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We present what we argue is the generic generalization of Conway's "Game of Life" to a continuous domain. We describe the theoretical model and the explicit implementation on a computer.
Consider an infinite graph with nodes initially labeled by independent Bernoulli random variables of parameter p. We address the density classification problem, that is, we want to design a (probabilistic or deterministic) cellular automaton or a finite-range interacting particle system that evolves on this graph and decides whether p is smaller or larger than 1/2. Precisely, the trajectories should converge to the uniform configuration with only 0's if p<1/2, and only 1's if p>1/2. We present solutions to that problem on the d-dimensional lattice, for any d>1, and on the regular infinite trees. For Z, we propose some candidates that we back up with numerical simulations.
We study intrinsic simulations between cellular automata and introduce a new necessary condition for a CA to simulate another one. Although expressed for general CA, this condition is targeted towards surjective CA and especially linear ones. Following the approach introduced by the first author in an earlier paper, we develop proof techniques to tell whether some linear CA can simulate another linear CA. Besides rigorous proofs, the necessary condition for the simulation to occur can be heuristically checked via simple observations of typical space-time diagrams generated from finite configurations. As an illustration, we give an example of linear reversible CA which cannot simulate the identity and which is 'time-asymmetric', i.e. which can neither simulate its own inverse, nor the mirror of its own inverse.
Cellular Automata(CA) is a discrete computing model which provides simple, flexible and efficient platform for simulating complicated systems and performing complex computation based on the neighborhoods information. CA consists of two components 1) a set of cells and 2) a set of rules . Programmable Cellular Automata(PCA) employs some control signals on a Cellular Automata(CA) structure. Programmable Cellular Automata were successfully applied for simulation of biological systems, physical systems and recently to design parallel and distributed algorithms for solving task density and synchronization problems. In this paper PCA is applied to develop cryptography algorithms. This paper deals with the cryptography for a parallel AES encryption algorithm based on programmable cellular automata. This proposed algorithm based on symmetric key systems.
The Mima-mound-and-vernal-pool topography of California is rich in endemic plant and invertebrate species, but we do not know how this unusual environment is created or maintained. Burrowing rodents have been observed to move soil upwards at annual rates sufficient to maintain the mounds despite erosion, but there is no tested explanation of this behavior. We propose that the mounds are an emergent effect of small-scale (10 cm, 1 day) interactions between topography, hydrology, plant growth, and rodent burrowing. A cellular automata simulation of these processes both generates and maintains mound-pool topography with minimal dependence on initial conditions, and can also describe mound morphogenesis on slopes, where observed mound geometry is distinct from that on level ground.
Microscopic traffic models have recently gained considerable importance as a mean of optimising traffic control strategies. Computationally efficient and sufficiently accurate microscopic traffic models have been developed based on the cellular automata theory. However, the real-time application of the available cellular automata models in traffic control systems is a difficult task due to their discrete and stochastic nature. This paper introduces a novel method of traffic streams modelling, which combines cellular automata and fuzzy calculus. The introduced fuzzy cellular traffic model eliminates main drawbacks of the cellular automata approach i.e. necessity of multiple Monte Carlo simulations and calibration issues. Experimental results show that the evolution of a simulated traffic stream in the proposed fuzzy cellular model is consistent with that observed for stochastic cellular automata. The comparison of both methods confirms that the computational cost of traffic simulation is considerably lower for the proposed model. The model is suitable for real-time applications in traffic control systems.
We explore the possible connections between the dynamic behaviour of a system and Turing universality in terms of the system's ability to (effectively) transmit and manipulate information. Some arguments will be provided using a defined compression-based transition coefficient which quantifies the sensitivity of a system to being programmed. In the same spirit, a list of conjectures concerning the ability of Busy Beaver Turing machines to perform universal computation will be formulated. The main working hypothesis is that universality is deeply connected to the qualitative behaviour of a system, particularly to its ability to react to external stimulus--as it needs to be programmed--and to its capacity for transmitting this information.
We study two-player \emph{take-away} games whose outcomes emulate two-state one-dimensional cellular automata, such as Wolfram's rules 60 and 110. Given an initial string consisting of a central data pattern and periodic left and right patterns, the rule 110 cellular automaton was recently proved Turing-complete by Matthew Cook. Hence, many questions regarding its behavior are algorithmically undecidable. We show that similar questions are undecidable for our \emph{rule 110} game.
