automata, certain important properties of their transition monoids, and a characterization of the class of automata which can be simulated  ...  with a direct product of transition monoids of soliton automata based on indecomposable soliton graphs.  ... 
doi:10.1016/0022-0000(90)90010-i fatcat:2zvcj66n3jck3ixlboh6ehl5cy

Computing with Classical Soliton Collisions [chapter]

Mariusz H. Jakubowski, Ken Steiglitz, Richard Squier
2016 Emergence, Complexity and Computation  
We review work on computing with solitons, from the discovery of solitons in cellular automata, to an abstract model for particle computation, information transfer in collisions of optical solitons, state  ...  transformations in collisions of vector solitons, a proof of the universality of blinking spatial solitons, and the demonstration of multistable collision cycles and their application to state-restoring  ...  A soliton is a solitary wave which asymptotically preserves its shape and velocity upon nonlinear interaction with other solitary waves, or, more generally, with another (arbitrary) localized disturbance  ... 
doi:10.1007/978-3-319-33921-4_12 fatcat:24f4ezqo65fozb42lmpmtelxpy

Page 4622 of Mathematical Reviews Vol. , Issue 2003f [page]

2003 Mathematical Reviews  
Some of the subjects covered in Chapter 3 (Computation on and with graphs) are the approx- imation of shortest paths by excitation waves spreading in data space, cellular automata approximations of a spanning  ...  in a billiard ball model, a lattice where each cell can be excited to change its state under certain rules, the interactions of two- and three-dimensional solitons (solitary wave pulses) and those of  ... 

Towards Cytoskeleton Computers. A proposal [article]

Andrew Adamatzky, Jack Tuszynski, Joerg Pieper, Dan V. Nicolau, Rossalia Rinalndi, Georgios Sirakoulis, Victor Erokhin, Joerg Schnauss, David M. Smith
2018 arXiv   pre-print
Collision-based cytoskeleton computers implement logical gates via interactions between travelling localisation (voltage solitons on AF/MT chains and AF/MT polymerisation wave fronts).  ...  Data signals are travelling localisations (solitons, conformational defects) at the network terminals.  ...  AF/MT are nonlinear inhomogeneous transmission lines supporting propagation of non-linear dispersing waves and localized waves in the form of solitons.  ... 
arXiv:1810.04981v1 fatcat:umhtzg3s5zeqtjhysbv4knrvna

Generative complexity of Gray-Scott model [article]

Andrew Adamatzky
2016 arXiv   pre-print
(similar to wave-fragments in sub-excitable media) and travelling localisations (similar to quasi-dissipative solitons and gliders in Conway's Game of Life).  ...  We analyse behaviour of the systems with highest values of the generative morphological complexity and show that the Gray-Scott systems expressing highest levels of the complexity are composed of the wave-fragments  ...  Formation of the new wave-fragments and their multiplication continues (Fig. 6c-h) till there is a space available.  ... 
arXiv:1610.09097v1 fatcat:ymdh24nvobcktfnvy4wkzqytuq

Deterministic soliton automata with at most one cycle

J. Dassow, H. Jürgensen
1993 Journal of computer and system sciences (Print)  
cycles are not permitted in the soliton graphs belonging to strongly deterministic soliton automata.  ...  In the present paper, we focus on a special class of deterministic soliton automata, that of deterministic soliton automata whose underlying graphs contain at most one cycle.  ...  With the concatenation as multiplication, X* and Xf are the free monoid and the free semigroup over X. For a word w E X*, 1 WJ is the length of w; in particular, 1~1 = 0.  ... 
doi:10.1016/0022-0000(93)90002-e fatcat:65jjiu7so5gfrn7ubc7trit7t4

Probabilistic cellular automata for interacting fermionic quantum field theories [article]

C. Wetterich
2020 arXiv   pre-print
Classical cellular automata with probabilistic initial conditions admit a description in the formalism of quantum mechanics.  ...  Our model exhibits interesting features as spontaneous symmetry breaking or solitons. The same model can be formulated as a generalized Ising model.  ...  We deal here with classical cellular automata with a local updating, as proposed by Ulam and von Neumann, not with the quantum cellular automata proposed by Feynman, see ref. [1] for an overview.  ... 
arXiv:2007.06366v2 fatcat:6p2vqc3ck5f2rojk54neub65qa

Deciding the deterministic property for soliton graphs

Miklós Bartha, Miklós Krész
2009 Ars Mathematica Contemporanea  
Soliton automata are a graph theoretic model for electronic switching at the molecular level.  ...  In the design of soliton circuits, the deterministic property of the corresponding automata is of primary importance.  ...  Soliton graphs and automata By a graph G = (V (G), E(G)), throughout the paper, we mean a finite undirected graph with multiple edges and loops allowed.  ... 
doi:10.26493/1855-3974.46.b2f fatcat:54km6v7ufzge3piieqwj22ta4i


2011 International Journal of Modern Physics C  
Gliders in one-dimensional cellular automata are compact groups of non-quiescent and non-ether patterns (ether represents a periodic background) translating along automaton lattice.  ...  They can be considered as binary strings or symbols travelling along a one-dimensional ring, interacting with each other and changing their states, or symbolic values, as a result of interactions.  ...  Figure 7 : 7 Ballistic collisions simulating the identity relation, or a solitonic reaction: (a) with ϕ R54 and (b) with φ R9maj:4 .  ... 
doi:10.1142/s0129183111016348 fatcat:6nxlv2z2jzfofig3eeflsxa6zm

Discrete symmetry analysis of lattice systems

V. V. Kornyak
2009 Physics of Particles and Nuclei Letters  
We reveal also the group origin of moving soliton-like structures similar to spaceships in cellular automata.  ...  The solitons Å like shape preserving moving structures in cellular automata Å often arise for rather arbitrary initial data. Cellular Automata with Symmetric Local Rules.  ...  Such soliton-like structures are typical of cellular automata. They are called spaceships in the cellular automata community.  ... 
doi:10.1134/s1547477109070139 fatcat:ocmoere6brapzmevstnackfq6i

Cyclic cellular automata in 3D

Clifford A. Reiter
2011 Chaos, Solitons & Fractals  
We also observe the patterns include nested shells with the appropriate forms but that the nesting is far more complex than the spirals that occur in two dimensions.  ...  Cyclic cellular automata in two dimensions have long been intriguing because they self organize into spirals and that behavior can be analyzed.  ...  Thus, the sum of the differences must be a multiple of N . If the multiple is not zero, then the loop is part of a defect.  ... 
doi:10.1016/j.chaos.2011.06.014 fatcat:sdktclfsivhyfc3jovvgbh4lve
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