The Multi-n-Dimensional Cellular Automaton: A Unified Framework for Tensorial, Discrete, and Continuous Simulations—A Computational Definition of Time

Abstract

Cellular automata are powerful tools for simulating dynamic environments. Their ability to model complex systems where the environment actively influences outcomes makes them invaluable for studying phenomena such as wildfires, marine pollution, and population dynamics. However, traditional cellular automata are limited by discrete representations and rigid data structures, hindering their application in spatially complex scenarios. This paper introduces a generalized cellular automaton designed to overcome these challenges. By incorporating continuous space evolution and leveraging tensorial data structures, our model offers a more accurate, flexible, and computationally efficient framework for simulating real-world systems. This approach significantly simplifies the integration of geographical information into discrete simulations, expanding the potential of cellular automata in fields such as environmental science, population ecology, or theoretical physics. Moreover, our work contributes to a deeper understanding of tensorial representations and the concept of time using a computational approach.