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In this paper, we construct a weakly universal cellular automaton on the tessellation $\{9,3\}$ which has two states and which is not rotation invariant but which is truly planar.
In this paper, we construct a weakly universal cellular automaton on the tessellation $\{8,3\}$ which is not rotation invariant but which is truly planar.
One of the simplest multilevel cellular automata - the hodgepodge machine - was modified to best match the chemical trajectory observed in the Belousov-Zhabotinsky reaction. Noise introduces watersheding of the central regular pattern into the circular target pattern. This article analyzes influences of the neighborhood and internal excitation kinds of noise. We have found that configurations of ignition points, which give circular waves - target patterns, occur only in the interval of the neighborhood excitation noise from 30% to 34% and at the internal excitation noise of 12%. Noisy hodgepodge machine with these parameters is the best approximation to the experimental Belousov-Zhabotinsky reaction.
Open-ended evolution (OEE) is relevant to a variety of biological, artificial and technological systems, but has been challenging to reproduce in silico. Most theoretical efforts focus on key aspects of open-ended evolution as it appears in biology. We recast the problem as a more general one in dynamical systems theory, providing simple criteria for open-ended evolution based on two hallmark features: unbounded evolution and innovation. We define unbounded evolution as patterns that are non-repeating within the expected Poincare recurrence time of an equivalent isolated system, and innovation as trajectories not observed in isolated systems. As a case study, we implement novel variants of cellular automata (CA) in which the update rules are allowed to vary with time in three alternative ways. Each is capable of generating conditions for open-ended evolution, but vary in their ability to do so. We find that state-dependent dynamics, widely regarded as a hallmark of life, statistically out-performs other candidate mechanisms, and is the only mechanism to produce open-ended evolution in a scalable manner, essential to the notion of ongoing evolution. This analysis suggests a new framework for unifying mechanisms for generating OEE with features distinctive to life and its artifacts, with broad applicability to biological and artificial systems.
The purpose of the present study is to search one-dimensional Cellular Automata (CA) rules which will solve the density classification task (DCT) perfectly. The mathematical analysis of number conserving functions over binary strings of length n gives an indication of its corresponding number conserving cellular automata rules (either uniform or non-uniform). The state transition diagrams (STDs) of number conserving CA rules have been analyzed where it has been found that these STDs can generate different DCT solutions. While studying the properties of STDs, an interesting classification of binary strings could be made where equal weight strings form a class and the cardinality of each class is same as the binomial coefficient nCk; n is the length and k is the weight of the binary string. Apart from STDs, other deterministic methods have been proposed to obtain the exact solution of DCT. All these exact solutions of DCT using different deterministic methods can be viewed as an improvement over the soft computing techniques used earlier to obtain approximate solutions.
One of the most fundamental problems in science is to define {\it quantitatively} the complexity of organized matters, i.e., {\it organized complexity}. Although many measures have been proposed toward this aim in previous decades, there is no agreed upon definition. This paper presents a new quantitative definition of organized complexity. This definition {\it simultaneously} captures the three major features of complexity: computational (similar to logical depth), descriptional (similar to the Kolmogorov complexity and effective complexity) and distributional (similar to statistical complexity). In addition, the proposed definition is computable and can measure both probabilistic and deterministic forms of objects in a unified manner. The proposed definition is based on circuits rather than Turing machines and $ε$-machines. We give several criteria required for organized complexity measures and show that the proposed definition satisfies all of them for the first time. We then apply this quantitative definition to formulate a {\it semantic information theory}. We present the first formal definition of a {\it semantic information amount}, which is the core concept of the semantic information theory, that is based only on concretely defined notions. Previous semantic information theories defined this amount under some a priori information which is not concretely specified. We then unveil several fundamental properties in the semantic information theory, e.g., a semantic source coding theorem, semantic channel coding theorem, and effectiveness coding theorem. Although the semantic information theory has a long history of research going back more than six decades, there has been no study on its relation to organized complexity. This paper offers the first unified paradigm of organized complexity and semantic information theory.
