Lenia Whitepaper Biological Simulations for Next-Gen Science

This document outlines the Lenia framework for biological simulations through continuous cellular automata. It explains technical foundations, applications, and future research directions.

Introduction

Lenia is an open-source framework revolutionizing biological simulations through continuous cellular automata. Unlike traditional Boolean-based systems, Lenia uses continuous density values to model biological processes more naturally. This whitepaper explains the framework's architecture, core algorithms, and applications.

Conceptual Foundation

Cellular Automata Evolution

Lenia extends traditional cellular automata by using continuous values (0-1) to represent cell density. This allows for smooth transitions and more realistic biological behavior.

Gaussian Diffusion Kernels

The framework employs Gaussian kernels for cell interactions. This mathematical approach creates organic patterns resembling natural diffusion of nutrients/cells.

Core Architecture

Simulation Engine

High-performance engine using WebGL and WebAssembly for real-time 2D/3D simulations.

Ruleset System

Configurable rules for cell birth, growth, death based on custom mathematical functions.

Visualization

Multi-layered visualization API allowing real-time rendering and heatmaps.

Applications & Research

Biological Pattern Formation

Lenia can recreate natural patterns like zebrafish stripes and seashell formations, aiding in evolutionary morphogenesis research.

Tissue Engineering

Model how stem cells differentiate and organize into tissues through 3D simulation parameters.

Medical Research

Simulate tumor growth dynamics to explore cancer treatment strategies in a risk-free environment.

Neuroscience

Recreate neural network development and test synaptic plasticity theories without requiring lab infrastructure.

Methodology Overview

1. State Transition

Cells transition continuously between 0 (dead) and 1 (fully alive) states using smooth mathematical functions instead of binary changes.

2. Diffusion Kernel

G(x,y) = σe^-(x²+y²)/(2σ²) ensures cells influence neighboring cells in Gaussian distribution patterns.

Pseudocode Example

for each cell in grid:
    new_state = (diffusion_kernel * surrounding_cells) 
              + growth_function(current_state) 
              - death_function(current_state)

Development Roadmap

Q1 2024

  • 3D Simulation Engine
  • GPU Optimization

Q2 2024

  • Multiplayer Mode
  • Cloud Integration

Q3 2024+

  • Machine Learning Integration
  • Virtual Reality Support

Get Involved

Contributing

Lenia is an open project. You can contribute by:

  • Reporting bugs via GitHub
  • Suggesting new features
  • Sponsoring development

Community

Lenia Discord

Live discussions

Join Community Discussion

GitHub Repository

Source code and issues

Open GitHub

References

[1] M. Schaller, Lenia: Continuous Cellular Automata for Biological Simulations - arXiv:1807.04463

[2] GitHub Repository: github.com/lenia

[3] Lenia Whitepaper, v1.0 - September 2025

[4] Cellular Automata in Biology - Journal of Theoretical Biology, 2020