Automating the Search for Artificial Life With Foundation Models.

This paper presents a novel approach for studying the relationship between the properties of isolated cells and the emergent behavior that occurs in cellular systems formed by coupling such cells. The novelty of our approach consists of a method for precisely partitioning the cell parameter space into subdomains via the failure boundaries of the piecewise-linear CNN (cellular neural network) cells [Dogaru & Chua, 1999a] of a generalized cellular automata [Chua, 1998]. Instead of exploring the rule space via statistically defined parameters (such as λ in [Langton, 1990]), or by conducting an exhaustive search over the entire set of all possible local Boolean functions, our approach consists of exploring a deterministically structured parameter space built around parameter points corresponding to "interesting" local Boolean logic functions. The well-known "Game of Life" [Berlekamp et al., 1982] cellular automata is reconsidered here to exemplify our approach and its advantages. Starting from a piecewise-linear representation of the classic Conway logic function called the "Game of Life", and by introducing two new cell parameters that are allowed to vary continuously over a specified domain, we are able to draw a "map-like" picture consisting of planar regions which cover the cell parameter space. A total of 148 subdomains and their failure boundaries are precisely identified and represented by colored paving stones in this mosaic picture (see Fig. 1), where each stone corresponds to a specific local Boolean function in cellular automata parlance. Except for the central "paving stone" representing the "Game of Life" Boolean function, all others are mutations uncovered by exploring the entire set of 148 subdomains and determining their dynamic behaviors. Some of these mutations lead to interesting, "artificial life"-like behavior where colonies of identical miniaturized patterns emerge and evolve from random initial conditions. To classify these emergent behaviors, we have introduced a nonhomogeneity measure, called cellular disorder measure, which was inspired by the local activity theory from [Chua, 1998]. Based on its temporal evolution, we are able to partition the cell parameter space into a class U "unstable-like" region, a class E "edge of chaos"-like region, and a class P "passive-like" region. The similarity with the "unstable", "edge of chaos" and "passive" domains defined precisely and applied to various reaction–diffusion CNN systems [Dogaru & Chua, 1998b, 1998c] opens interesting perspectives for extending the theory of local activity [Chua, 1998] to discrete-time cellular systems with nonlinear couplings. To demonstrate the potential of emergent computation in generalized cellular automata with cells designed from mutations of the "Game of Life", we present a nontrivial application of pattern detection and reconstruction from very noisy environments. In particular, our example demonstrates that patterns can be identified and reconstructed with very good accuracy even from images where the noise level is ten times stronger than the uncorrupted image.

Cellular automata are widely used in undergraduate physics courses to educate students in elementary programming and for project work. Cellular automata are coded with simple rules yet provide a rich if well-trodden landscape for exploring aspects of physics such as diffusion and magnetism. Mathematical games, such as the minority game or the prisoner's dilemma, are also amenable to project work with the added dimension of applications in finance, econophysics, and social physics. Conway's classical game of life is both a mathematical game and a cellular automaton. We exploit adaptations of Conway's game of life as an opportunity for undergraduate students to explore new territory within the safe haven of an easy-to-implement cellular automaton. Students may discover new “lifeforms” comprising collections of live, dead, and part-live cells, and explore the escalation of floating-point errors leading to chaos-like behavior, amongst many phenomena not observed in Conway's classical counterpart.

In 1952, Alan Turing who is considered as a father of Computer Science, based on his previous scientific research on the theory of computation, he emphasized how important is the analysis of pattern formation in nature and developed a theory. In his theory, he described specific patterns in nature that could be formed from basic chemical systems. Turing in his previous studies in the theory of computation, he had constantly worked on symmetrical patterns that could be formed simultaneously and realized the necessity for further analysis of pattern formation in biological problems. However, it was until the late 1960s, when John Conway was the first to introduce the "Game of Life", an innovative mathematical game based on cellular automata, having a purpose to utilize the fundamental entities, called as cells, in two possible states described as "dead" or "alive". This paper tries to contribute to a better understanding of the "Game of Life" by implementing algorithmic approaches of this problem in PASCAL and Python programming languages. Also, inside the paper numerous variations and extensions of the Conway's Game of Life are proposed that introduce new ideas and concepts. Furthermore, several machine learning algorithms to learn patterns from large sets of Game of Life simulations and generate new rules or strategies are described in detail

<i>Introduction to the Modeling and Analysis of Complex Systems.</i> H. Sayama (Ed.). (2015, Open SUNY Textbooks). Free open access PDF, 498 pp. ISBN 978-1-942341-06-2 (deluxe color edition). ISBN 978-1-942341-08-6 (print edition). ISBN 978-1-942341-09-3 (ebook).