The original local, discrete example of Linear Unitary Cellular Automata (LUCA) is analyzed in terms of a new representation previously introduced in [1] for classical CA. Several important underlying symmetries are reviewed and their tight relationship with both signal and coding theory as well as with combinatorics is underlined. A class of analog implementations in the form of Linear Transmission Line Networks (LTLN) is described as possible emulators of this type of dynamics.
We propose and analyze extended floor field cellular automaton models for evacuation dynamics of inhomogeneous pedestrian pairs which are coupled by asymmetric group interactions. Such pairs consist of a leader, who mainly determines the couple's motion and a follower, who has a defined tendency to follow the leader. Examples for such pairs are mother and child or two siblings of different age. We examine the system properties and compare them to the case of a homogeneous crowd. We find a strong impact on evacuation times for the regime of strong pair coupling due to the occurrence of a clogging phenomenon. In addition we obtain a non-trivial dependence of evacuation times on the followers' coupling to the static floor field, which carries the information of the shortest way to the exit location. In particular we find that systems with fully passive followers, who are solely coupled to their leaders, show lower evacuation times than homogeneous systems where all pedestrians have an equal tendency to move towards the exit. We compare the results of computer simulations with recently performed experiments.
In this work we present a model for the evacuation of pedestrians from an enclosure considering a continuous space substrate and discrete time. We analyze the influence of behavioral features that affect the use of the empty space, that can be linked to the attitudes or characters of the pedestrians. We study how the interaction of different behavioral profiles affects the needed time to evacuate completely a room and the occurrence of clogging. We find that neither fully egotistic nor fully cooperative attitudes are optimal from the point of view of the crowd. In contrast, intermediate behaviors provide lower evacuation times. This lead us to identify some phenomena closely analogous to the {\em faster-is-slower} effect. The proposed model enables for the introduction of Game Theory elements to solve conflicts between pedestrians which try to occupy the same space. Moreover, it allows for distinguishing between the role of the attitudes in the search for empty space and the attitudes in the conflicts. In the present version we only focus on the first of these instances.
A cellular automaton collider is a finite state machine build of rings of one-dimensional cellular automata. We show how a computation can be performed on the collider by exploiting interactions between gliders (particles, localisations). The constructions proposed are based on universality of elementary cellular automaton rule 110, cyclic tag systems, supercolliders, and computing on rings.
A novel, information-based classification of elementary cellular automata is proposed that circumvents the problems associated with isolating whether complexity is in fact intrinsic to a dynamical rule, or if it arises merely as a product of a complex initial state. Transfer entropy variations processed by the system split the 256 elementary rules into three information classes, based on sensitivity to initial conditions. These classes form a hierarchy such that coarse-graining transitions observed among elementary cellular automata rules predominately occur within each information- based class, or much more rarely, down the hierarchy.
To help mitigate road congestion caused by the unrelenting growth of traffic demand, many transit authorities have implemented managed lane policies. Managed lanes typically run parallel to a freeway's standard, general-purpose (GP) lanes, but are restricted to certain types of vehicles. It was originally thought that managed lanes would improve the use of existing infrastructure through incentivization of demand-management behaviors like carpooling, but implementations have often been characterized by unpredicted phenomena that is often to detrimental system performance. This paper presents several macroscopic traffic modeling tools we have used for study of freeways equipped with managed lanes, or "managed lane-freeway networks." The proposed framework is based on the widely-used first-order kinematic wave theory. In this model, the GP and the managed lanes are modeled as parallel links connected by nodes, where certain type of traffic may switch between GP and managed lane links. Two types of managed lane topologies are considered: full-access, where vehicles can switch between the GP and the managed lanes anywhere; and separated, where such switching is allowed only at certain locations called gates. We also describe methods to incorporate in three phenomena into our model that are particular to managed lane-freeway networks. The inertia effect reflects drivers' inclination to stay in their lane as long as possible and switch only if this would obviously improve their travel condition. The friction effect reflects the empirically-observed driver fear of moving fast in a managed lane while traffic in the adjacent GP lanes moves slowly due to congestion. The smoothing effect describes how managed lanes can increase throughput at bottlenecks by reducing lane changes. We present simple models for each of these phenomena that fit within the general macroscopic theory.
