Towards Arithmetical Chips in Sub-Excitable Media

2011 ◽  
pp. 223-238
Author(s):  
Liang Zhang ◽  
Andrew Adamatzky
Keyword(s):  
Cellular Automaton ◽  
Resting State ◽  
General Purpose ◽  
Excitable Medium ◽  
Boolean Logic ◽  
Excitable Media ◽  
Two Dimensional ◽  
Resting Cell ◽  
Theoretical Design ◽  
Refractory State

We discuss a theoretical design of an arithmetical chip built on an excitable medium substrate. The chip is simulated in a two-dimensional three-state cellular automaton with eight-cell neighborhoods. Every resting cell is excited if it has exactly two excited neighbors, the excited cells takes refractory state unconditionally. A transition from refractory back to resting state also happens irrelevantly to a state of the cell neighborhood. The design is based on principles of collision-based computing. Boolean logic values are encoded by traveling localizations, or particles. Logical gates are realized in collisions between the particles. Detailed blue prints of collision-based adders and multipliers presented in the article pave the way to future laboratory experimental prototypes of general-purpose chemical computers.

PHENOMENOLOGY OF RETAINED EXCITATION

2007 ◽  
Vol 17 (11) ◽  
pp. 3985-4014 ◽  
Author(s):  
ANDREW ADAMATZKY
Keyword(s):  
Cellular Automaton ◽  
Resting State ◽  
State Transition ◽  
Space Time ◽  
Two Dimensional ◽  
Time Activity ◽  
Cell State ◽  
Resting Cell ◽  
Refractory State ◽  
Activity Dynamics

In a two-dimensional cellular automaton model of retained excitation every excited cell stays excited if the number of excited neighbors belong to some interval, the cell takes refractory state otherwise. Every resting cell is excited if the number of excited cells in its neighborhood belong to some other interval; cell-state transition from refractory to resting state is unconditional. We classify 1296 rules of retained excitation based on how dynamics of excitable lattices develop after initial stimulation. Several modes of space-time activity dynamics are discovered: not growing but persistent domains of activity, domains with rectangular, octagonal and almost circular growth, amoeba-like growing patterns, mobile and still localizations.

scholarly journals The cellular automaton model for the nonlinear waves in the two-dimensional excitable media

2009 ◽  
Vol 58 (7) ◽  
pp. 4493
Author(s):  
Zhang Li-Sheng ◽  
Deng Min-Yi ◽  
Kong Ling-Jiang ◽  
Liu Mu-Ren ◽  
Tang Guo-Ning
Keyword(s):  
Cellular Automaton ◽  
Nonlinear Waves ◽  
Cellular Automaton Model ◽  
Excitable Media ◽  
Two Dimensional

scholarly journals Crystal growth as an excitable medium

2012 ◽  
Vol 370 (1969) ◽  
pp. 2866-2876 ◽  
Author(s):  
Julyan H. E. Cartwright ◽  
Antonio G. Checa ◽  
Bruno Escribano ◽  
C. Ignacio Sainz-Díaz
Keyword(s):  
Crystal Growth ◽  
Crystal Surface ◽  
Layer Growth ◽  
Excitable Medium ◽  
Excitable Media ◽  
Two Dimensional ◽  
Physical Systems ◽  
Physics Of Crystal Growth ◽  
Superficial Resemblance ◽  
Biological Liquid

Crystal growth has been widely studied for many years, and, since the pioneering work of Burton, Cabrera and Frank, spirals and target patterns on the crystal surface have been understood as forms of tangential crystal growth mediated by defects and by two-dimensional nucleation. Similar spirals and target patterns are ubiquitous in physical systems describable as excitable media. Here, we demonstrate that this is not merely a superficial resemblance, that the physics of crystal growth can be set within the framework of an excitable medium, and that appreciating this correspondence may prove useful to both fields. Apart from solid crystals, we discuss how our model applies to the biomaterial nacre, formed by layer growth of a biological liquid crystal.

scholarly journals Cell-to-cell Mathematical modeling of arrhythmia phenomena in excitable media

2019 ◽  
Author(s):  
Gabriel López Garza
Keyword(s):  
Mathematical Modeling ◽  
Differential Equations ◽  
Cellular Automaton ◽  
Ordinary Differential Equations ◽  
Excitable Media ◽  
Similar Distribution ◽  
Two Dimensional ◽  
Self Similar

