created: 20260507000000000
modified: 20260507000000000
tags: ResearchStack Topology MengerSponge Fractal Compression
title: Menger Sponge Fractal Addressing
type: text/vnd.tiddlywiki

! Menger Sponge Fractal Addressing

Menger sponge fractal addressing (`0-Core-Formalism/lean/Semantics/Semantics/MengerSpongeFractalAddressing.lean`, Python: `5-Applications/scripts/menger_sponge_fractal_addressing.py`) provides hierarchical void-based routing. Each iteration removes center cubes (7 per 3x3x3 block), creating addressable voids with Hausdorff dimension ~2.7268. Used by [[Networked Self Solving Space]] for distributed quine addressing, the [[Meta Manifold Language Merging]] framework for torus-void routing channels, and the composite manifold (sponge nodes mounted on Gabriel's horn). OpenSCAD model at `3-Mathematical-Models/cad_models/menger_sponge.scad` visualizes level-2 sponge with 20 remaining subcubes and 7 removed voids. One of three pathological manifold structures for [[Hutter Prize Compression]].

* [[Pathological Menger-Horn Composite]]
* [[FiveD Torus Topology]]
* [[Hutter Prize Compression]]
* [[Lean Semantics Overview]]