The Game of Life is the exemplar of a cellular automaton (CA) and hence serves as a good starting point for our work with cellular automaton programming. Originally developed by John Conway, a British mathematician, the Game of Life was supposedly the first program run on a parallel processing computer. In fact, it has been estimated that more computer time has been spent running the Game of Life program than any other computer program. While the Game of Life is an abstract “toy” system that has not (yet) been found to directly represent any specific natural system, it has been the springboard for the study of so-called “artificial life” systems because of the amazingly complex behaviors displayed by some of the patterns that occur during the running of the CA. We will implement the Game of Life CA in the fastest high-level way we know of, by generating and using a lookup table consisting of 512 rules for updating sites on the Game of Life lattice.

This study presents the mathematical development of a cellular automata model for the species Caulerpa taxifolia for closed or intermittently closed waterways along the Australian coast. The model is used to assess the spatial coverage of C. taxifolia by describing changes in growth, spread and total biomass for the species. Building upon a foundation model developed by the authors, this study was designed to enhance the predictive capabilities of a model based upon a discrete version of Laplace's equation. The improvements relate to several components integrated into the Laplacian coefficients; a periodic function which represents the seasonal variations in growth, the incorporation of the prevailing wind to represent the most likely direction of spread, and growth restrictions based on lake depth. The additional complexity improved the predictive capability of the model. Cellular Automata (CA) have been used to model changing plant distributions over the last 20 years, providing efficient models for complex environmental systems, particularly of exotic species. In this project the discrete CA algorithm is designed to determine the state or biomass B = f1; 0;1;2g of the current cell using the primary rule of the discrete Laplacian system. Biomass of1 refers to land, and the other values represent the relative quantity of the weed in the cell; none, sparse or dense respectively. Cell interactions are governed by the coefficients of the Laplacian system which is discussed. The foundation model incorporated simple rules, not unlike those of John Conway's Game of Life. The biomass of the surrounding cells at time t determines the state of the central cell at time t + 1. The boundary conditions were catered for by allocating a biomass of negative one to the land cells adjacent to the water. The results indicate that the model is able to predict the total surface coverage and total biomass at levels of accuracy commensurate with the input data, which is important for control measures. Also, high accuracy in the predicted locational data at Lake Conjola indicates that the model is able to identify appropriate growing conditions to aid in the eradication efforts. At successive time steps, the model produces accurate patch location data with a slight overestimation on patch size due to slight error prediction of the decay in the initial winter season. The principle objective of this new study is to improve the predictive capabilities of the model developed by the authors, by taking into account the biological and environmental factors of growth and spread and in doing so, more accurately predict the spatial coverage and colonization locations of C. taxifolia growth and spread in a closed or intermittently closed estuary. This model is designed to inform resource managers and government bodies of the most effective methods of eradication.

This paper studies a phenomenon called density demand management (DDM) of microgrids, and shows that this phenomenon can be modeled by variants of Conway's Game of Life (GL) cellular automata. The density and activity reflecting fluctuation of all games are similar to the GL. An important task is to share the load demand using multiple distributed generation (DG) units in order to implement the operation of autonomous microgrids. The density of microgrids must be adjusted to a certain level to meet the load demand. In this paper we propose a self-adaptive algorithm to find stable density range methods in variants of GL. The configuration is based on the standard GL rules and its variants. The pentadecathlon (PD) is represented as the basic computational unit, and it is shown how it can be adjusted in variants of GL while achieving stable density range. The details of self-adaptive algorithm mechanism and its working are described, and the simulations and experimental results validate the feasibility of the proposed method. This paper offers a useful contribution for cellular automata based modeling, explores why such models are particularly useful for microgrids density management dynamics simulations.

Conway's Game of Life in Quantum-dot Cellular Automata

We investigate a special class of cellular automata (CA) evolving in a environment filled by an electromagnetic wave. The rules of the Conway's Game of Life are modified to account for the ability to retrieve life-sustenance from the field energy. Light-induced self-structuring and self-healing abilities and various dynamic phases are displayed by the CA. Photo-driven genetic selection and the nonlinear feedback of the CA on the electromagnetic field are included in the model, and there are evidences of self-organized light-localization processes. The evolution of the electromagnetic field is based on the Finite Difference Time Domain (FDTD) approach. Applications are envisaged in evolutionary biology, artificial life, DNA replication, swarming, optical tweezing and field-driven soft-matter.

Over 40 years ago, the Chilean biologists Humberto Maturana and Francisco Varela put forward the notion of autopoiesis as a way to understand living systems and their phenomenology. Varela and others subsequently extended this framework to an enactive approach that places biological autonomy at the foundation of situated and embodied behavior and cognition. In this talk, I will describe an attempt to place these ideas on a firmer foundation by studying them within the context of a toy model universe, John Conway's Game of Life (GoL) cellular automata. The talk has both pedagogical and theoretical goals. Simple concrete models provide an excellent vehicle for introducing some of the core concepts of autopoiesis and enaction and explaining how these concepts fit together into a broader whole. In addition, a careful analysis of such toy models can hone our intuitions about these concepts, probe their strengths and weaknesses, and move the entire enterprise in the direction of a more mathematically rigorous theory. In particular, I will identify the primitive processes that can occur in GoL, show how these can be linked together into mutually-supporting networks, map the responses of such entities to environmental perturbations, and investigate the paths of mutual perturbation that these entities and their environments can undergo. Some of the topics that can be examined in GoL include the structure/organization distinction, organizational/operational closure, self-production, self-individuation, destructive vs. nondestructive perturbations, precariousness, cognitive domain, subjectivity, significance, sense-making, structural coupling, and enaction. I will end with some comments on the limitations of the GoL model and directions for future work.

