We present computational evidence for a novel framework suggesting that the critical line σ = 1 2 in the Riemann zeta function exhibits mathematical attractor properties for zero formation and gap prediction. Through systematic analysis of Dirichlet partial sum approximations across verified nontrivial zeros, we demonstrate that metrics measuring zero-formation dynamics consistently peak at σ = 1 2 with remarkable stability across parameter variations. Our bootstrap resampling analysis yields a zero-collapse attractor location of σ = 0.500000±0.000000 across 20 independent trials (n=500 each). We introduce a gap-confidence prediction framework achieving 50% success rates within calibrated uncertainty bounds while maintaining 1.23% relative prediction accuracy. Comparative analysis between ζ(s) and 1/ζ(s) reveals identical predictive behavior, suggesting functional invariance of gap patterns. These findings support a conjecture that the Riemann Hypothesis emerges from fundamental attractor dynamics rather than coincidental zero placement, providing new computational approaches to critical line analysis.