342 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
Factorization, reduction and embedding in integrable cellular automata
Factorized dynamics in soliton cellular automata with quantum group symmetry
is identified with a motion of particles and anti-particles exhibiting pair
creation and annihilation. An embedding scheme is presented showing that the
D^{(1)}_n-automaton contains, as certain subsectors, the box-ball systems and
all the other automata associated with the crystal bases of non-exceptional
affine Lie algebras. The results extend the earlier ones to higher
representations by a certain reduction and to a wider class of boundary
conditions.Comment: LaTeX2e, 20 page
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
Lenia and Expanded Universe
We report experimental extensions of Lenia, a continuous cellular automata
family capable of producing lifelike self-organizing autonomous patterns. The
rule of Lenia was generalized into higher dimensions, multiple kernels, and
multiple channels. The final architecture approaches what can be seen as a
recurrent convolutional neural network. Using semi-automatic search e.g.
genetic algorithm, we discovered new phenomena like polyhedral symmetries,
individuality, self-replication, emission, growth by ingestion, and saw the
emergence of "virtual eukaryotes" that possess internal division of labor and
type differentiation. We discuss the results in the contexts of biology,
artificial life, and artificial intelligence.Comment: 8 pages, 5 figures, 1 table; submitted to ALIFE 2020 conferenc
Simple Algorithm for Factorized Dynamics of g_n-Automaton
We present an elementary algorithm for the dynamics of recently introduced
soliton cellular automata associated with quantum affine algebra U_q(g_n) at
q=0. For g_n = A^{(1)}_n, the rule reproduces the ball-moving algorithm in
Takahashi-Satsuma's box-ball system. For non-exceptional g_n other than
A^{(1)}_n, it is described as a motion of particles and anti-particles which
undergo pair-annihilation and creation through a neutral bound state. The
algorithm is formulated without using representation theory nor crystal basis
theory.Comment: LaTex2e 9 pages, no figure. For proceedings of SIDE IV conferenc
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 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
Cellular Automata and Ultra-Discrete Painlev\'e Equations
Starting from integrable cellular automata we present a novel form of
Painlev\'e equations. These equations are discrete in both the independent
variable and the dependent one. We show that they capture the essence of the
behavior of the Painlev\'e equations organizing themselves into a coalescence
cascade and possessing special solutions. A necessary condition for the
integrability of cellular automata is also presented.Comment: 8 pages, plainTeX, 2 figure
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