Zeta Trunk Explorer

Riemann ζ partial-sum spirals extracted into a 3D trunk. Drag on the s-plane picker or use sliders.

Real · Imaginary drift animation

σ t steps/s

◀/▶ = play reverse/forward (tap again to pause) · ◀◀/▶▶ = ∓1 steps/s. only lower bound at t = 0.

Gram clock (M4) adaptive Δt (M5)

⚠ Δt·log N > π — high arms strobing

Zero Nr.

step

steps/s

secondary spirals trace

count decay

K packets below the infinite each drop a vertical axis to the imag plane with a colored dot. During play they leave a bezier-smoothed decaying trace on the plane.

σ (real) 0.5000

t (imag) 14.1347

100000

N terms 500

auto-N (⌈4·t/(3π)⌉ + 45 · uncheck to grow taller manually)

β depth 0.30

depth mode

window 4

radius 2.0

auto scale to fit

drift 1.0

Spiral detection (rotation reversals)

polarity (which zero-crossings; m=1 top-flip always ON)

smoothing scale 0.6

floor window 2

Look & extras

main spiral trunk volume mesh drift-additive (mesh) peak-hold (mesh) Bézier smooth raw path centers dots residual r_k (M3) theory rings (k=1..) saddles/eyes (M7) spiral skeleton mirror chain (M8) co-rotating θ (M4)

residual magnification ×√t

coloring mode

colour

S-plane picker

live curves zero markers critical strip grid

axis mode

Mini flat spiral

Metrics

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Detected segments (legend)

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Batch analysis · export CSV

zeros range

# → #

include midpoints (0.5, 1.5, …) σ used 0.5000

N (terms) used 1200

idle

S-PLANE · PREIMAGE CURVES

σ [,] · t [,]

ζ real (Im=0) ζ imag (Re=0) critical strip non-trivial zeros your s click=set s · shift-click=snap to nearest zero

FLAT DIRICHLET SPIRAL · OUTPUT PLANE

centers backbone

ZETA TRUNK · 3D ▾

orthographic imag plane adaptive zoom in adaptive zoom out sec. spirals · order sec. spirals · position sec. spirals · distance

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