Discovery in Larger than Life Cellular Automata

📌 Project Overview

Faculty Advisor: Dr. Kellie Evans
Institution: California State University, Northridge
Dates of Research: Aug. 2023 – Present
Funding: Learning-Aligned Employment Program (Discontinued)

This project explores the emergent behavior of Larger than Life (LtL) cellular automata, a generalization of Conway’s Game of Life, through automation and scripting in the Golly simulation platform. The work focuses on developing Lua-based tools to analyze dynamic structures such as bugs, gliders, and oscillators across a large parameter space. The goal is to better understand the statistical and structural properties of LtL patterns.

🎯 Objectives

• Automate the discovery of patterns such as bugs and spaceships in LtL rules
• Analyze how parameters affect emergence and movement in cellular automata
• Build an extensible pipeline for pattern classification and parameter exploration

🧠 Big Research Questions

• Do discovered bug patterns in LtL converge to behaviors that resemble Euclidean limits?
• How does the neighborhood radius and birth/survival rule shape the search space?
• Can we develop a general-purpose framework for automated CA behavior analysis?

🛠️ Methods & Tools

• Data Source: Simulation data generated using Golly with custom Lua scripts
• Algorithms / Models: Custom search algorithms for pattern detection; Nonparamentric spline fitting for pattern trajectory
• Software/Environments: Golly, Lua, MATLAB, Python (for post-processing and plotting)
• Model Evaluation/Analysis: Pattern frequency analysis, velocity tracking, population trends

🖼️ Visuals

An intitial configuration resembling an ellipse can produce two asymmetric, non-identical mobile patterns—referred to as “alien bugs”—that propagate in divergent, non-perpendicular directions. Unlike canonical glider behavior in Conway’s Game of Life, these structures exhibit asymmetry in form and directionality, with angles between their trajectories deviating from the standard 90° or 180°, revealing new classes of motion symmetry in the Larger than Life rule set. (See image below)

More Formally:

Let \( \mathbf{v}_1 \) and \( \mathbf{v}_2 \) be the velocity vectors of the two emergent bugs. Then,
\[ \angle(\mathbf{v}_1, \mathbf{v}_2) = \theta, \quad \text{where } \theta \in (0, 180^\circ) \setminus {90^\circ, 180^\circ}. \]
The propagation paths are thus neither orthogonal nor directly opposing.
Each structure preserves its identity under translation through the lattice, with a consistent direction and speed
\[ |\mathbf{v}_i|, \]
characteristic of a traveling wave solution in the automaton’s rule space.

How can we best fit a curve to the trajectory of a jiiter bug? (See applet below)

• This figure depicts the centroid trajectories of a class of traveling structures in Larger-than-Life cellular automata we refer to as “jitter bugs.” Unlike typical gliders or bugs that move along a relatively straight or smoothly curved trajectory, jitter bugs exhibit oscillatory, irregular movement patterns that defy simple parametric modeling. The black dots represent the geometric centroids at discrete time steps, forming a visibly non-linear and non-uniform path through the lattice.
• A sinusoidal curve (in green) is overlaid to provide a baseline for comparison. Although it loosely captures the wave-like shape of the motion, it fails to model the intricacies and irregular frequency of the bug’s path. Due to the non-uniformity in both amplitude and spacing, a nonparametric spline or locally adaptive smoothing technique is better suited for approximating the true trajectory of these bugs. This fitting challenge reflects the complex, quasi-periodic nature of certain emergent behaviors in LtL rule space.

Cal-Bridge 2024 Fall Conference Slides

📦 Deliverables

• First-author paper published at IEEE CCWC 2025
• Talk given at Cal-Bridge 2024 Fall Conference
• Lua toolset for automating LtL parameter exploration in Golly
• GitHub repo with codebase for Golly scripts

📈 Outcomes

• Developed a Lua scripts for automated bug detection, pattern data extraction, and visualization
• Discovered bugs in previously unexplored LtL parameter ranges
• Provided a reproducible framework for other researchers to study LtL patterns

🔁 Ongoing / Future Work

• Exploring probabilistic models of bug trajectories and emergent dynamics
• Writing a second paper expanding on convergence hypotheses and visualizations

🧠 What I Learned

Through this project, I gained hands-on experience in scripting complex search behaviors, navigating simulation limitations, and analyzing emergent phenomena. It deepened my interest in dynamical systems and gave me the confidence to lead future theoretical-computational projects in mathematical modeling and complexity science.

🙏 Acknowledgments

Thanks to Dr. Kellie Evans for her unwavering support, enthusiasm, and motivation in advancing the study of Larger than Life cellular automata. Thanks to the Golly Gang for developing the crucial tools needed to perform these works.