Steiner Funnel Visualizer
Watch A(x,n) and B(x,n) Steiner circuits trace 3-D helices that together form a tapering funnel. Each circuit spirals upward at most one full revolution before the next begins. A circuits wind counter-clockwise; B circuits reverse direction. Angle θ = 2π·n / (N+1). Drag to rotate.
↻ drag to rotate • use controls to customise
Funnel Parameters
Display
Presets
A(x,n) counter-clockwise
B(x,n) clockwise
Active Circuit
Animation starting…
The Steiner Funnel
Circuit Construction
- A circuit is characterised by parameter x and element count N
- Element n is placed at angle: θ = 2π n / (N+1)
- Both radius and height-rise equal x
- 3-D position of element n:
( x cosθ, x sinθ, zbase + x n/(N+1) ) - Each circuit spans at most one revolution (2π)
- End of circuit → drop to start of next circuit
A and B Functions
- A(x, n): θ = +2π n/(N+1) — counter-clockwise
- B(x, n): θ = −2π n/(N+1) — clockwise
- Both evaluate to value m at the top of the circuit
- Circuits alternate A and B as the funnel descends
The Funnel Shape
- x decreases with each successive circuit
- Shrinking radius & height build the tapering funnel / cone
- Total height: ∑ xi
- Envelope surface: a cone of revolution
- A + B alternate to produce a double-helix winding
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