The Tree and Its Shadow

Interactive phase diagram of ultrametric organization and resistance.

Companion visualization for the paper: The Tree and Its Shadow: A Unified Phase Diagram of Ultrametric Organization and Resistance (DOI: 10.5281/zenodo.20348370).

What It Shows

The ultrametric tree — where every triangle is isosceles — is the signature of isolated hierarchical branching. But isolation is rare. This visualization lets you explore the complete phase diagram from pure tree to lateral network.

• Cool indigo branches = the hierarchical tree structure
• Amber/orange threads = lateral connections breaking the tree
• Dark network below = the tree's "shadow" — the network that actually grows
• Live phase indicator = which of five regimes from the paper you're viewing

Parameters

Slider	What It Controls
Branching Depth (3–8)	How many levels the tree grows
Branching Ratio (2–4)	Children per node
Lateral Edge Probability (0–0.80)	Fraction of cross-branch connections
Growth Speed (1–10)	Animation pacing

Run Locally

git clone https://github.com/QNFO/tree-and-shadow-viz.git
cd tree-and-shadow-viz
open index.html   # or double-click the file

No server needed. No dependencies. Just a browser.

Paper

Rowan Brad Quni-Gudzinas (2026). The Tree and Its Shadow: A Unified Phase Diagram of Ultrametric Organization and Resistance. DOI: 10.5281/zenodo.20348370

License

CC-BY-4.0

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Part of the QWAV research program -- Ultrametric Quantum Computing & AI.