47 research outputs found
Randomized Cellular Automata
We define and study a few properties of a class of random automata networks.
While regular finite one-dimensional cellular automata are defined on periodic
lattices, these automata networks, called randomized cellular automata, are
defined on random directed graphs with constant out-degrees and evolve
according to cellular automaton rules. For some families of rules, a few
typical a priori unexpected results are presented.Comment: 13 pages, 7 figure
On the existence of a variational principle for deterministic cellular automaton models of highway traffic flow
It is shown that a variety of deterministic cellular automaton models of
highway traffic flow obey a variational principle which states that, for a
given car density, the average car flow is a non-decreasing function of time.
This result is established for systems whose configurations exhibits local jams
of a given structure. If local jams have a different structure, it is shown
that either the variational principle may still apply to systems evolving
according to some particular rules, or it could apply under a weaker form to
systems whose asymptotic average car flow is a well-defined function of car
density. To establish these results it has been necessary to characterize among
all number-conserving cellular automaton rules which ones may reasonably be
considered as acceptable traffic rules. Various notions such as free-moving
phase, perfect and defective tiles, and local jam play an important role in the
discussion. Many illustrative examples are given.Comment: 19 pages, 4 figure
Number-conserving cellular automaton rules
A necessary and sufficient condition for a one-dimensional q-state n-input
cellular automaton rule to be number-conserving is established. Two different
forms of simpler and more visual representations of these rules are given, and
their flow diagrams are determined. Various examples are presented and
applications to car traffic are indicated. Two nontrivial three-state
three-input self-conjugate rules have been found. They can be used to model the
dynamics of random walkers.Comment: 4 figure