Radial wavefronts form immediately after excitation, followed by standing wave nodes stabilized by nonlinear feedback.
Emergence of ring-like structures and phase vortices in 2D simulations.
In 3D, the blink can produce bubble-like spatial energy condensates that resemble metric curvature zones.
2. Resonant Geometric Modes
We identify several stable resonant structures from simulations:
Each of these modes emerges as a resonant response to the blink, showcasing that the field geometry is not externally imposed, but self-generated from internal nonlinear dynamics.
3. Energy and Spectrum Response
The system exhibits spectral selectivity---only certain frequency components resonate post-blink.
Spectrograms show transient broadband excitation collapsing into discrete, stable frequency peaks, indicating self-organized frequency filtering.
A correspondence is drawn between the dominant modes and natural eigenfrequencies of the nonlinear lattice---analogous to vacuum mode excitations in early cosmology.
4. Interpretation: Geometry from Information Flux
These results suggest that spatial structure is emergent from energy flux, not from preset metrics.
The blink serves as a synthetic analog to quantum vacuum fluctuation spikes, wherein local amplification of information flux leads to curvature concentration.
In the analogy with general relativity, the emergent localized patterns mimic proto-metrics, implying that information resonances act as effective geometric seeds.
5. Transition Thresholds and Critical Regimes
We observe that resonance and geometry emergence occur only above a critical excitation energy EcritE_{\text{crit}}Ecrit.
Below threshold, the field diffuses linearly with no pattern formation.
At threshold, a nonlinear bifurcation emerges: the system selects a stable pattern attractor, indicating a chaos-to-order transition driven by energy input.
B. Energy Localization and Curvature Emergence
Mapping the correspondence between high-energy nodes and emergent geometric curvature in nonlinear field media
This section delves deeper into the connection between localized energy density and effective curvature emergence within the simulated nonlinear field system. Inspired by gravitational theories where energy-momentum dictates curvature (e.g., via Einstein's field equations), we seek to understand whether a similar mechanism emerges in our analog system---not through mass-energy, but through information flux and field intensity gradients.
1. Curvature from Localized Field Energy
