7,437 research outputs found
Universal pattern generation by cellular automata
AbstractWe construct a reversible, one-dimensional cellular automaton that has the property that a finite initial configuration generates all finite patterns over its state alphabet. We also conjecture that a related cellular automaton satisfies the stronger property that every finite pattern gets generated in every position, so that the forward orbit of the finite initial configuration is dense
Pattern Generation by Cellular Automata (Invited Talk)
A one-dimensional cellular automaton is a discrete dynamical system
where a sequence of symbols evolves synchronously according to a local update rule. We discuss simple update rules that make the automaton perform multiplications of numbers by a constant. If the constant and the number base are selected suitably the automaton becomes a universal pattern generator: all finite strings over its state alphabet appear from a finite seed. In particular we consider
the automata that multiply by constants 3 and 3/2 in base 6. We discuss the connections of these automata to some difficult open questions in number theory, and we pose several further questions concerning pattern generation in cellular automata
Pattern Generation by Cellular Automata (Invited Talk)
A one-dimensional cellular automaton is a discrete dynamical system where a sequence of symbols evolves synchronously according to a local update rule. We discuss simple update rules that make the automaton perform multiplications of numbers by a constant. If the constant and the number base are selected suitably the automaton becomes a universal pattern generator: all finite strings over its state alphabet appear from a finite seed. In particular we consider the automata that multiply by constants 3 and 3/2 in base 6. We discuss the connections of these automata to some difficult open questions in number theory, and we pose several further questions concerning pattern generation in cellular automata
3D cellular automata
A cellular automaton (CA) is a set of rules which determines the state of individual cells on a grid, based on neighbourhood relations. CAs have been used by researchers to model a wide range of systems from cell growth to cosmology to universal computation. However nearly all such models have been on one or two dimensional grids. This article provides a brief history of the development of CAs and then extends the models to three dimensions using open source software; Blender and Python. New 3D rules are examined and the development of 3D cell configurations explored and visualized
Revisiting the Edge of Chaos: Evolving Cellular Automata to Perform Computations
We present results from an experiment similar to one performed by Packard
(1988), in which a genetic algorithm is used to evolve cellular automata (CA)
to perform a particular computational task. Packard examined the frequency of
evolved CA rules as a function of Langton's lambda parameter (Langton, 1990),
and interpreted the results of his experiment as giving evidence for the
following two hypotheses: (1) CA rules able to perform complex computations are
most likely to be found near ``critical'' lambda values, which have been
claimed to correlate with a phase transition between ordered and chaotic
behavioral regimes for CA; (2) When CA rules are evolved to perform a complex
computation, evolution will tend to select rules with lambda values close to
the critical values. Our experiment produced very different results, and we
suggest that the interpretation of the original results is not correct. We also
review and discuss issues related to lambda, dynamical-behavior classes, and
computation in CA. The main constructive results of our study are identifying
the emergence and competition of computational strategies and analyzing the
central role of symmetries in an evolutionary system. In particular, we
demonstrate how symmetry breaking can impede the evolution toward higher
computational capability.Comment: 38 pages, compressed .ps files (780Kb) available ONLY thru anonymous
ftp. (Instructions available via `get 9303003' .
Celulární automat a CML systémy
The main aim of this thesis is the study of cellular automata and discrete dynamical systems on a lattice.
Both tools, cellular automata as well as dynamical systems on a lattice are introduced and elementary properties described.
The relation between cellular automata and dynamical system on lattice is derived.
The main goal of the thesis is also the use of the cellular automata as that mathematical tool of evolution visualization of discrete dynamical systems.
The theory of cellular automata is applied to the discrete dynamical systems on a lattice Laplacian type and implemented in Java language.Hlavním cílem práce je studium vztahu celulárních automatů a diskrétních dynamických systémů na mřížce. Oba nástroje, jak celulární automat tak dynamický systém na mřížce, jsou zavedeny a jejich základní vlastnosti popsány. Vztah mezi celulárními automaty a dynamickými systémy na mřížce je podrobně popsán. Hlavním cílem práce je dále použití nástroje celulárního automatu jako matematického vizualizačního prostředku evoluce diskrétních dynamických systémů. Teorie celulárních automatů je použita na dynamické systémy na mřížce Lamplaceova typu a implementována v prostředí Java.470 - Katedra aplikované matematikyvelmi dobř
Self-Replicating Machines in Continuous Space with Virtual Physics
JohnnyVon is an implementation of self-replicating machines in
continuous two-dimensional space. Two types of particles drift
about in a virtual liquid. The particles are automata with
discrete internal states but continuous external relationships.
Their internal states are governed by finite state machines but
their external relationships are governed by a simulated physics
that includes Brownian motion, viscosity, and spring-like attractive
and repulsive forces. The particles can be assembled into patterns
that can encode arbitrary strings of bits. We demonstrate that, if
an arbitrary "seed" pattern is put in a "soup" of separate individual
particles, the pattern will replicate by assembling the individual
particles into copies of itself. We also show that, given sufficient
time, a soup of separate individual particles will eventually
spontaneously form self-replicating patterns. We discuss the implications
of JohnnyVon for research in nanotechnology, theoretical biology, and
artificial life
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