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The Mandelbrot Set as a Quasi-Black Hole

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The Mandelbrot Set as a Quasi-Black Hole

Author: Lori-Anne Gardi (2017)

This paper explores a speculative and philosophically distinct approach to cosmology by proposing the mathematical Mandelbrot Set (M-Set) as a direct, self-similar analog to black holes—termed a “Quasi-Black Hole.” The author conducts a thought experiment: What if the discovery of fractal geometry predated Einstein’s theory of general relativity?

Key Analogies and Mappings

The anatomy of a classic Schwarzschild black hole is mapped directly to the behavior of points in the complex plane under the Mandelbrot iteration ():

  • The Black Hole: The area of convergence in the M-Set (the core black shape). Points inside this region are “trapped” and collapse iteratively, similar to matter falling into a black hole.
  • The Singularity: Referred to as “Quasi-Singularities”—trajectories inside the M-Set that collapse past precision limits towards infinitely small regions. Unlike standard relativity, these can collapse toward multiple regions in the complex plane.
  • The Event Horizon: The boundary separating the domain of convergence from the domain of divergence. It exhibits asymptotic behavior on both sides, implying it takes as much “energy/iterations” to fall into the black hole as it does to escape.
  • The Photon Sphere: The domain of divergence (the gray-scale region outside the core shape) acts like the photon sphere, where points travel in complex, expanding orbits before eventually “escaping” the 2.0 radius limit of the complex plane boundary.

Cosmological Implications

By decoupling time from the spatial manifold (treating time purely as emergent from iterative change), the author presents several unconventional hypotheses:

  • Space-Time Curvature: MODELED as a fractal gradient generator. The closer one looks towards the M-Set event horizon, the steeper the gradient becomes—conceptually similar to gravitational wells.
  • Cosmological Red-shift & Entropy: Argues against accelerated expansion. Instead, uses scale relativity: if the universal “measuring sticks” (pixels) are shrinking over time to resolve smaller fractal details, earlier atomic light signatures would appear elongated (red-shifted) today.
  • The Atom as a Quasi-Black Hole: Postulates that atoms, bound by the weak force (acting like an event horizon), reflect the self-similarity of macroscopic black holes at a quantum scale. Electrons mimic the photon sphere while the nucleus mimics the black hole singularity.
  • Chiral Symmetry: Identifies transitions from chiral to axial symmetry deep within the M-Set geometry that match visual morphologies observed in spiral galaxies and quasar emissions (e.g., M87’s offset black hole and Quasar 3C-186).

While highly speculative and detached from standard relativity models, the paper emphasizes that our universe appears profoundly “Mandelbrot-like.”

Fractal Non-Locality & Entheogens

If the universe is profoundly “Mandelbrot-like,” this fractal self-similarity extends into human consciousness. The non-local, recursive geometry visualized in the M-Set offers an objective, mathematical corollary to the subjective experiences documented in the Entheogen Hypothesis. When initiates in ancient mysteries (e.g., Eleusis) report experiencing the infinite contained within a single drop or the cyclical collapse of ego boundaries, they are phenomenologically traversing the quasi-singularities and event horizons of Gardi’s fractal cosmology.

  • ER_EPR_Conjecture — standard physics context for the black hole structures Gardi maps the Mandelbrot Set onto
  • Copenhagen_vs_Everett_Susskind — Susskind’s wormhole geometry provides the conventional framework against which Gardi’s fractal alternative can be contrasted
  • ASAL_Foundation_Models — both papers explore emergent, self-similar complexity: Gardi in cosmological geometry, ASAL in digital substrates

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