Conway's cellular automaton Game of Life has been conjectured to be a critical (or quasicritical) dynamical system. This criticality is generally seen as a continuous order-disorder transition in cellular automata (CA) rule space. Life's mean-field return map predicts an absorbing vacuum phase (ρ = 0) and an active phase density, with ρ = 0.37, which contrasts with Life's absorbing states in a square lattice, which have a stationary density of ρ(2D) ≈ 0.03. Here, we study and classify mean-field maps for 6144 outer-totalistic CA and compare them with the corresponding behavior found in the square lattice. We show that the single-site mean-field approach gives qualitative (and even quantitative) predictions for most of them. The transition region in rule space seems to correspond to a nonequilibrium discontinuous absorbing phase transition instead of a continuous order-disorder one. We claim that Life is a quasicritical nucleation process where vacuum phase domains invade the alive phase. Therefore, Life is not at the "border of chaos," but thrives on the "border of extinction."

Cellular automatons and computer simulation games are widely used as heuristic devices in biology, to explore implications and consequences of specific theories. Conway's Game of Life has been widely used for this purpose. This game was designed to explore the evolution of ecological communities. We apply it to other biological processes, including symbiopoiesis. We show that Conway's organization of rules reflects the epigenetic principle, that genetic action and developmental processes are inseparable dimensions of a single biological system, analogous to the integration processes in symbiopoiesis. We look for similarities and differences between two epigenetic models, by Turing and Edelman, as they are realized in Game of Life objects. We show the value of computer simulations to experiment with and propose generalizations of broader scope with novel testable predictions. We use the game to explore issues in symbiopoiesis and evo-devo, where we explore a fractal hypothesis: that self-similarity exists at different levels (cells, organisms, ecological communities) as a result of homologous interactions of two as processes modeled in the Game of Life

Over 40 years ago, the Chilean biologists Humberto Maturana and Francisco Varela put forward the notion of autopoiesis as a way to understand living systems and their phenomenology. Varela and others subsequently extended this framework to an enactive approach that places biological autonomy at the foundation of situated and embodied behavior and cognition. In this talk, I will describe an attempt to place these ideas on a firmer foundation by studying them within the context of a toy model universe, John Conway's Game of Life (GoL) cellular automata. The talk has both pedagogical and theoretical goals. Simple concrete models provide an excellent vehicle for introducing some of the core concepts of autopoiesis and enaction and explaining how these concepts fit together into a broader whole. In addition, a careful analysis of such toy models can hone our intuitions about these concepts, probe their strengths and weaknesses, and move the entire enterprise in the direction of a more mathematically rigorous theory. In particular, I will identify the primitive processes that can occur in GoL, show how these can be linked together into mutually-supporting networks, map the responses of such entities to environmental perturbations, and investigate the paths of mutual perturbation that these entities and their environments can undergo. Some of the topics that can be examined in GoL include the structure/organization distinction, organizational/operational closure, self-production, self-individuation, destructive vs. nondestructive perturbations, precariousness, cognitive domain, subjectivity, significance, sense-making, structural coupling, and enaction. I will end with some comments on the limitations of the GoL model and directions for future work.

Most readers are familiar with cellular automata (CA) utilizing squares as cells, and are also familiar with the most famous automaton, Conway's Game of Life. This game is played on an infinite grid of squares, and has been thoroughly explored in many publications [1, 2] as well as on numerous websites. In 1994 in this journal the author introduced several games of life in the triangular tessellation [3]. It now appears, not surprisingly, that other tessellations also support games of life.

Conway's Game of Life is one of the most famous and frequently studied cellular automata. This paper introduces a network representation of the Game of Life and studies its relation to self-organized criticality. Self-organized criticality in the Game of Life is reconfirmed by studying power-law scaling for the distributions of avalanche scales: lifetimes, sizes, and out-degrees in a rest-state network. Avalanches are caused by one-cell perturbations of the rest state. Finite-size scaling analysis shows that avalanche lifetime and out-degree can be regarded as order parameters with characteristic lengths dependent on lattice size. The rest-state network of the Game of Life expresses a power-law degree distribution of out-links with a cut-off. Rule T52 of the one-dimensional binary five-neighbor totalistic cellular automata is also discussed in terms of the out-degrees of the rest-state network. Network representations of binary cellular automata can be used to assess their self-organized criticality.