Fractal Information Structure of the Universe

We demonstrate that the Hertault Axiom of Informational Dark Geometry (IDG) implies a fractal structure for the universe, where black holes act as holographic compression nodes connecting different levels of reality. Each universe possesses a maximum information capacity Imax = Ahorizon/(4ℓ2Pl) determined by its cosmological horizon. When local information density approaches the Bekenstein bound-threatening to violate the Hertault Axiom-spacetime responds by forming a black hole, which compresses the excess information and decompresses it into a child universe. We derive the compression ratio C = e4|σ| and show that for stellar-mass black holes C ∼ 10^76. The child universe has a finite but cosmologically brief existence from the parents perspective, after which all information returns to the parent universe via Hawking evaporation and the σ field. This resolves an apparent paradox: child universes exist as necessary consequences of the Hertault Axiom, yet no information is permanently lost to them.

The resulting picture is a holographic file system: the universe processes information through compression (black hole formation), storage (child universe), and retrieval (evaporation). We derive the complete information flow equations, establish the fractal dimension of this structure, and discuss observational implications.

Keywords: holographic principle, fractal cosmology, black holes, information theory, Bekenstein bound, multi-level universe, quantum gravity