5,830 research outputs found
Memristive excitable cellular automata
The memristor is a device whose resistance changes depending on the polarity
and magnitude of a voltage applied to the device's terminals. We design a
minimalistic model of a regular network of memristors using
structurally-dynamic cellular automata. Each cell gets info about states of its
closest neighbours via incoming links. A link can be one 'conductive' or
'non-conductive' states. States of every link are updated depending on states
of cells the link connects. Every cell of a memristive automaton takes three
states: resting, excited (analog of positive polarity) and refractory (analog
of negative polarity). A cell updates its state depending on states of its
closest neighbours which are connected to the cell via 'conductive' links. We
study behaviour of memristive automata in response to point-wise and spatially
extended perturbations, structure of localised excitations coupled with
topological defects, interfacial mobile excitations and growth of information
pathways.Comment: Accepted to Int J Bifurcation and Chaos (2011
A Max-Plus Model of Asynchronous Cellular Automata
This paper presents a new framework for asynchrony. This has its origins in
our attempts to better harness the internal decision making process of cellular
automata (CA). Thus, we show that a max-plus algebraic model of asynchrony
arises naturally from the CA requirement that a cell receives the state of each
neighbour before updating. The significant result is the existence of a
bijective mapping between the asynchronous system and the synchronous system
classically used to update cellular automata. Consequently, although the CA
outputs look qualitatively different, when surveyed on "contours" of real time,
the asynchronous CA replicates the synchronous CA. Moreover, this type of
asynchrony is simple - it is characterised by the underlying network structure
of the cells, and long-term behaviour is deterministic and periodic due to the
linearity of max-plus algebra. The findings lead us to proffer max-plus algebra
as: (i) a more accurate and efficient underlying timing mechanism for models of
patterns seen in nature, and (ii) a foundation for promising extensions and
applications.Comment: in Complex Systems (Complex Systems Publications Inc), Volume 23,
Issue 4, 201
Simulating city growth by using the cellular automata algorithm
The objective of this thesis is to develop and implement a Cellular Automata
(CA) algorithm to simulate urban growth process. It attempts to satisfy the
need to predict the future shape of a city, the way land uses sprawl in the
surroundings of that city and its population. Salonica city in Greece is
selected as a case study to simulate its urban growth. Cellular automaton
(CA) based models are increasingly used to investigate cities and urban
systems. Sprawling cities may be considered as complex adaptive systems,
and this warrants use of methodology that can accommodate the space-time
dynamics of many interacting entities. Automata tools are well-suited for
representation of such systems. By means of illustrating this point, the
development of a model for simulating the sprawl of land uses such as
commercial and residential and calculating the population who will reside in
the city is discussed
Automatic Filters for the Detection of Coherent Structure in Spatiotemporal Systems
Most current methods for identifying coherent structures in
spatially-extended systems rely on prior information about the form which those
structures take. Here we present two new approaches to automatically filter the
changing configurations of spatial dynamical systems and extract coherent
structures. One, local sensitivity filtering, is a modification of the local
Lyapunov exponent approach suitable to cellular automata and other discrete
spatial systems. The other, local statistical complexity filtering, calculates
the amount of information needed for optimal prediction of the system's
behavior in the vicinity of a given point. By examining the changing
spatiotemporal distributions of these quantities, we can find the coherent
structures in a variety of pattern-forming cellular automata, without needing
to guess or postulate the form of that structure. We apply both filters to
elementary and cyclical cellular automata (ECA and CCA) and find that they
readily identify particles, domains and other more complicated structures. We
compare the results from ECA with earlier ones based upon the theory of formal
languages, and the results from CCA with a more traditional approach based on
an order parameter and free energy. While sensitivity and statistical
complexity are equally adept at uncovering structure, they are based on
different system properties (dynamical and probabilistic, respectively), and
provide complementary information.Comment: 16 pages, 21 figures. Figures considerably compressed to fit arxiv
requirements; write first author for higher-resolution version
Phenomenology of retained refractoriness: On semi-memristive discrete media
We study two-dimensional cellular automata, each cell takes three states:
resting, excited and refractory. A resting cell excites if number of excited
neighbours lies in a certain interval (excitation interval). An excited cell
become refractory independently on states of its neighbours. A refractory cell
returns to a resting state only if the number of excited neighbours 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
symbolises low-resistance and refractory state high-resistance. The medium is
semi-memristive because only transition from high- to low-resistance is
controlled by density of local excitation. We present phenomenological
classification of the automata behaviour for all possible excitation intervals
and recovery intervals. We describe eleven classes of cellular automata with
retained refractoriness based on criteria of space-filling ratio, morphological
and generative diversity, and types of travelling localisations
Complexity in city systems: Understanding, evolution, and design
6.4 Exemplars of complex systems There are many signatures of complexity revealed in the space-time patterning of cities (Batty, 2005) and here we will indicate three rather different but nevertheless linked exemplars. Our first deals with ..
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