Tornado
(3u/tau · cos(10u + t), 4u/tau − 2, 3u/tau · sin(10u + t))
Open in the app The dials and keys named below are the app's.
What it draws
The second expression, 4u/τ − 2, is the height. Since τ = 2π makes u/τ run from 0 to 1 over one turn of u, the height climbs at a steady rate from −2 at the start to 2 at the end. The other two expressions set the same 3u/τ against a cosine and a sine of the angle 10u + t, which is a circle of radius 3u/τ. So the point turns about the vertical axis while its distance from that axis grows evenly from 0 to 3.
The 10 gives it ten turns in the climb, one coil every 0.4 of height. Every point satisfies distance = 0.75 · (height + 2): the funnel is a cone standing on its point, with a half angle of arctan(3/4) ≈ 36.9°.
Why it spins
The clock enters only as a phase added to the angle, so t does not change the shape at all. It rotates the whole cone about its vertical axis, one full turn every 2π ≈ 6.28 seconds at Speed 1. That is why the figure reads as a funnel rather than as a static wire. Unlike most curve presets this one is open, not closed: it has a bottom tip on the axis and a top rim of radius 3.
Try
- Top: from above the coils flatten into a spiral whose radius grows in step with its angle, ten turns of an Archimedean spiral.
- Front: the straight sloping sides of the cone, and the coils crossing them.
- Change both 10u to 20u: twenty coils in the same funnel, one every 0.2 of height.
- Replace 3u/τ with 3 in the first and third expressions: the cone becomes a cylinder and the curve is a plain helix.
- Raise Trail to 80: the swept copies fill the coils in, and the wire reads as a solid skirt.