Ulam Spirals in Nature, Cosmos, and Systems: A Unified Framework of Emergent Patterns

1. Expanded CODES Framework (Empirical Studies + Theory) 🔹 CODES: The Chirality of Dynamic Emergent Systems (Main Paper) 2. Introduction & High-Level Overview 🔹 CODES: High-Level Introduction 3. Structured Resonance & Emergent Intelligence 🔹 Structured Resonance and the Nature of Intelligence Abstract This paper explores the surprising recurrence of Ulam spiral-like structures—geometrical patterns based on the distribution of prime numbers—across multiple domains, from galactic formations to biological growth and natural systems. We propose that these spirals represent a universal emergent pattern in both physical and abstract systems, driven by fundamental constraints on growth, energy distribution, and structured resonance. Seven distinct examples are highlighted, showcasing the potential for multi-scale symmetry across cosmic, biological, and computational systems.