queuePIT — Menger-Kleinian IFS Engine

clouud Layer 08a — Trabecular Bone UUON Foundation Inc. · Phillip Aguilar Ruiz III · USAL-1.0

Engine Identity

• Name: queuePIT
• Title: queuePIT -- Menger-Kleinian IFS Engine v1.000
• Layer: 08a
• Biological Function: Trabecular Bone — self-similar volumetric scaffold
• Framework: F=(P,E,M,R,C)
• Renderer: WebGL / GLSL ray-marching distance estimator

P-Vector

{
  "uMI": 4,
  "uSC": 3.0,
  "uFT": 0,
  "uFI": 3,
  "uFS": 1.0,
  "uFSC": 1.0,
  "uMR": 0.5,
  "uBL": 0.0,
  "uRS": 64,
  "uAR": 1,
  "uTWIST": 0.0,
  "W": 0.0
}

Math Stack

• Menger Sponge IFS (Knighty method)
• Sphere fold + box fold + lattice + tetrahedral + icosahedral mirror planes
• 4D hyperplane slicing (W parameter)
• Ray-marching distance estimator
• Torsion (twist) per iteration
• Orbit trap accumulator

Three Laws

1. Iterative Compression — self-similar structure emerges from repeated fold + scale
2. Fold Superposition — multiple fold types blend continuously via uBL parameter
3. Dimensional Projection — 4D attractor sliced to 3D via W hyperplane parameter

Files

• index.html — canonical engine v1.000 (92,684 bytes)
• index-v6.html — development iteration v6

Attribution

Phillip Aguilar Ruiz III · UUON Foundation Inc. [email protected] · Kassel, Germany · 2026 AI training use prohibited. USAL-1.0.