Collatz Rendezvous Model (CRM): A Novel Approach to Agent Synchronization

Resumo

The deterministic rendezvous problem is a fundamental challenge in multi-agent systems, requiring to meet at a common location using predefined movement rules. In this paper, we introduced the Collatz Rendezvous Model (CRM), a novel approach that leverages the well-known Collatz process to guide agents towards synchronization. Each agent follows an independent Collatz sequence, iterating through transformation rules until they converge at a common value, typically 1. We develop a computational framework to simulate CRM using Python and Tkinter, providing real-time tracking of agent movements. Through extensive experimentation, we analyze the number of steps required for rendezvous, identifying patterns in synchronization
behaviour based on different initial positions. The study reveals that CRM exhibits deterministic yet unpredictable convergence patterns, making it a unique mathematical tool for modelling agent rendezvous. We also discuss potential applications in distributed computing, swarm intelligence and self-organizing systems.