110 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
Designing complex dynamics in cellular automata with memory
Since their inception at Macy conferences in later 1940s, complex systems have remained the most controversial topic of interdisciplinary sciences. The term "complex system" is the most vague and liberally used scientific term. Using elementary cellular automata (ECA), and exploiting the CA classification, we demonstrate elusiveness of "complexity" by shifting space-time dynamics of the automata from simple to complex by enriching cells with memory. This way, we can transform any ECA class to another ECA class - without changing skeleton of cell-state transition function - and vice versa by just selecting a right kind of memory. A systematic analysis displays that memory helps "discover" hidden information and behavior on trivial - uniform, periodic, and nontrivial - chaotic, complex - dynamical systems. © World Scientific Publishing Company
A Computation in a Cellular Automaton Collider Rule 110
A cellular automaton collider is a finite state machine build of rings of
one-dimensional cellular automata. We show how a computation can be performed
on the collider by exploiting interactions between gliders (particles,
localisations). The constructions proposed are based on universality of
elementary cellular automaton rule 110, cyclic tag systems, supercolliders, and
computing on rings.Comment: 39 pages, 32 figures, 3 table
Simple networks on complex cellular automata: From de Bruijn diagrams to jump-graphs
We overview networks which characterise dynamics in cellular automata. These
networks are derived from one-dimensional cellular automaton rules and global
states of the automaton evolution: de Bruijn diagrams, subsystem diagrams,
basins of attraction, and jump-graphs. These networks are used to understand
properties of spatially-extended dynamical systems: emergence of non-trivial
patterns, self-organisation, reversibility and chaos. Particular attention is
paid to networks determined by travelling self-localisations, or gliders.Comment: 25 pages, 14 figure
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