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The rapid advancement of AI has changed the character of HPC usage such as dimensioning, provisioning, and execution. Not only has energy demand been amplified, but existing rudimentary continual learning capabilities limit ability of AI to…
We propose a four-way classification of two-dimensional semi-totalistic cellular automata that is different than Wolfram's, based on two questions with yes-or-no answers: do there exist patterns that eventually escape any finite bounding…
Cellular automata (CA) are quintessential ALife and ubiquitous in many studies of collective behaviour and emergence, from morphogenesis to social dynamics and even brain modelling. Recently, there has been an increased interest in…
Agent-based (AB) or Cellular Automata (CA) models are rule based and are a relatively simple discrete method that can be used to simulate complex interactions of many agents or cells. The relative ease of implementing the computational…
We present a method for the automated discovery of system-level dynamics in Flow-Lenia--a continuous cellular automaton (CA) with mass conservation and parameter localization-using a curiosity--driven AI scientist. This method aims to…
We investigate critical properties of a class of number-conserving cellular automata (CA) which can be interpreted as deterministic models of traffic flow with anticipatory driving. These rules are among the only known CA rules for which…
The theory of cellular automata in operational probabilistic theories is developed. We start introducing the composition of infinitely many elementary systems, and then use this notion to define update rules for such infinite composite…
The relationship between reaction-diffusion (RD) systems, characterized by continuous spatiotemporal states, and cellular automata (CA), marked by discrete spatiotemporal states, remains poorly understood. This paper delves into this…
Recent experiments by Springer and Kenyon have shown that a deep neural network can be trained to predict the action of $t$ steps of Conway's Game of Life automaton given millions of examples of this action on random initial states.…
Deep learning techniques have recently demonstrated broad success in predicting complex dynamical systems ranging from turbulence to human speech, motivating broader questions about how neural networks encode and represent dynamical rules.…
We present Mass-Conserving Evolution (MaCE), a general method for implementing mass conservation in Cellular Automata (CA). MaCE is a simple evolution rule that can be easily 'attached' to existing CAs to make them mass-conserving, which…
Cellular automata provide models of parallel computation based on cells, whose connectivity is given by an action of a monoid on the cells. At each step in the computation, every cell is decorated with a state that evolves in discrete steps…
We investigate the dynamics of a conservative version of Conway's Game of Life, in which a pair consisting of a dead and a living cell can switch their states following Conway's rules but only by swapping their positions, irrespective of…
Without loss of generalisation to other systems, including possibly non-deterministic ones, we demonstrate the application of methods drawn from algorithmic information dynamics to the characterisation and classification of emergent and…
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.
Scientists world-wide are putting together massive efforts to understand how the biodiversity that we see on Earth evolved from single-cell organisms at the origin of life and this diversification process is represented through the Tree of…
Reversible Cellular Automata (RCA) are a particular kind of shift-invariant transformations characterized by a dynamics composed only of disjoint cycles. They have many applications in the simulation of physical systems, cryptography and…
Cellular automata (CA) are simulation models that can produce complex emergent behaviors from simple local rules. Although state-of-the-art GPU solutions are already fast due to their data-parallel nature, their performance can rapidly…
Evolutionary theorizing resembles building an aircraft while also piloting it; new results change the scaffold for older ideas, requiring revised strategy to remain airborne. A calculated kinetic pathway exists that, under explicit…
We propose a chaotic encryption method based on Cellular Automata(CA), specifically on the family called the "Life-Like" type. Thus, the encryption process lying on the pseudo-random numbers generated (PRNG) by each CA's evolution, which…