786 research outputs found
A Survey of Cellular Automata: Types, Dynamics, Non-uniformity and Applications
Cellular automata (CAs) are dynamical systems which exhibit complex global
behavior from simple local interaction and computation. Since the inception of
cellular automaton (CA) by von Neumann in 1950s, it has attracted the attention
of several researchers over various backgrounds and fields for modelling
different physical, natural as well as real-life phenomena. Classically, CAs
are uniform. However, non-uniformity has also been introduced in update
pattern, lattice structure, neighborhood dependency and local rule. In this
survey, we tour to the various types of CAs introduced till date, the different
characterization tools, the global behaviors of CAs, like universality,
reversibility, dynamics etc. Special attention is given to non-uniformity in
CAs and especially to non-uniform elementary CAs, which have been very useful
in solving several real-life problems.Comment: 43 pages; Under review in Natural Computin
Characterization of Single Cycle CA and its Application in Pattern Classification
AbstractThe special class of irreversible cellular automaton (CA) with multiple attractors is of immense interest to the CA researchers. Characterization of such a CA is the necessity to devise CA based solutions for diverse applications. This work explores the essential properties of CA attractors towards characterization of the 1-dimensional cellular automata with point states (single length cycle attractors). The concept of Reachability Tree is introduced for such characterization. It enables identification of the pseudo-exhaustive bits (PE bits) of a CA defining its point states. A theoretical framework has been developed to devise schemes for synthesizing a single length cycle multiple attractor CA with the specific set of PE bits. It also results in a linear time solution while synthesizing a CA for the given set of attractors and its PE bits. The experimentation establishes that the proposed CA synthesis scheme is most effective in designing the efficient pattern classifiers for wide range of applications
Spatio-Temporal Patterns act as Computational Mechanisms governing Emergent behavior in Robotic Swarms
open access articleOur goal is to control a robotic swarm without removing its swarm-like nature. In other words, we aim to intrinsically control a robotic swarm emergent behavior. Past attempts at governing robotic swarms or their selfcoordinating emergent behavior, has proven ineffective, largely due to the swarm’s inherent randomness (making it difficult to predict) and utter simplicity (they lack a leader, any kind of centralized control, long-range communication, global knowledge, complex internal models and only operate on a couple of basic, reactive rules). The main problem is that emergent phenomena itself is not fully understood, despite being at the forefront of current research. Research into 1D and 2D Cellular Automata has uncovered a hidden computational layer which bridges the micromacro gap (i.e., how individual behaviors at the micro-level influence the global behaviors on the macro-level). We hypothesize that there also lie embedded computational mechanisms at the heart of a robotic swarm’s emergent behavior. To test this theory, we proceeded to simulate robotic swarms (represented as both particles and dynamic networks) and then designed local rules to induce various types of intelligent, emergent behaviors (as well as designing genetic algorithms to evolve robotic swarms with emergent behaviors). Finally, we analysed these robotic swarms and successfully confirmed our hypothesis; analyzing their developments and interactions over time revealed various forms of embedded spatiotemporal patterns which store, propagate and parallel process information across the swarm according to some internal, collision-based logic (solving the mystery of how simple robots are able to self-coordinate and allow global behaviors to emerge across the swarm)
Boolean Delay Equations: A simple way of looking at complex systems
Boolean Delay Equations (BDEs) are semi-discrete dynamical models with
Boolean-valued variables that evolve in continuous time. Systems of BDEs can be
classified into conservative or dissipative, in a manner that parallels the
classification of ordinary or partial differential equations. Solutions to
certain conservative BDEs exhibit growth of complexity in time. They represent
therewith metaphors for biological evolution or human history. Dissipative BDEs
are structurally stable and exhibit multiple equilibria and limit cycles, as
well as more complex, fractal solution sets, such as Devil's staircases and
``fractal sunbursts``. All known solutions of dissipative BDEs have stationary
variance. BDE systems of this type, both free and forced, have been used as
highly idealized models of climate change on interannual, interdecadal and
paleoclimatic time scales. BDEs are also being used as flexible, highly
efficient models of colliding cascades in earthquake modeling and prediction,
as well as in genetics. In this paper we review the theory of systems of BDEs
and illustrate their applications to climatic and solid earth problems. The
former have used small systems of BDEs, while the latter have used large
networks of BDEs. We moreover introduce BDEs with an infinite number of
variables distributed in space (``partial BDEs``) and discuss connections with
other types of dynamical systems, including cellular automata and Boolean
networks. This research-and-review paper concludes with a set of open
questions.Comment: Latex, 67 pages with 15 eps figures. Revised version, in particular
the discussion on partial BDEs is updated and enlarge
An Experimental Study of Robustness to Asynchronism for Elementary Cellular Automata
Cellular Automata (CA) are a class of discrete dynamical systems that have
been widely used to model complex systems in which the dynamics is specified at
local cell-scale. Classically, CA are run on a regular lattice and with perfect
synchronicity. However, these two assumptions have little chance to truthfully
represent what happens at the microscopic scale for physical, biological or
social systems. One may thus wonder whether CA do keep their behavior when
submitted to small perturbations of synchronicity.
