We simulate galaxy spin orientation using a modified tidal torque theory (TTT) applied to a fractal mass distribution seeded in a 3D cubic volume.
2.1. Initial Fractal Density Field
We generate a synthetic matter field (x)\rho(\vec{x}) with a fractal correlation function:
(r)(rr0)DH3,DH(2.0,2.9)\xi(r) \sim \left( \frac{r}{r_0} \right)^{D_H - 3}, \quad D_H \in (2.0, 2.9)
This mass field is evolved using Zel'dovich approximation, enhanced to account for layer-dependent expansion rates as defined in Section IV.1.
2.2. Angular Momentum Generation
For each protogalactic halo:
We calculate the inertia tensor IijI_{ij} from local mass distribution,
Estimate the tidal shear tensor TijT_{ij} using smoothed potential gradients,
Apply the TTT angular momentum approximation:
LkijkIilTljL_k \propto \epsilon_{ijk} I_{il} T_{lj}
Fractal-induced anisotropy enters both IijI_{ij} and TijT_{ij}, leading to directional preferences in L\vec{L}.
2.3. Orientation Statistics
We record:
