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arXiv2021

The Effects of Interaction Functions Between Two Cellular Automata

Biological systems are notorious for complex behavior within short timescales (e.g. metabolic activity) and longer time scales (e.g. evolutionary selection), along with their complex spatial organization. Because of their complexity and their ability to innovate with respect to their environment, living systems are considered to be open-ended. Historically, it has been difficult to model open-ended evolution and innovation. As a result, our understanding of the exact mechanisms that distinguish open-ended living systems from non-living ones is limited. One of the biggest barriers is understanding how multiple, complex parts within a single system interact and contribute to the complex, emergent behavior of the system as a whole. How do interactions between parts of a system lead to more complex behavior of the system as a whole? This paper presents two interacting cellular automata (CA) as an abstract model to address the effects of complex interactions between two individual entities embedded within a larger system. Unlike elementary CA, each CA changes its update rules as a function of the system's state as a whole. The resulting behavior of the two-CA system suggests that complex interaction functions between the two CA have little to no effect on the complexity of each individual CA behavior and structure. However, having an interaction function that is random results in open-ended evolution regardless of the specific type of state-dependency.

nlin.CG↗

arXiv2020

Probabilistic Cellular Automata for Granular Media in Video Games

Granular materials are very common in the everyday world. Media such as sand, soil, gravel, food stuffs, pharmaceuticals, etc. all have similar irregular flow since they are composed of numerous small solid particles. In video games, simulating these materials increases immersion and can be used for various game mechanics. Computationally, full scale simulation is not typically feasible except on the most powerful hardware and tends to be reduced in priority to favor other, more integral, gameplay features. Here we study the computational and qualitative aspects of side profile flow of sand-like particles using cellular automata (CA). Our CA uses a standard square lattice that updates via a custom, modified Margolus neighborhood. Each update occurs using a set of probabilistic transitions that can be tuned to simulate friction between particles. We focus on the look of the sandpile structure created from an hourglass shape over time using different transition probabilities and the computational impact of such a simulation.

nlin.CG↗

arXiv2021

Isotropic Cellular Automata: the DDLab iso-rule paradigm

To respect physics and nature, cellular automata (CA) models of self-organisation, emergence, computation and logical universality should be isotropic, having equivalent dynamics in all directions. We present a novel paradigm, the iso-rule, a concise expression for isotropic CA by the output table for each isotropic neighborhood group, allowing an efficient method of navigating and exploring iso-rule-space. We describe new functions and tools in DDLab to generate iso-groups and iso-rules, for multi-value as well as binary, in one, two and three dimensions. These methods include filing, filtering, mutating, analysing dynamics by input-frequency and entropy, identifying the critical iso-groups for glider-gun/eater dynamics, and automatically classifying iso-rule-space. We illustrate these ideas and methods for two dimensional CA on square and hexagonal lattices.

nlin.CG↗

arXiv2020

A Data-driven Understanding of COVID-19 Dynamics Using Sequential Genetic Algorithm Based Probabilistic Cellular Automata

COVID-19 pandemic is severely impacting the lives of billions across the globe. Even after taking massive protective measures like nation-wide lockdowns, discontinuation of international flight services, rigorous testing etc., the infection spreading is still growing steadily, causing thousands of deaths and serious socio-economic crisis. Thus, the identification of the major factors of this infection spreading dynamics is becoming crucial to minimize impact and lifetime of COVID-19 and any future pandemic. In this work, a probabilistic cellular automata based method has been employed to model the infection dynamics for a significant number of different countries. This study proposes that for an accurate data-driven modeling of this infection spread, cellular automata provides an excellent platform, with a sequential genetic algorithm for efficiently estimating the parameters of the dynamics. To the best of our knowledge, this is the first attempt to understand and interpret COVID-19 data using optimized cellular automata, through genetic algorithm. It has been demonstrated that the proposed methodology can be flexible and robust at the same time, and can be used to model the daily active cases, total number of infected people and total death cases through systematic parameter estimation. Elaborate analyses for COVID-19 statistics of forty countries from different continents have been performed, with markedly divergent time evolution of the infection spreading because of demographic and socioeconomic factors. The substantial predictive power of this model has been established with conclusions on the key players in this pandemic dynamics.

q-bio.QM↗

arXiv2020

Singular function emerging from one-dimensional elementary cellular automaton Rule 150

In this paper, we give a singular function on a unit interval derived from the dynamic of the one-dimensional elementary cellular automaton Rule 150. We describe properties of the resulting function, that is strictly increasing, uniformly continuous, and differentiable almost everywhere, and we show that it is not differentiable at dyadic rational points. We also give functional equations that the function satisfies, and show that the function is the only solution of the functional ones.

math.DS↗

arXiv2020

Closure under Coupling of Cellular-DEVS for the Optimization of Memory Resource: Wildfire Spread Case Study

