Field Complexity Measure

The Field Complexity Measure is the quantity that rates how much computational complexity a field configuration holds, by combining its information content with the strength of its spatial curvature. It joins two things the book computes for the collective field: the field information content I⟐ = −∫ ρ_I(x) log_2(ρ_I(x)) dx, an entropy of the normalized energy density, and the integrated squared Laplacian of the field, a measure of how sharply it bends in space. Their product is read as the complexity of the recursive binary substrate expressed in that configuration. Among the Chapter 7.5 predictions, the information storage of field patterns is to be quantified through information-theoretic analysis. The formal statement is C⟐ = I⟐ × ∫ |∇²Ψ|² dx, where C⟐ is the Field Complexity Measure, I⟐ the field information content, Ψ the collective field function, ∇²Ψ its spatial Laplacian and dx the spatial volume element. Dimensions as the book gives them: C⟐ [𝕃⁻⁴·1ᵇ], I⟐ [1ᵇ], |∇²Ψ|² [𝕃⁻⁷], ∇²Ψ [𝕃⁻⁷/²], Ψ [𝕃⁻³/²], dx [𝕃³]. It connects to the Energy Density Distribution, Collective Field Function and Information Density Criterion.