created: 20260506230000000
modified: 20260506230000000
tags: ResearchStack Compression Hutter CAD Geometry MengerSponge GabrielHorn
title: Pathological Menger-Horn Composite
type: text/vnd.tiddlywiki

! Pathological Menger-Horn Composite

Composite manifold: Menger sponge nodes mounted as structural attachment points
along Gabriel's horn backbone (x-axis curve y = 1/x). PIST shell coordinates are
nested inside each sponge node.

The horn provides infinite surface area with finite volume — the byte container
surface. The Menger sponge provides fractal addressing (Hausdorff dimension
~2.7268) for routing between shells. Together they form one of three pathological
manifolds for Hutter Prize compression-geometry folding.

Composite structure is Torus-Menger-Horn, as referenced in
[[04_Hutter_Prize_Equation.md|Hutter Prize Equation §Torus-Menger-Horn folding]].

!! Links

* [[Hutter Prize Compression]]
* [[Pathological Manifold Torus]]
* [[Pathological PIST Shells]]

!! Durable Source

`../../3-Mathematical-Models/cad_models/composite_manifold.scad`