✳ 118 elements / seven electronic periods

Elemental whorl

The periodic table on a toroidal continuum
⊙ Carbon-anchored · horn R = r

VIEW LABORATORYHORN · R = r

Geometric reading

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Electronic period

Rendering performance

Layers

Shell filling trajectory Element symbols Period boundary meridians Slow orbital rotation

⊙ Carbon fixed-point laboratory

Anchor C at horn pinch Four-valence tetrahedron Show selected ↔ re-entry pair

C is a chosen fixed-point witness; the torus alone does not single out a unique element.

∿ Horn → Bernoulli / toric section

MAJOR / MINOR RADIUSR/r = 1.000

1.0 · horn/tangent circles2.0 · exact ∞

Tangent cutting plane · x = R − r Exact toric section · gold Phase-locked sweep · cyan 2D equations / curve laboratory

Section: (y²+z²)² = 4Rr y² − 4R(R−r)z²
Sweep: φ = θ = t, ρ = R+r cos(t)

At R=r: the section is two tangent circles; the sweep projects to a cardioid.

At R=2r the exact Bernoulli section appears. This is a ring torus, not still a horn; the horn is its limiting member.

Four orbital blocks

118 of 118 elements visible
Drag: orbit · right drag: pan · wheel: zoom

R = r = 1.9 · horn / pinched torus

2 · 8 · 8 · 18 · 18 · 32 · 32

mode: seven-turn shell braid

INTERACTIVE PROJECTION · NOT A DERIVED LAW OF ATOMIC GEOMETRY

⊙ CARBON / CHOSEN FIXED POINT

J_C(φ, θ) = (2φ_C − φ, 2θ_C − θ)
J_C² = id · J_C(C) = C

At R=r, Carbon is pinned to the horn singularity

gold · exact plane section

cyan · φ=θ sweep

01 / 09The horn appears

Seven electronic periods meet a self-pinched toroidal surface.

0:00 / 1:10

UNWRAPPED PROJECTION / 32 × 7

Long-form periodic atlas

Elements ordered by electron-shell period; f-series expanded after group 3.

Click any element to select it on the horn torus. The f-series placement is one common long-form convention (La/Ac in group 3; Ce–Lu and Th–Lr in the f insert).