Solving Nonlinear Differential Equations with Neural Networks
Date:
Abstract
Cellular automata, particularly Conway’s Game of Life and its variants, offer a rich playground for discovering and analyzing dynamic patterns such as spaceships. This research presents an approach using Lua scripting to automate the creation, simulation, and classification of initial configurations in Larger-than-Life cellular automata. Building on current methods that use geometric initial configurations to discover patterns, this approach targets the systematic exploration and analysis of dynamic patterns, including alien and invariant bugs. A suite of Lua scripts has been developed to support this work. These scripts allow users to define initial configurations using shapes like circles, ellipses, and rectangles, automate placement based on user-defined parameters, and import configurations from CSV files. The scripts generate combinations of these shapes, simulate their evolution, and identify persistent patterns, classifying them by behavior, period, and displacement. Unlike existing methods that start from random soups and seek any pattern, our approach concentrates on specific geometric configurations, enhancing its utility for exploring intricate spaceship behaviors. While the classification script is experimental and struggles with complex behaviors such as exploding patterns, it provides valuable insights and data for further refinement. Detailed logs of each configuration, including dimensions and parameters, are invaluable for forming and testing conjectures about the conditions under which specific rules generate dynamic patterns. This work aims to advance the understanding of cellular automata mechanics and contribute to the discovery of new patterns. The presentation will cover the development and functionality of the Lua scripts, demonstrate their application through various examples, and discuss the potential implications and future directions for research. This systematic method offers a new perspective on dynamic pattern searches in cellular automata and provides a robust tool for researchers.