Abidin's Game of Death

A Collatz-inspired cellular automaton where life and death are governed by integer dynamics rather than fixed Conway rules.

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Overview

Abidin's Game of Death is an experimental two-dimensional cellular automaton inspired by:

• Conway's Game of Life
• The Collatz Conjecture (3n + 1)
• Cellular automata
• Integer dynamics
• Emergent systems

Unlike Conway's Game of Life, this automaton does not use simple neighbor counts.

Every cell carries an integer state.

During each generation, neighboring cells interact through Collatz transformations, producing new candidate states. Survival is then determined dynamically using percentile thresholds.

The result is an evolving system that often produces organic-looking structures, clusters and wave fronts while remaining mathematically driven.

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Features

• Interactive Tkinter GUI
• Real-time simulation
• Collatz-based evolution rules
• Integer-valued cell states
• Multiple seed patterns
• Adjustable simulation speed
• Grid on/off
• Toroidal wrapping
• Multiple color palettes
• Percentile survival rule
• Percentile color mapping
• PNG export
• Live statistics panel
• Stopping-time visualization

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Core Idea

Instead of counting neighbors like Conway:

2-3 -> survive
3   -> birth

this project computes a new integer state.

For every cell:

1. Collect 8 neighboring cells
2. Apply one Collatz step to every live neighbor
3. Sum transformed values
4. Generate a candidate state
5. Compute the selected percentile over the active field
6. Compare the candidate against that threshold

candidate <= threshold
        ↓
      Death

candidate > threshold
        ↓
      Alive

This makes the automaton adaptive.

The survival threshold changes automatically as the system evolves.

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Color Modes

Percentile Color

Maps stopping times according to their percentile.

Advantages:

• Uses the entire palette
• Better visual contrast
• Adapts automatically
• Suitable for exploration

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Log Scale

Maps stopping time using a logarithmic scale.

Advantages:

• Preserves absolute differences
• Stable across generations
• Useful for analysis

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Controls

Control	Description
Start	Start simulation
Stop	Stop simulation
Step	Single generation
Random	Generate random world
Seed	Load predefined pattern
Life Percentile	Survival threshold
Palette	Select color palette
Color Mode	Percentile or Log scale
Grid	Toggle grid
Wrap	Toroidal world
Export	Save PNG

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Seed Patterns

• Abidin Spiral
• R-pentomino
• Collatz Cross
• Prime Sparks
• Nebula

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Statistics

The right panel displays:

• Generation
• Alive cells
• Births
• Deaths
• Average state
• Maximum state
• Life percentile
• Threshold
• Simulation speed

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Why?

The purpose of this project is not to reproduce Conway's Game of Life.

Instead, it explores what happens when

• integer dynamics,
• Collatz transformations,
• adaptive thresholds,
• and cellular automata

are combined into a single simulation.

The resulting behavior is intentionally different from Conway's original universe.

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Technologies

• Python 3
• Tkinter
• NumPy
• Pillow

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Installation

Clone the repository

git clone https://github.com/SKR-35/Abidin-s-Game-of-Death.git
cd Abidin-s-Game-of-Death

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Create a Conda environment

conda create -n automata python=3.12

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Activate the environment

Windows / Linux

conda activate automata

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Install dependencies

pip install -r requirements.txt

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Run the application

python abidins_game_of_death.py

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Deactivate the environment

conda deactivate

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Future Ideas

• GPU acceleration
• 3D automata
• Additional integer rules
• Prime-number universes
• Multi-state automata
• Custom rule editor
• GIF / MP4 recording

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Dedicated to the memory of Abidin.