No Structure Without Amplification

Timestamp: March 31, 2026 — 09:56

This simulation shows the behavior of the system without nonlinear amplification.

Experimental Setup

A 2D grid is initialized with random noise. The system evolves using diffusion and weak nonlinear terms, but without effective amplification (γ ≈ 0).

Homogeneous noisy state — no structure formation

Result

The system remains in a diffuse and homogeneous state. No structure or dominant region appears over time.

Interpretation

Diffusion and weak nonlinear interactions alone are insufficient to generate structure. The system remains symmetric, preventing any region from becoming dominant.

Without a mechanism of amplification or selection, all fluctuations remain equivalent.

Conclusion

Structure does not emerge without amplification.

This confirms that a selection mechanism is required for the emergence of stable structures in the Φ-model.