329 research outputs found
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
Localization dynamics in a binary two-dimensional cellular automaton: the Diffusion Rule
We study a two-dimensional cellular automaton (CA), called Diffusion Rule
(DR), which exhibits diffusion-like dynamics of propagating patterns. In
computational experiments we discover a wide range of mobile and stationary
localizations (gliders, oscillators, glider guns, puffer trains, etc), analyze
spatio-temporal dynamics of collisions between localizations, and discuss
possible applications in unconventional computing.Comment: Accepted to Journal of Cellular Automat
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
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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