research

Mathematical foundations, biological inspirations, and theoretical analysis for the Unstable Kernel project.

Contents

graph LR
    R[research/] --> T[theory.md<br/>Mathematical proofs]
    R --> B[biology/<br/>Biological inspirations]

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Document	Description
theory.md	Full mathematical treatment: agent state space, boids equilibrium, signal diffusion PDE, population dynamics, stability proofs
biology/inspirations.md	Accessible explanations of biological systems (flocking, ant colonies, mycelium, predator-prey) for non-technical readers

Key Results

• Flock equilibrium distance: d* = r_sep * sqrt(w_s / w_c)
• Signal half-life: t_half = ln(2) / evaporation_rate
• Trail persistence condition: agent_density > evaporation / deposition
• Predator population bounded by prey density and kill mechanics
• Bidirectional mutation creates self-correcting oscillator

References

1. Reynolds (1987) - Boids flocking model
2. Dorigo et al. (1996) - Ant Colony Optimization
3. Jones (2010) - Physarum transport networks
4. Lotka (1925) / Volterra (1926) - Population dynamics
5. Tero et al. (2010) - Biologically inspired network design

License

MIT