Spatiotemporal Dynamics of Conway's Game of Life in the Entropy--Complexity Plane
Abstract
We investigate the dynamics of Conway's Game of Life (GoL) through the lens of Ordinal Pattern analysis. Each GoL generation is transformed into a one-dimensional time series, from which ordinal patterns are extracted to characterize its underlying dynamics. The resulting ordinal distributions are then represented in the Entropy--Statistical Complexity (H × C) plane, enabling a quantitative analysis of the system's evolution. We evaluate different encoding strategies, including patch sizes and linearization methods, and assess their impact on the resulting H × C trajectories. Finally, we characterize the emergent dynamics in terms of convergence behavior, trajectory patterns, and statistical complexity, showing how the proposed entropy--complexity framework provides insights into the dynamics of cellular automata.
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BibTeX
@misc{astore2026spatiotemporal,
title = {{Spatiotemporal Dynamics of Conway's Game of Life in the Entropy--Complexity Plane}},
author = {Lucas Malacarne Astore and Alejandro C. Frery and Petrônio Cândido de Lima e Silva and Frederico Gadelha Guimarães},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31708},
eprint = {2610.31708},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.31708},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Spatiotemporal Dynamics of Conway's Game of Life in the Entropy--Complexity Plane
AU - Lucas Malacarne Astore
AU - Alejandro C. Frery
AU - Petrônio Cândido de Lima e Silva
AU - Frederico Gadelha Guimarães
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.31708
UR - https://arxiv.org/abs/2610.31708
AB - We investigate the dynamics of Conway's Game of Life (GoL) through the lens of Ordinal Pattern analysis. Each GoL generation is transformed into a one-dimensional time series, from which ordinal patterns are extracted to characterize its underlying dynamics. The resulting ordinal distributions are then represented in the Entropy--Statistical Complexity (H × C) plane, enabling a quantitative analysis of the system's evolution. We evaluate different encoding strategies, including patch sizes and linearization methods, and assess their impact on the resulting H × C trajectories. Finally, we characterize the emergent dynamics in terms of convergence behavior, trajectory patterns, and statistical complexity, showing how the proposed entropy--complexity framework provides insights into the dynamics of cellular automata.
ER -