ALGORITHMIC IMPLEMENTATION OF QUANTUM FLUCTUATIONS MODELING IN THREE-DIMENSIONAL CELLULAR AUTOMATA FOR COSMOLOGICAL SIMULATIONS

Abstract

This scientific work examines the algorithmic implementation of quantum fluctuations modeling in three-dimensional cellular automata (3D CA) for their application in cosmological simulations of Universe evolution. Cellular automata are inherently massively parallel systems, as all cells update simultaneously (or at least independently within a single time step). This makes them effective for modeling systems with a large number of interacting elements. Thus, the evolution of cellular automata is viewed as a computational process. From this perspective, the Universe itself can be considered a vast computational system, and its history - the result of executing certain fundamental program or algorithm. This idea underlies the paradigm of digital physics. Our research focuses on the theoretical foundation of quantum fluctuations phenomenon, their fundamental role in forming the large-scale structure of the Universe as primary perturbations that initiate gravitational collapse of matter. The methodology for implementing the stochastic mechanism of fluctuation generation in the discrete space-time paradigm of 3D CA is described in detail. The definition of cell states characterized by intensities of cosmological components (matter-energy, dark matter, dark energy), as well as the "Void" state is considered. Algorithmic steps for generating random perturbations that model quantum fluctuations and their impact on local intensities of these components are presented. Special attention is paid to integrating the developed algorithm into a broader modeling system that includes algorithms for gravitational interaction, space expansion under dark energy influence, and diffusion processes. The role of the stochastic algorithm in breaking symmetry, generating primary "seeds" of inhomogeneities, and increasing the realism of the cosmological model is examined. The proposed approach to constructing a mathematical model using cellular automata is a simplified model of Universe creation, and the selection of fluctuation parameters requires further research, analysis, refinement, and calibration.

Keywords: cellular automaton, three-dimensional modeling, quantum fluctuations, evolution of the Universe, cosmological simulations, algorithm, stochastic processes, structure.