We undertake an investigation of combinatorial designs engendered by cellular automata (CA), focusing in particular on orthogonal Latin squares and orthogonal arrays. The motivation is of cryptographic nature. Indeed, we consider the problem of employing CA to define threshold secret sharing schemes via orthogonal Latin squares. We first show how to generate Latin squares through bipermutive CA. Then, using a characterization based on Sylvester matrices, we prove that two linear CA induce a pair of orthogonal Latin squares if and only if the polynomials associated to their local rules are relatively prime.
In this paper, the performance of two lattice Boltzmann method formulations for yield-stress (i.e. viscoplastic) fluids has been investigated. The first approach is based on the popular Papanastasiou regularisation of the fluid rheology in conjunction with explicit modification of the lattice Boltzmann relaxation rate. The second approach uses a locally-implicit formulation to simultaneously solve for the fluid stress and the underlying particle distribution functions. After investigating issues related to the lattice symmetry and non-hydrodynamic Burnett stresses, the two models were compared in terms of spatial convergence and their behaviour in transient and inertial flows. The choice of lattice and the presence of Burnett stresses was found to influence the results of both models, however the latter did not significantly degrade the velocity field. Using Bingham flows in ducts and synthetic porous media, it was found that the implicitly-regularised model was superior in capturing transient and inertial fluid behaviour. This result presents potential implications for the application of the Papanastasiou-regularised model in such scenarios. In creeping flows the performance of both models was found to be both similar and satisfactory.
We advance our approach of analyzing the dynamics of interacting complex systems with the nonlinear dynamics of interacting nonlinear elements. We replace the widely used lattice-like connection topology of cellular neural networks (CNN) by complex topologies that include both short- and long-ranged connections. With an exemplary time-resolved analysis of asymmetric nonlinear interdependences between the seizure generating area and its immediate surrounding we provide first evidence for complex CNN connection topologies to allow for a faster network optimization together with an improved approximation accuracy of directed interactions.
It was recently shown how graphs can be used to provide descriptions of psychopathologies, where symptoms of, say, depression, affect each other and certain configurations determine whether someone could fall into a sudden depression. To analyse changes over time and characterise possible future behaviour is rather difficult for large graphs. We describe the dynamics of networks using one-dimensional discrete time dynamical systems theory obtained from a mean field approach to (elementary) probabilistic cellular automata (PCA). Often the mean field approach is used on a regular graph (a grid or torus) where each node has the same number of edges and the same probability of becoming active. We show that we can use variations of the mean field of the grid to describe the dynamics of the PCA on a random and small-world graph. Bifurcation diagrams for the mean field of the grid, random, and small-world graphs indicate possible phase transitions for certain parameter settings. Extensive simulations indicate for different graph sizes (number of nodes) that the mean field approximation is accurate. The mean field approach allows us to provide possible explanations of 'jumping' behaviour in depression.
We investigate the speed time series of the vehicles recorded by a camera at a section of a highway in the city of Isfahan, Iran. Using $k$-means clustering algorithm, we find that the natural number of clustering for this set of data is $3$. This is in agreement with the three-phase theory of uninterrupted traffic flows. According to this theory, the three traffic phases are categorized as {\em free flow} (F), {\em synchronized} (S) and {\em wide moving jam} (J). We obtain the transition speeds and densities at F-S and also S-J transitions. We also apply the Shannon entropy analysis on the speed time series over finite windows, which equips us to monitor in areal time the instant state of a traffic flow.
Fix a simple graph $G=(V,E)$ and choose a random initial 3-coloring of vertices drawn from a uniform product measure. The 3-color cycle cellular automaton is a process in which at each discrete time step in parallel, every vertex with color $i$ advances to the successor color $(i+1)$ mod 3 if in contact with a neighbor with the successor color, and otherwise retains the same color. In the Greenberg-Hastings Model, the same update rule applies only to color 0, while other two colors automatically advance. The limiting behavior of these processes has been studied mainly on the integer lattices. In this paper, we introduce a monotone comparison process defined on the universal covering space of the underlying graph, and characterize the limiting behavior of these processes on arbitrary connected graphs. In particular, we establish a phase transition on the Erdös-Rényi random graph. On infinite trees, we connect the rate of color change to the cloud speed of an associated tree-indexed walk. We give estimates of the cloud speed by generalizing known results to trees with leaves.