11,288 research outputs found
Cellular Automata are Generic
Any algorithm (in the sense of Gurevich's abstract-state-machine
axiomatization of classical algorithms) operating over any arbitrary unordered
domain can be simulated by a dynamic cellular automaton, that is, by a
pattern-directed cellular automaton with unconstrained topology and with the
power to create new cells. The advantage is that the latter is closer to
physical reality. The overhead of our simulation is quadratic.Comment: In Proceedings DCM 2014, arXiv:1504.0192
On Damage Spreading Transitions
We study the damage spreading transition in a generic one-dimensional
stochastic cellular automata with two inputs (Domany-Kinzel model) Using an
original formalism for the description of the microscopic dynamics of the
model, we are able to show analitically that the evolution of the damage
between two systems driven by the same noise has the same structure of a
directed percolation problem. By means of a mean field approximation, we map
the density phase transition into the damage phase transition, obtaining a
reliable phase diagram. We extend this analysis to all symmetric cellular
automata with two inputs, including the Ising model with heath-bath dynamics.Comment: 12 pages LaTeX, 2 PostScript figures, tar+gzip+u
Complexity of Generic Limit Sets of Cellular Automata
The generic limit set of a topological dynamical system of the smallest
closed subset of the phase space that has a comeager realm of attraction. It
intuitively captures the asymptotic dynamics of almost all initial conditions.
It was defined by Milnor and studied in the context of cellular automata, whose
generic limit sets are subshifts, by Djenaoui and Guillon. In this article we
study the structural and computational restrictions that apply to generic limit
sets of cellular automata. As our main result, we show that the language of a
generic limit set can be at most -hard, and lower in various
special cases. We also prove a structural restriction on generic limit sets
with a global period.Comment: 13 pages, 2 figure
Exploring Ancient Architectural Designs with Cellular Automata\ud
The paper discusses the utilization of three-dimensional cellular automata employing the two-dimensional totalistic cellular automata to simulate how simple rules could emerge a highly complex architectural designs of some Indonesian heritages. A detailed discussion is brought to see the simple rules applied in Borobudur Temple, the largest ancient Buddhist temple in the country with very complex detailed designs within. The simulation confirms some previous findings related to measurement of the temple as well as some other ancient buildings in Indonesia. This happens to open further exploitation of the explanatory power presented by cellular automata for complex architectural designs built by civilization not having any supporting sophisticated tools, even standard measurement systems
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