batara-guru: Python-based rule 30 cellular automaton analyzer

A fundamental implementation of Rule 30 cellular automaton with parallel processing for educational and research purposes.

Context

Rule 30 is an elementary cellular automaton introduced by Stephen Wolfram that exhibits complex, chaotic behavior from simple deterministic rules.

Mathematical Definition: Let $s_i^t \in {0,1}$ denote the state of cell $i$ at time $t$. The evolution rule is:

$$s_i^{t+1} = s_{i-1}^t \oplus (s_i^t \lor s_{i+1}^t),$$

where $\oplus$ is XOR, $\lor$ is OR.

Binary representation: $00011110_2 = 30_{10}$

The system exhibits:

• Chaos: Sensitive dependence on initial conditions
• Irreversibility: Information loss over time
• Complexity: Wolfram Class III behavior

Features

This implementation provides basic tools for studying Rule 30:

• Parallel Numba JIT: Multi-core evolution for computational efficiency
• Entropy Analysis: Shannon entropy $H = -\sum p_i \log_2 p_i$ and local complexity
• Complete Pyramids: Non-truncated patterns for boundary-free analysis
• NetCDF & CSV Output: Standard formats for data archiving and analysis
• Publication Figures: High-resolution plots (350-600 DPI)

Installation

From PyPI:

pip install batara-guru

From source:

git clone https://github.com/sandyherho/batara-guru.git
cd batara-guru
pip install -e .

Quick Start

Command line:

# Run single case (uses all CPU cores by default)
batara-guru case1

# Run all test cases
batara-guru --all

# Specify CPU cores
batara-guru case1 --cores 4

# Custom DPI
batara-guru case1 --dpi 600

Python API:

from batara_guru import Rule30Solver

solver = Rule30Solver(width=501, steps=250, n_cores=8)
result = solver.evolve(initial_condition='single')

print(f"Final entropy: {result['entropy'][-1]:.4f}")
print(f"Mean complexity: {result['mean_complexity']:.4f}")

Test Cases

Provided test cases for pedagogical purposes:

Case	Description	Width	Steps	DPI	Purpose
1	Small	251	125	350	Quick demonstration
2	Medium	501	250	400	Standard analysis
3	Large	1001	500	500	High-detail study
4	Extra Large	2001	1000	600	Publication quality

All cases maintain $t < w/2$ to ensure complete pyramidal patterns without boundary interactions.

Configuration

Example configuration file:

grid_width = 501           # Number of cells
time_steps = 250           # Evolution steps (< width/2 for full pyramid)
initial_condition = single # Single center cell (standard)
center_position = 250      # Auto-calculated if not specified
plot_dpi = 400            # Output image resolution
save_netcdf = true        # Save NetCDF file
save_plot = true          # Save PNG plot
colormap = binary         # Color scheme

Output Files

For each simulation, the following files are generated:

NetCDF (.nc):

• grid(time, x): Complete evolution history
• entropy(time): Shannon entropy $H(t)$
• complexity(time): Normalized transition density

CSV (.csv):

• {scenario}_entropy.csv: Time series of entropy values
• {scenario}_complexity.csv: Time series of complexity values
• {scenario}_composite.csv: Combined entropy and complexity

PNG (.png):

• Spatio-temporal visualization of evolution

Metrics

Shannon Entropy: $$H(t) = -p_1 \log_2 p_1 - p_0 \log_2 p_0$$ where $p_1 = N_1/N$ is the fraction of alive cells.

Local Complexity: $$C(t) = \frac{1}{N} \sum_{i=1}^{N} |s_i^t - s_{i+1}^t|$$ measuring spatial transition density.

Parallel Processing

Utilizes all available CPU cores by default. Override with:

batara-guru case3 --cores 8

Or programmatically:

solver = Rule30Solver(width=1001, steps=500, n_cores=8)

Citation

If this tool is useful for your research or teaching, please cite:

@software{batara_guru_2025,
  author = {Herho, Sandy H. S. and Napitupulu, Gandhi},
  title = {\texttt{batara-guru}: Python-based Rule 30 cellular automaton analyzer},
  year = {2025},
  version = {0.0.1},
  url = {https://github.com/yourusername/batara-guru},
  license = {MIT}
}

Authors

• Sandy H. S. Herho (sandy.herho@email.ucr.edu)
• Gandhi Napitupulu

License

MIT License - See LICENSE for details.

Acknowledgments

This is an educational implementation inspired by Wolfram's pioneering work on cellular automata. For comprehensive cellular automata research, see Wolfram's A New Kind of Science.