The present work aims to show one of the advantages of using the property of closure under coupling in the DEVS specification. The advantage concerned in this paper attempts to address the need for memory resources during the simulation of systems by cellular-DEVS. This improvement of performance is based on the usage of the property closure under coupling in the DEVS formalism. With this property and taking account of the iterative behavior of each cellular-DEVS atomic model, we provide simulation of many models simultaneously. The method starts with the specification of the cellular-DEVS coupled model which is then converted into its equivalent DEVS atomic model. Thus, the goal of this conversion is to transform large quantities of atomic models coupled together, which require huge computational resources, into one DEVS atomic model. A case study is presented at the end of the work on modeling and simulation of forest fire propagation using DEVS and cellular-DEVS. A specification by cellular-DEVS of the forest fire model and its non-modular equivalent DEVS atomic model are presented. Finally, a comparison between both methods is presented in term of consumption of resources.

nlin.CG↗

arXiv2020

When the future alters the present: how Discrete Dynamical Systems replicate images

Agents affected by their own future states in a one-dimensional discrete dynamical system (1-DDS) can replicate two-dimensional images. It is shown that such replication requires a toroidal spacetime and three rules are needed to calculate the number of iterations required for exact replication. It is argued that retrocausal updation used by 1-DDS can replicate any n-dimensional digital object. It is shown that the way iterations reach a final image are different for randomly generated images and non-random, meaningful images. Two instances of real-world events that seem to imply such retrocausal replication are discussed.

nlin.CG↗

arXiv2020

On complex dynamics from reversible cellular automata

Complexity has been a recurrent research topic in cellular automata because they represent systems where complex behaviors emerge from simple local interactions. A significant amount of previous research has been conducted proposing instances of complex cellular automata; however, most of the proposed methods are based on a careful search or a meticulous construction of evolution rules. This paper presents the emergence of complex behaviors based on reversible cellular automata. In particular, this paper shows that reversible cellular automata represent an adequate framework to obtain complex behaviors adding only new random states. Experimental results show that complexity can be obtained from reversible cellular automata appending a proportion of about two times more states at random than the original number of states in the reversible automaton. Thus, it is possible to obtain complex cellular automata with dozens of states. Complexity appears to be commonly obtained from reversible cellular automata, and using other operations such as permutations of states or row and column permutations in the evolution rule. The relevance of this paper is to present that reversibility can be a useful structure to implement complex behaviors in cellular automata.

nlin.CG↗

arXiv2020

Random Expansion Method for the Generation of Complex Cellular Automata

The emergence of complex behaviors in cellular automata is an area that has been widely developed in recent years with the intention to generate and analyze automata that produce space-moving patterns or gliders that interact in a periodic background. Frequently, this type of automata has been found through either an exhaustive search or a meticulous construction of the evolution rule. In this study, the specification of cellular automata with complex behaviors was obtained by utilizing randomly generated specimens. In particular, it proposed that a cellular automaton of $n$ states should be specified at random and then extended to another automaton with a higher number of states so that the original automaton operates as a periodic background where the additional states serve to define the gliders. Moreover, this study presented an explanation of this method. Furthermore, the random way of defining complex cellular automata was studied by using mean-field approximations for various states and local entropy measures. This specification was refined with a genetic algorithm to obtain specimens with a higher degree of complexity. With this methodology, it was possible to generate complex automata with hundreds of states, demonstrating that randomly defined local interactions with multiple states can construct complexity.

nlin.CG↗

arXiv2020

Simulation of Pedestrian Movements on Slope Using Fine Grid Cellular Automata

Cellular automata crowd simulation models have been extensively used to determine the performance and the safety of crowded structures. In conventional cellular automata systems, all the cells are of the size of a typical pedestrian. The free flow speed of a pedestrian is around 1.3m/s, and the typical size of a cell in conventional CA models is around 45cm. In order to maintain the upper boundary of movement speed, pedestrians should move 0, 1, 2 or 3 cells at each second in the simulation. These limited number of speed values pose a limitation on the accuracy of the simulated speed of pedestrians. Movement speed of pedestrians on a slope depends on the angel of the slope. The conventional CA limitations do not allow accurate simulation of pedestrian movements on slopes with different angels. Fine grid cellular automata model uses much smaller cells (e.g. 5cm or smaller). The model therefore allows much more possible speed values. In this article, fine grid cellular automata model is used to model and simulate the movements of pedestrians on a slope. A walkway scenario is used for the evaluation of the model.

nlin.CG↗

arXiv2020

Study on particulate matter emissions from traffic by cellular automaton model with slow-to-start effect

Based on the empirical particulate emission model, we studied Particulate Matter (PM) emission of some typical cellular automata VDR model and TT model with slow-to-start rules under periodic condition and open boundary condition. By simulations, it is found that the emission of the slow-to-start rule model reaches the maximum emission at metastable state under periodic boundary condition. Under open boundary condition, the phase diagram to reflect traffic congestion is obtained. The injection probability and removal probability have a great impact on PM emissions. Moreover, the effects of motion status on emissions in the VDR model and TT model are studied under two different boundary conditions. Numerical simulation shows that the PM emission of decelerating traffic flow reaches the maximum in the congestion state under periodic boundary condition. Under the open boundary conditions with the same departure probability, the variation trend of particulate emission varies with the state of different vehicle movements. For different removal probabilities, the different maximum concentration of particulate matter is emitted even if the vehicle is in the same motion state.

