Emergent Multi-Cluster Phases in a Unified τ-Field Model with Four Effective Forces: A Self-Organizing Computational Universe

We present a minimal computational model where N = 80 particlesinteract via four distinct effective forces—strong, electromagnetic, gravitational, and weak—each mathematically simple yet physically meaningful.The entire system is governed by a single scalar field τ (tau) representing local “personality” or stability. Through local synchronization of τ,noise, and carefully balanced force couplings, the system spontaneouslyforms stable multi-cluster structures without explicit programming. Wederive a unified τ-field evolution equation containing diffusion, dissipation, source, and noise terms, and define an order parameter Φ4 quantifying structural complexity. Systematic parameter scanning reveals arobust multi-cluster phase occupying 23.7% of parameter space, with optimal structure at Φ4 = 54.2±3.1. Force-switch experiments confirm eachforce’s distinct role: removing strong forces eliminates clusters; disablingweak forces freezes dynamics; turning off electromagnetic forces reducespattern diversity; and removing gravity prevents large-scale organization.The complete model is implemented in under 400 lines of Python, fullyreproducible, and provides insights into emergence, self-organization, andthe origin of complexity from simple rules