NPPR IFS Swarm Topology Simulator

Based on the core concepts from "Deterministic Chaos Constraints for Control of Massive Swarms" by Josef Schaff (2021).

This project is a lightweight, high-performance HTML5 Canvas simulator that demonstrates how Iterated Function Systems (IFS) and deterministic chaos can be used to control massive swarms (e.g., thousands of drones or MANET nodes) without incurring a combinatorial explosion of computational cost.

visit this link to try: [https://alphonse-lin.github.io/Non-predetermined-Parametric-Random-Iterated-Function-System/swarm-simulator.html]

🌟 The Core Concept

Traditional swarm control or ad-hoc networking requires nodes to be aware of each other, leading to exponential routing and coordination costs as the swarm scales.

This approach solves the issue by leveraging Adaptive Fractals. Instead of peer-to-peer coordination, every agent independently executes a simple Iterated Function System (IFS) equation:

X(n) = M × X(n-1) + Z

• X: The agent's position (or state).
• Z: A randomly selected "Attractor" vertex from a globally shared, minimal set of points (e.g., vertices of a geometric shape).
• M: A shared scaling factor ($|M| < 1$, per the Banach Contraction Theorem).

By sharing just a single floating-point number (M) and a few coordinates (Z), tens of thousands of agents can achieve situational awareness and emergent self-organization in real-time.

🚀 Simulator Features

• Massive Scale: Smoothly simulates and renders 20,000+ agents using lightweight Float32Arrays and Canvas batching.
• Topology Phase Transitions:
  • Ordered ($M \approx 0.33$): Agents neatly arrange themselves into distinct clusters.
  • Transit ($M \approx 0.50$): Agents form loosely connected, space-filling networks (similar to Sierpinski gaskets).
  • Chaotic/Scatter ($M \approx 0.70$): Agents scatter into a bounded chaotic cloud.
• Dynamic Attractors: Add, remove, or drag attractor vertices in real-time to watch the swarm instantly adapt and self-heal.
• Visual Modes: Toggle Voronoi partitioning, connection links, grids, and agent glow.

🛠️ Usage

Simply open swarm-simulator.html in any modern web browser. No external dependencies, build steps, or servers required.

Controls:

• Scale Parameter M Slider: Smoothly transition between Ordered and Chaotic swarm states.
• Display Options: Switch on Voronoi approximation to see the underlying clustering boundaries.
• Canvas Interaction:
  • Click empty space to add a new Attractor vertex.
  • Drag a vertex to move it.
  • Right-Click a vertex to remove it.

🤖 Application in AI Agent Systems

Beyond physical drones, this mathematical framework is highly applicable to Multi-Agent AI Systems (MAS):

• Semantic Attractors: Instead of physical coordinates, $Z$ can represent tasks, goals, or topics in a latent space.
• Zero-Communication Coordination: Agents naturally cluster around tasks without needing a manager agent to assign them or spending tokens negotiating.
• Dynamic Reallocation: Modifying $M$ acts as a "temperature" control for the agent swarm (low $M$ = high focus on specific tasks; high $M$ = creative scatter/exploration).
• Self-Healing: If agents crash or are rate-limited, the remaining agents will naturally maintain the density distribution across the active task attractors.

📄 References

• Schaff, Josef. (2021). Deterministic Chaos Constraints for Control of Massive Swarms. Naval Air Systems Command. Published in Unifying Themes in Complex Systems X.