AbstractIn this document are modeled arrhythmias with cellular automaton and ordinary differential equations systems. With an aperiodic, self-similar distribution of two-dimensional arrangement of cells, it is possible to simulate such phenomena as fibrillation, fluttering and a sequence of fibrillation-fluttering. The topology of the cytoarchitecture of a network of cells may determine the initiation and development of arrhythmias.

scholarly journals PHENOMENOLOGY OF RETAINED REFRACTORINESS: ON SEMI-MEMRISTIVE DISCRETE MEDIA

2012 ◽  
Vol 22 (11) ◽  
pp. 1230036 ◽  
Author(s):  
ANDREW ADAMATZKY ◽  
LEON O. CHUA
Keyword(s):  
Cellular Automata ◽  
Resting State ◽  
Filling Ratio ◽  
Low Resistance ◽  
Recovery Interval ◽  
Resting Cell ◽  
Spatially Extended ◽  
Refractory State ◽  
Discrete Media

We study two-dimensional cellular automata, each cell takes three states: resting, excited and refractory. A resting cell excites if the number of excited neighbors lies in a certain interval (excitation interval). An excited cell becomes refractory independently on states of its neighbors. A refractory cell returns to a resting state only if the number of excited neighbors belong to recovery interval. The model is an excitable cellular automaton abstraction of a spatially extended semi-memristive medium where a cell's resting state symbolizes low-resistance and refractory state high-resistance. The medium is semi-memristive because only transition from high- to low-resistance is controlled by the density of local excitation. We present a phenomenological classification of the automata behavior for all possible excitation intervals and recovery intervals. We describe eleven classes of cellular automata with retained refractoriness based on the criteria of space-filling ratio, morphological and generative diversity, and types of traveling localizations.

THE CRITICAL BEHAVIOR OF THE 2D SPIN-1 ISING MODEL WITH THE BILINEAR AND POSITIVE BIQUADRATIC NEAREST NEIGHBOR INTERACTIONS ON A CELLULAR AUTOMATON

2004 ◽  
Vol 15 (10) ◽  
pp. 1425-1438 ◽  
Author(s):  
A. SOLAK ◽  
B. KUTLU
Keyword(s):  
Cellular Automaton ◽  
Phase Boundary ◽  
Critical Behavior ◽  
Nearest Neighbor ◽  
Finite Size ◽  
Square Lattice ◽  
Two Dimensional ◽  
Finite Size Scaling ◽  
Creutz Cellular Automaton ◽  
Beg Model

The two-dimensional BEG model with nearest neighbor bilinear and positive biquadratic interaction is simulated on a cellular automaton, which is based on the Creutz cellular automaton for square lattice. Phase diagrams characterizing phase transitions of the model are presented for comparison with those obtained from other calculations. We confirm the existence of the tricritical points over the phase boundary for D/K>0. The values of static critical exponents (α, β, γ and ν) are estimated within the framework of the finite size scaling theory along D/K=-1 and 1 lines. The results are compatible with the universal Ising critical behavior except the points over phase boundary.

A STUDY OF BIFURCATIONS IN A CIRCULAR REAL CELLULAR AUTOMATON

1993 ◽  
Vol 03 (02) ◽  
pp. 293-321 ◽  
Author(s):  
JÜRGEN WEITKÄMPER
Keyword(s):  
Hopf Bifurcation ◽  
Dynamical Systems ◽  
Cellular Automata ◽  
Cellular Automaton ◽  
Parallel Computers ◽  
Discrete Dynamical Systems ◽  
Two Dimensional ◽  
Bifurcation Structure ◽  
Logistic Mapping ◽  
Henon Mapping

Real cellular automata (RCA) are time-discrete dynamical systems on ℝN. Like cellular automata they can be obtained from discretizing partial differential equations. Due to their structure RCA are ideally suited to implementation on parallel computers with a large number of processors. In a way similar to the Hénon mapping, the system we consider here embeds the logistic mapping in a system on ℝN, N>1. But in contrast to the Hénon system an RCA in general is not invertible. We present some results about the bifurcation structure of such systems, mostly restricting ourselves, due to the complexity of the problem, to the two-dimensional case. Among others we observe cascades of cusp bifurcations forming generalized crossroad areas and crossroad areas with the flip curves replaced by Hopf bifurcation curves.

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