nlin.CG↗

arXiv2020

An Improved Algorithm for Coarse-Graining Cellular Automata

In studying the predictability of emergent phenomena in complex systems, Israeli & Goldenfeld (Phys. Rev. Lett., 2004; Phys. Rev. E, 2006) showed how to coarse-grain (elementary) cellular automata (CA). Their algorithm for finding coarse-grainings of supercell size $N$ took doubly-exponential $2^{2^N}$-time, and thus only allowed them to explore supercell sizes $N \leq 4$. Here we introduce a new, more efficient algorithm for finding coarse-grainings between any two given CA that allows us to systematically explore all elementary CA with supercell sizes up to $N=7$, and to explore individual examples of even larger supercell size. Our algorithm is based on a backtracking search, similar to the DPLL algorithm with unit propagation for the NP-complete problem of Boolean Satisfiability.

nlin.CG↗

arXiv2021

Sequential Monte Carlo algorithms for agent-based models of disease transmission

Agent-based models of disease transmission involve stochastic rules that specify how a number of individuals would infect one another, recover or be removed from the population. Common yet stringent assumptions stipulate interchangeability of agents and that all pairwise contact are equally likely. Under these assumptions, the population can be summarized by counting the number of susceptible and infected individuals, which greatly facilitates statistical inference. We consider the task of inference without such simplifying assumptions, in which case, the population cannot be summarized by low-dimensional counts. We design improved particle filters, where each particle corresponds to a specific configuration of the population of agents, that take either the next or all future observations into account when proposing population configurations. Using simulated data sets, we illustrate that orders of magnitude improvements are possible over bootstrap particle filters. We also provide theoretical support for the approximations employed to make the algorithms practical.

stat.CO↗

arXiv2021

Flying V and Reference Aircraft Evacuation Simulation and Comparison

A preliminary comparison of evacuation times of the Flying V and the Airbus A350-900 is presented in this study. A simple simulation tool based on the technique of cellular automata was created to model the evacuation process for different closed door configurations. Certification regulations state that the time to evacuate a civil aircraft in case of an emergency with half of all exit doors closed must be less than 90 seconds. The results of this study indicate that the shorter V shaped cabin has advantages over the longer conventional reference cabin for cases when passengers need to evacuate towards the front or the back of the aircraft. Disadvantages occur when the passengers in the V shaped cabin need to evacuate more towards one side (left or right wing) of the aircraft. A more detailed simulation model to further investigate these cases is currently created by the authors.

cond-mat.soft↗

arXiv2021

Weak Stefan Formulation for Bulk Crystal Growth with Non-smooth Interfaces

Most heat transfer models for bulk crystal growth rely on the classical Stefan formulation to evaluate interface motion during phase change. However, when the interface is non-smooth the use of the classical Stefan formulation may lead to singularities. To address this problem, we propose a simulation model based on the weak formulation of the Stefan problem. Numerical solutions of the weak Stefan formulation are obtained using the finite volume method. This approach provides an energy conserving discretization scheme that accurately evaluates heat transfer around non-smooth interfaces. We apply the weak formulation to numerically simulate the solidification of silicon in the horizontal ribbon growth process. Results exhibit a limitation on the ribbon's pull speed, which previous classical Stefan models have failed to demonstrate. A comparison of heat transfer between radiation and gas cooling shows that gas cooling increases the pull speed limit for the same amount of heat removed.

cond-mat.mtrl-sci↗

arXiv2021

Cellular Automata and Kan Extensions

In this paper, we formalize precisely the sense in which the application of cellular automaton to partial configuration is a natural extension of its local transition function through the categorical notion of Kan extension. In fact, the two possible ways to do such an extension and the ingredients involved in their definition are related through Kan extensions in many ways. These relations provide additional links between computer science and category theory, and also give a new point of view on the famous Curtis-Hedlung theorem of cellular automata from the extended topological point of view provided by category theory. These relations provide additional links between computer science and category theory. No prior knowledge of category theory is assumed.

cs.DC↗

arXiv2021

Millions of 5-State n^3 Sequence Generators via Local Mappings

In this paper, we come back on the notion of local simulation allowing to transform a cellular automaton into a closely related one with different local encoding of information. In a previous paper, we applied it to the Firing Squad Synchronization Problem. In this paper, we show that the approach is not tied to this problem by applying it to the class of Real-Time Sequence Generation problems. We improve in particular on the generation of n 3 sequence by using local mappings to obtain millions of 5state solution, one of them using 58 transitions. It is based on the solution of Kamikawa and Umeo that uses 6 states and 74 transitions. Then, we explain in which sense even bigger classes of problems can be considered.

cs.DC↗

arXiv2021

Accretive Computation of Global Transformations

Global transformations form a categorical framework adapting graph transformations to describe fully synchronous rule systems on a given data structure.In this work we focus on data structures that can be captured as presheaves and study the computational aspects of such synchronous rule systems.To obtain an online algorithm, a complete study of the sub-steps within each synchronous step is done at the semantic level.This leads to the definition of accretive rule systems and a local criterion to characterize these systems.Finally an online computation algorithm for theses systems is given.

cs.DC↗