Localization dynamics in a binary two-dimensional cellular automaton: the Diffusion Rule

We study a two-dimensional cellular automaton (CA), called Diffusion Rule (DR), which exhibits diffusion-like dynamics of propagating patterns. In computational experiments we discover a wide range of mobile and stationary localizations (gliders, oscillators, glider guns, puffer trains, etc), analyze spatio-temporal dynamics of collisions between localizations, and discuss possible applications in unconventional computing.Comment: Accepted to Journal of Cellular Automat

A framework for the local information dynamics of distributed computation in complex systems

The nature of distributed computation has often been described in terms of the component operations of universal computation: information storage, transfer and modification. We review the first complete framework that quantifies each of these individual information dynamics on a local scale within a system, and describes the manner in which they interact to create non-trivial computation where "the whole is greater than the sum of the parts". We describe the application of the framework to cellular automata, a simple yet powerful model of distributed computation. This is an important application, because the framework is the first to provide quantitative evidence for several important conjectures about distributed computation in cellular automata: that blinkers embody information storage, particles are information transfer agents, and particle collisions are information modification events. The framework is also shown to contrast the computations conducted by several well-known cellular automata, highlighting the importance of information coherence in complex computation. The results reviewed here provide important quantitative insights into the fundamental nature of distributed computation and the dynamics of complex systems, as well as impetus for the framework to be applied to the analysis and design of other systems.Comment: 44 pages, 8 figure

Detecting emergent processes in cellular automata with excess information

Many natural processes occur over characteristic spatial and temporal scales. This paper presents tools for (i) flexibly and scalably coarse-graining cellular automata and (ii) identifying which coarse-grainings express an automaton's dynamics well, and which express its dynamics badly. We apply the tools to investigate a range of examples in Conway's Game of Life and Hopfield networks and demonstrate that they capture some basic intuitions about emergent processes. Finally, we formalize the notion that a process is emergent if it is better expressed at a coarser granularity.Comment: 8 pages, 6 figure

Lenia and Expanded Universe

We report experimental extensions of Lenia, a continuous cellular automata family capable of producing lifelike self-organizing autonomous patterns. The rule of Lenia was generalized into higher dimensions, multiple kernels, and multiple channels. The final architecture approaches what can be seen as a recurrent convolutional neural network. Using semi-automatic search e.g. genetic algorithm, we discovered new phenomena like polyhedral symmetries, individuality, self-replication, emission, growth by ingestion, and saw the emergence of "virtual eukaryotes" that possess internal division of labor and type differentiation. We discuss the results in the contexts of biology, artificial life, and artificial intelligence.Comment: 8 pages, 5 figures, 1 table; submitted to ALIFE 2020 conferenc

Evolving Structures in Complex Systems

In this paper we propose an approach for measuring growth of complexity of emerging patterns in complex systems such as cellular automata. We discuss several ways how a metric for measuring the complexity growth can be defined. This includes approaches based on compression algorithms and artificial neural networks. We believe such a metric can be useful for designing systems that could exhibit open-ended evolution, which itself might be a prerequisite for development of general artificial intelligence. We conduct experiments on 1D and 2D grid worlds and demonstrate that using the proposed metric we can automatically construct computational models with emerging properties similar to those found in the Conway's Game of Life, as well as many other emergent phenomena. Interestingly, some of the patterns we observe resemble forms of artificial life. Our metric of structural complexity growth can be applied to a wide range of complex systems, as it is not limited to cellular automata.Comment: IEEE Symposium Series on Computational Intelligence 2019 (IEEE SSCI 2019

Complete characterization of structure of rule 54

The dynamics of rule 54 one-dimensional two-state cellular automaton (CA) are a discrete analog of a space-time dynamics of excitations in nonlinear active medium with mutual inhibition. A cell switches its state 0 to state 1 if one of its two neighbors is in state 1 (propagation of a perturbation) and a cell remains in state 1 only if its two neighbors are in state 0. A lateral inhibition is because a 1-state neighbor causes a 1-state cell to switch to state 0. The rule produces a rich spectrum of space-time dynamics, including gliders and glider guns just from four primitive gliders. We construct a catalogue of gliders and describe them by tiles. We calculate a subset of regular expressions $\Psi_{R54}$ to encode gliders. The regular expressions are derived from de Bruijn diagrams, tile-based representation of gliders, and cycle diagrams sometimes. We construct an abstract machine that recognizes regular expressions of gliders in rule 54 and validate $\Psi_{R54}$. We also propose a way to code initial configurations of gliders to depict any type of collision between the gliders and explore self-organization of gliders, formation of larger tiles, and soliton-like interactions of gliders and computable devices

Spatio-Temporal Patterns act as Computational Mechanisms governing Emergent behavior in Robotic Swarms

open access articleOur goal is to control a robotic swarm without removing its swarm-like nature. In other words, we aim to intrinsically control a robotic swarm emergent behavior. Past attempts at governing robotic swarms or their selfcoordinating emergent behavior, has proven ineffective, largely due to the swarm’s inherent randomness (making it difficult to predict) and utter simplicity (they lack a leader, any kind of centralized control, long-range communication, global knowledge, complex internal models and only operate on a couple of basic, reactive rules). The main problem is that emergent phenomena itself is not fully understood, despite being at the forefront of current research. Research into 1D and 2D Cellular Automata has uncovered a hidden computational layer which bridges the micromacro gap (i.e., how individual behaviors at the micro-level influence the global behaviors on the macro-level). We hypothesize that there also lie embedded computational mechanisms at the heart of a robotic swarm’s emergent behavior. To test this theory, we proceeded to simulate robotic swarms (represented as both particles and dynamic networks) and then designed local rules to induce various types of intelligent, emergent behaviors (as well as designing genetic algorithms to evolve robotic swarms with emergent behaviors). Finally, we analysed these robotic swarms and successfully confirmed our hypothesis; analyzing their developments and interactions over time revealed various forms of embedded spatiotemporal patterns which store, propagate and parallel process information across the swarm according to some internal, collision-based logic (solving the mystery of how simple robots are able to self-coordinate and allow global behaviors to emerge across the swarm)