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A necessary and suucient condition for a one-dimensional q-state n-input cellular automaton rule to be number-conserving is established. Two diierent forms of simpler and more visual representations of these rules are given, and their ow diagrams are determined. Various examples are presented and applications to car traac are indicated. Two nontrivial… (More)

We investigate simplified models of computer data networks and examine how the introduction of additional random links influences the performance of these networks. In general, the impact of additional random links on the performance of the network strongly depends on the routing algorithm used in the network. Significant performance gains can be achieved… (More)

We present a rigorous derivation of the flow at arbitrary time in a deterministic cellular automaton model of traffic flow. The derivation employs regularities in preimages of blocks of zeros, reducing the problem of preimage enumeration to a well-known lattice path counting problem. Assuming infinite lattice size and random initial configuration, the flow… (More)

We present a lattice gas cellular automaton (LGCA) to study spatial and temporal dynamics of an epidemic of SIR (susceptible-infected-removed) type. The automaton is fully discrete, i.e. space, time and number of individuals are discrete variables. The automaton can be applied to study spread of epidemics in both human and animal populations. We investigate… (More)

We investigate individual packet delay in a model of data networks with table-free, partial table and full table routing. We present analytical estimation for the average packet delay in a network with small partial routing table. Dependence of the delay on the size of the network and on the size of the partial routing table is examined numerically.… (More)

- Bruno Di, Stefano, Henryk Fukś, Anna T Lawniczak
- 2000

The authors have applied the CA/LGCA (" Cellular Automata " / " Lattice Gas Cellular Automata ") methodology to develop and analyse models of spread of epidemics of infectious diseases. Object-Oriented Analysis and Design of the computer models has been performed using the Unified Modelling Language (UML). All required algorithms and data structures have… (More)

We investigate second order additive invariants in elementary cellular automata rules. Fundamental diagrams of rules which possess additive invariants are either linear or exhibit singularities similar to singularities of rules with first-order invariant. Only rules which have exactly one invariants exhibit singularities. At the singularity, the current… (More)

- Nino Boccara, Henryk Fuks
- 1997

We present a family of one-dimensional cellular automata mod-eling the diffusion of an innovation in a population. Starting from simple deterministic rules, we construct models parameterized by the interaction range and exhibiting a second-order phase transition. We show that the number of individuals who eventually keep adopting the innovation strongly… (More)

We present a method of solving of the probabilistic initial value problem for cellular automata (CA) using CA rule 172 as an example. For a disordered initial condition on an infinite lattice, we derive exact expressions for the density of ones at arbitrary time step. In order to do this, we analyze topological structure of preimage trees of finite strings… (More)