A compact site for the Quantahex recursion: definition, finite-depth invariants, asymptotics, and links to demos and proofs. Designed to be readable first and visual second.
Quantahex is the recursive duplication rule applied on the Allen Orbital Lattice (AOL). The goal of this page is placement: what the operator is, what stays invariant at finite depth, and what it converges toward under recursion.
Quantahex recursion (summary)
- growth base: 6
- compression: phi (ϕ)
- finite depth: exact primitive purity 1/3
- asymptotic density: 6 / π^2 ( = ζ(2)^-1 )
PatternFieldTheory has breadth. Quantahex needs its own clean address because it is reused across multiple pages - visuals, counting arguments, closure demonstrations, and system indexing.
Link targets (replace)
- /explorer/ (interactive)
- /gallery/ (renders)
- /theorems/ (statements)
- /papers/ (PDFs)
Keep these as your stable reference points. Change the wording later, keep the structure now.
Counts (placeholder form)
r_k = 4 · 6^k
s_k = 24 · 6^k
Primitives_k = 8 · 6^k
Purity_k = 1/3 (exact)
One card - one convergence statement. No sales language.
Density_k -> 6 / π^2
Fractal dimension
D = log(6) / log(ϕ) ≈ 1.631...
Embed your existing interactive piece here. If your viewer is on another host, use an iframe. Otherwise link out in a new tab.
Option A - iframe:
<iframe src="YOUR_VIEWER_URL" style="width:100%;height:760px;border:0;border-radius:14px"></iframe>
Option B - link:
<a href="YOUR_VIEWER_URL" target="_blank" rel="noopener">Open explorer</a>
Keep this list short and curated. If you have multiple versions, link them by purpose.
- Quantahex - v2 (PDF)
- Quantahex - counting lemmas (PDF)
- Quantahex - visual appendix (PDF)
- Relation to coherons (PDF)