Spatial Correlation (with diffusion)

Correlation Map

Spatial correlation map showing extended coherence and anisotropic structure.

Correlation vs Distance

Correlation decays gradually with distance, indicating long-range interactions. The slight increase at large distances is due to periodic boundary conditions.

Interpretation

The system exhibits clear spatial coherence, with correlations extending over multiple length scales. Unlike the baseline case, interactions are no longer purely local but propagate across the system.

The anisotropic patterns observed in the correlation map suggest structured directional dynamics, likely emerging from the combined effects of diffusion and particle interactions.

These results confirm that the model generates non-trivial spatial organization, consistent with a dynamically evolving field rather than random fluctuations.