This work focuses on the study of one-dimensional (1D) asynchronous CA with
two states and nearest-neighbors. We define what we mean by ``the behavior of
CA is robust to asynchronism'' using a statistical approach with macroscopic
parameters. and we present an experimental protocol aimed at finding which are
the robust 1D elementary CA. To conclude, we examine how the results exposed
can be used as a guideline for the research of suitable models according to
robustness criteria.Comment: Version : Feb 13th, 2004, submitted to Complex System
Layered Cellular Automata
Layered Cellular Automata (LCA) extends the concept of traditional cellular
automata (CA) to model complex systems and phenomena. In LCA, each cell's next
state is determined by the interaction of two layers of computation, allowing
for more dynamic and realistic simulations. This thesis explores the design,
dynamics, and applications of LCA, with a focus on its potential in pattern
recognition and classification. The research begins by introducing the
limitations of traditional CA in capturing the complexity of real-world
systems. It then presents the concept of LCA, where layer 0 corresponds to a
predefined model, and layer 1 represents the proposed model with additional
influence. The interlayer rules, denoted as f and g, enable interactions not
only from adjacent neighboring cells but also from some far-away neighboring
cells, capturing long-range dependencies. The thesis explores various LCA
models, including those based on averaging, maximization, minimization, and
modified ECA neighborhoods. Additionally, the implementation of LCA on the 2-D
cellular automaton Game of Life is discussed, showcasing intriguing patterns
and behaviors. Through extensive experiments, the dynamics of different LCA
models are analyzed, revealing their sensitivity to rule changes and block size
variations. Convergent LCAs, which converge to fixed points from any initial
configuration, are identified and used to design a two-class pattern
classifier. Comparative evaluations demonstrate the competitive performance of
the LCA-based classifier against existing algorithms. Theoretical analysis of
LCA properties contributes to a deeper understanding of its computational
capabilities and behaviors. The research also suggests potential future
directions, such as exploring advanced LCA models, higher-dimensional
simulations, and hybrid approaches integrating LCA with other computational
models.Comment: This thesis represents the culmination of my M.Tech research,
conducted under the guidance of Dr. Sukanta Das, Associate Professor at the
Department of Information Technology, Indian Institute of Engineering Science
and Technology, Shibpur, West Bengal, India. arXiv admin note: substantial
text overlap with arXiv:2210.13971 by other author
A framework for the local information dynamics of distributed computation in complex systems
The nature of distributed computation has often been described in terms of
the component operations of universal computation: information storage,
transfer and modification. We review the first complete framework that
quantifies each of these individual information dynamics on a local scale
within a system, and describes the manner in which they interact to create
non-trivial computation where "the whole is greater than the sum of the parts".
We describe the application of the framework to cellular automata, a simple yet
powerful model of distributed computation. This is an important application,
because the framework is the first to provide quantitative evidence for several
important conjectures about distributed computation in cellular automata: that
blinkers embody information storage, particles are information transfer agents,
and particle collisions are information modification events. The framework is
also shown to contrast the computations conducted by several well-known
cellular automata, highlighting the importance of information coherence in
complex computation. The results reviewed here provide important quantitative
insights into the fundamental nature of distributed computation and the
dynamics of complex systems, as well as impetus for the framework to be applied
to the analysis and design of other systems.Comment: 44 pages, 8 figure
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