The presented article attempts to characterize the encryption dynamics of delayed dynamics based block ciphers, designed for the encryption of binary data. For such encryption algorithms, the encryption process relies on a coupling dynamics with time delay between different bits in the plaintext (i.e.\ the "initial" message to be encrypted). Here, the principal dynamics of the encryption process is examined and the Hammingdistance is used to quantify the change in ciphertext (i.e.\ the plaintext after encryption) upon changing a single bit in the plaintext message or slightly perturbing the key used during encryption. More precisely, the previously proposed "encryption via delayed dynamics" (in short: EDDy) algorithm as well as its extended version (termed ExEDDy) are analyzed by means of numerical simulations. As a result it is found that while EDDy exhibits a rather poor perfomance, ExEDDy performes considerably better and hence constitutes a significant improvement over EDDy. Consequently, the results are contrasted with those obtained for a block cipher that implements the encryption/decryption dynamics by means of reversible cellular automata.
Central moment lattice Boltzmann method (LBM) is one of the more recent developments among the lattice kinetic schemes for computational fluid dynamics. A key element in this approach is the use of central moments to specify collision process and forcing, and thereby naturally maintaining Galilean invariance, an important characteristic of fluid flows. When the different central moments are relaxed at different rates like in a standard multiple relaxation time (MRT) formulation based on raw moments, it is endowed with a number of desirable physical and numerical features. Since the collision operator exhibits a cascaded structure, this approach is also known as the cascaded LBM. While the cascaded LBM has been developed sometime ago, a systematic study of its numerical properties, such as accuracy, grid convergence and stability for well defined canonical problems is lacking and the present work is intended to fulfill this need. We perform a quantitative study of the performance of the cascaded LBM for a set of benchmark problems of differing complexity, viz., Poiseuille flow, decaying Taylor-Green vortex flow and lid-driven cavity flow. We first establish its grid convergence and demonstrate second order accuracy under diffusive scaling for both the velocity field and its derivatives, i.e. components of the strain rate tensor, as well. The method is shown to quantitatively reproduce steady/unsteady analytical solutions or other numerical results with excellent accuracy. Numerical experiments further demonstrate that the central moment MRT LBM results in significant stability improvements when compared with certain existing collision models at moderate additional computational cost.
A universal map is derived for all deterministic 1D cellular automata (CA) containing no freely adjustable parameters. The map can be extended to an arbitrary number of dimensions and topologies and its invariances allow to classify all CA rules into equivalence classes. Complexity in 1D systems is then shown to emerge from the weak symmetry breaking of the addition modulo an integer number p. The latter symmetry is possessed by certain rules that produce Pascal simplices in their time evolution. These results elucidate Wolfram's classification of CA dynamics.
Soldier crabs Mictyris guinotae exhibit pronounced swarming behaviour. The swarms of the crabs tolerant of perturbations. In computer models and laboratory experiments we demonstrate that swarms of soldier crabs can implement logical gates when placed in a geometrically constrained environment.
We systematically study the boundaries of one-dimensional, 2-color cellular automata depending on 4 cells, begun from simple initial conditions. We determine the exact growth rates of the boundaries that appear to be reducible. Morphic words characterize the reducible boundaries. For boundaries that appear to be irreducible, we apply curve-fitting techniques to compute an empirical growth exponent and (in the case of linear growth) a growth rate. We find that the random walk statistics of irreducible boundaries exhibit surprising regularities and suggest that a threshold separates two classes. Finally, we construct a cellular automaton whose growth exponent does not exist, showing that a strict classification by exponent is not possible.
In this paper, linear Cellular Automta (CA) rules are recursively generated using a binary tree rooted at "0". Some mathematical results on linear as well as non-linear CA rules are derived. Integers associated with linear CA rules are defined as linear numbers and the properties of these linear numbers are studied.
The aim of this note is to systematize our knowledge about identical configurations of ASM.
Some contemporary views of the universe assume information and computation to be key in understanding and explaining the basic structure underpinning physical reality. We introduce the Computable Universe exploring some of the basic arguments giving foundation to these visions. We will focus on the algorithmic and quantum aspects, and how these may fit and support the computable universe hypothesis.
A two-state, three-dimensional, deterministic, reversible cellular automaton is shown to be capable of approximately circular orbits, wavelike undulations, and particle-like configurations that decay in accordance with a half-life law.
The NaSch model is a classical one-dimensional cellular automata (CA) model of freeway traffic. However, it is not suitable for simulating pedestrian dynamics due to the kinetic difference between vehicles and pedestrians. Based on NaSch model, we proposed a new safety interspace model to investigate the single-file pedestrian stream. We simulated and reproduced Seyfried's experiment in 2006 quantitatively and use the empirical data to validate our model. We defined the safety interspace as a linear function of current velocity and introduced a normal distributed random variable to describe the randomness of spatial cognition. Meanwhile, we extended NaSch model in space partition from single-grid mode to multi-gird mode to increase spatial resolution. It was found that through three model perimeters with appropriate values, the new model could reproduce faithfully the typical form of the fundamental diagram from empirical data. The velocity-density curve in simulation could indicate the discontinuity areas in fundamental diagram observed from empirical data. In addition, we reproduced the stop-and-go waves and phase separation into a stopping area and an area where pedestrians walk slowly at high density.