11,171 research outputs found
Cellular automaton supercolliders
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 are cellular-automaton analogous of
localizations or quasi-local collective excitations travelling in a spatially
extended non-linear medium. 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. We
analyse what types of interaction occur between gliders travelling on a
cellular automaton `cyclotron' and build a catalog of the most common
reactions. We demonstrate that collisions between gliders emulate the basic
types of interaction that occur between localizations in non-linear media:
fusion, elastic collision, and soliton-like collision. Computational outcomes
of a swarm of gliders circling on a one-dimensional torus are analysed via
implementation of cyclic tag systems
Complex dynamics of elementary cellular automata emerging from chaotic rules
We show techniques of analyzing complex dynamics of cellular automata (CA)
with chaotic behaviour. CA are well known computational substrates for studying
emergent collective behaviour, complexity, randomness and interaction between
order and chaotic systems. A number of attempts have been made to classify CA
functions on their space-time dynamics and to predict behaviour of any given
function. Examples include mechanical computation, \lambda{} and Z-parameters,
mean field theory, differential equations and number conserving features. We
aim to classify CA based on their behaviour when they act in a historical mode,
i.e. as CA with memory. We demonstrate that cell-state transition rules
enriched with memory quickly transform a chaotic system converging to a complex
global behaviour from almost any initial condition. Thus just in few steps we
can select chaotic rules without exhaustive computational experiments or
recurring to additional parameters. We provide analysis of well-known chaotic
functions in one-dimensional CA, and decompose dynamics of the automata using
majority memory exploring glider dynamics and reactions
Complex dynamics emerging in Rule 30 with majority memory
In cellular automata with memory, the unchanged maps of the conventional
cellular automata are applied to cells endowed with memory of their past states
in some specified interval. We implement Rule 30 automata with a majority
memory and show that using the memory function we can transform quasi-chaotic
dynamics of classical Rule 30 into domains of travelling structures with
predictable behaviour. We analyse morphological complexity of the automata and
classify dynamics of gliders (particles, self-localizations) in memory-enriched
Rule 30. We provide formal ways of encoding and classifying glider dynamics
using de Bruijn diagrams, soliton reactions and quasi-chemical representations
On Factor Universality in Symbolic Spaces
The study of factoring relations between subshifts or cellular automata is
central in symbolic dynamics. Besides, a notion of intrinsic universality for
cellular automata based on an operation of rescaling is receiving more and more
attention in the literature. In this paper, we propose to study the factoring
relation up to rescalings, and ask for the existence of universal objects for
that simulation relation. In classical simulations of a system S by a system T,
the simulation takes place on a specific subset of configurations of T
depending on S (this is the case for intrinsic universality). Our setting,
however, asks for every configurations of T to have a meaningful interpretation
in S. Despite this strong requirement, we show that there exists a cellular
automaton able to simulate any other in a large class containing arbitrarily
complex ones. We also consider the case of subshifts and, using arguments from
recursion theory, we give negative results about the existence of universal
objects in some classes
Cellular Automata as a Model of Physical Systems
Cellular Automata (CA), as they are presented in the literature, are abstract
mathematical models of computation. In this pa- per we present an alternate
approach: using the CA as a model or theory of physical systems and devices.
While this approach abstracts away all details of the underlying physical
system, it remains faithful to the fact that there is an underlying physical
reality which it describes. This imposes certain restrictions on the types of
computations a CA can physically carry out, and the resources it needs to do
so. In this paper we explore these and other consequences of our
reformalization.Comment: To appear in the Proceedings of AUTOMATA 200
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